FMML-Aug22-M1Lab2_.ipynb

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      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/lakshmilikithabonthu/Fmml/blob/main/FMML-Aug22-M1Lab2_.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
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    {
      "cell_type": "markdown",
      "source": [
        "## FMML Module 1, Lab 2<br>\n",
        "Module Coordinator : amit.pandey@research.iiit.ac.in <br>"
      ],
      "metadata": {
        "id": "JN97BfHPX7yo"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### The aim of this lab is to introduce DATA and FEATURES.\n",
        "We will study: Feature extraction and Data Augmentation.\n",
        "Let's get started.\n",
        "\n"
      ],
      "metadata": {
        "id": "Q0DQhRGLo3Tr"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Make a copy before running the cells"
      ],
      "metadata": {
        "id": "o4AtXdwvNRGS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Data can be anything like text, image , sound signals, and even a mix of multiple types (multimodal). We need to learn how to handle raw data, and how to use them for our analysis."
      ],
      "metadata": {
        "id": "gkEBupTXa1xo"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A6I1yI79fbLD"
      },
      "source": [
        "# Extracting features from data\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OimBnfcpvcNS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c123cb32-890f-43d4-e999-9024c6362d31"
      },
      "source": [
        "## Standard Imports.\n",
        "\n",
        "! pip install wikipedia\n",
        "\n",
        "import wikipedia\n",
        "import nltk\n",
        "from nltk.util import ngrams\n",
        "from collections import Counter\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import re\n",
        "import unicodedata\n",
        "import plotly.express as px\n",
        "import pandas as pd\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting wikipedia\n",
            "  Downloading wikipedia-1.4.0.tar.gz (27 kB)\n",
            "Requirement already satisfied: beautifulsoup4 in /usr/local/lib/python3.7/dist-packages (from wikipedia) (4.6.3)\n",
            "Requirement already satisfied: requests<3.0.0,>=2.0.0 in /usr/local/lib/python3.7/dist-packages (from wikipedia) (2.23.0)\n",
            "Requirement already satisfied: chardet<4,>=3.0.2 in /usr/local/lib/python3.7/dist-packages (from requests<3.0.0,>=2.0.0->wikipedia) (3.0.4)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.7/dist-packages (from requests<3.0.0,>=2.0.0->wikipedia) (2022.6.15)\n",
            "Requirement already satisfied: urllib3!=1.25.0,!=1.25.1,<1.26,>=1.21.1 in /usr/local/lib/python3.7/dist-packages (from requests<3.0.0,>=2.0.0->wikipedia) (1.24.3)\n",
            "Requirement already satisfied: idna<3,>=2.5 in /usr/local/lib/python3.7/dist-packages (from requests<3.0.0,>=2.0.0->wikipedia) (2.10)\n",
            "Building wheels for collected packages: wikipedia\n",
            "  Building wheel for wikipedia (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for wikipedia: filename=wikipedia-1.4.0-py3-none-any.whl size=11695 sha256=2c30797a36dec1e8cbdda06886c93ff0e707397a510bdaa52448f3136a5406f7\n",
            "  Stored in directory: /root/.cache/pip/wheels/15/93/6d/5b2c68b8a64c7a7a04947b4ed6d89fb557dcc6bc27d1d7f3ba\n",
            "Successfully built wikipedia\n",
            "Installing collected packages: wikipedia\n",
            "Successfully installed wikipedia-1.4.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## What are features?\n",
        "### Features are individual independent variables that act like an input to your system.\n",
        "A very basic example is: In z = x + y, x and y are the features.\n",
        "We can have simple features like above or even more complex features learned by our machine learning models (we will study these later on)."
      ],
      "metadata": {
        "id": "_f74mfnO8Rd_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "from matplotlib import cm\n",
        "import numpy as np\n",
        "\n",
        "from mpl_toolkits.mplot3d.axes3d import get_test_data\n",
        "\n",
        "\n",
        "# set up a figure twice as wide as it is tall\n",
        "fig = plt.figure(figsize=plt.figaspect(1))\n",
        "\n",
        "# =============\n",
        "# First subplot\n",
        "# =============\n",
        "# set up the axes for the first plot\n",
        "ax = fig.add_subplot(1, 1, 1, projection='3d')\n",
        "\n",
        "# plot a 3D surface like in the example mplot3d/surface3d_demo\n",
        "X = np.arange(-5, 5, 0.25) # feature 1\n",
        "Y = np.arange(-5, 5, 0.25) # feature 2\n",
        "X, Y = np.meshgrid(X, Y)\n",
        "R = np.sqrt(X**2 + Y**2)\n",
        "Z = np.sin(R) #output\n",
        "surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm,\n",
        "                       linewidth=0.4, antialiased=False)\n",
        "ax.set_zlim(-1.01, 1.01)\n",
        "fig.colorbar(surf, shrink=0.5, aspect=10)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "n9KMUJBd8QKx",
        "outputId": "be00dfd1-86dd-4434-d5c8-f1b81ad006f9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.colorbar.Colorbar at 0x7fb4bebaba50>"
            ]
          },
          "metadata": {},
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 288x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m6hGhIGiy4GP"
      },
      "source": [
        "# Part 2: Features of text\n",
        "How do we apply machine learning on text? We can't directly use the text as input to our algorithms. We need to convert them to features.They are converted into vectors (embeddings) or one hot encoded.  Let us explore a simple way of converting text to features.\n",
        "\n",
        "Let us download a few documents off Wikipedia."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lpUmCoEr2R3J"
      },
      "source": [
        "## set language and then download the data.\n",
        "\n",
        "topic1 = 'Giraffe'\n",
        "topic2 = 'Elephant'\n",
        "wikipedia.set_lang('en')\n",
        "eng1 = wikipedia.page(topic1).content\n",
        "eng2 = wikipedia.page(topic2).content\n",
        "wikipedia.set_lang('fr')\n",
        "fr1 = wikipedia.page(topic1).content\n",
        "fr2 = wikipedia.page(topic2).content\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Cj7RlhMiO5kd"
      },
      "source": [
        "This is what the text looks like:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GW0G-t912UXZ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 140
        },
        "outputId": "7732dac5-9c9e-4f1e-d641-2755702bc5b2"
      },
      "source": [
        "fr2 ## the french textual data describing the second topic."
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'Les éléphants sont des mammifères proboscidiens de la famille des Éléphantidés. Ils correspondent aujourd\\'hui à trois espèces réparties en deux genres distincts. L\\'éléphant de savane d\\'Afrique et l\\'éléphant de forêt d\\'Afrique, autrefois regroupés sous la même espèce d\\'« éléphant d\\'Afrique », appartiennent au genre Loxodonta, tandis que l\\'éléphant d\\'Asie, anciennement appelé « éléphant indien », appartient au genre Elephas. Ils se différencient par certaines caractéristiques anatomiques, les éléphants d\\'Asie étant en général plus petits avec des oreilles plus petites, ou encore une différence du bout de la trompe. Ces espèces survivantes font localement l\\'objet de programmes ou de projets de réintroduction et de protection.\\nLe mot français « éléphant » vient du mot latin elephantus qui tire son origine du grec ἐλέφας signifiant « ivoire » ou « éléphant ».\\nL\\'éléphant apparait dans de nombreuses cultures. Il est symbole de sagesse dans la culture asiatique, connu pour sa mémoire et son intelligence, qui est comparée à celle des cétacés et hominidés. Aristote avait dit que l\\'éléphant est « la bête qui dépasse toutes les autres par l\\'intelligence et l\\'esprit ».\\n\\n\\n== Description ==\\n\\nL\\'éléphant d\\'Afrique, qui peut atteindre 7 tonnes, est le plus gros animal terrestre actuel, mais il est loin derrière la Baleine bleue (Balaenoptera musculus) qui peut peser jusqu\\'à 200 tonnes et dépasser 30 mètres de long.\\n\\n\\n=== Squelette et muscles ===\\n\\nLe squelette de l\\'éléphant présente des caractéristiques dictées par la masse qu\\'il doit soutenir : il représente environ 16,5 % de la masse totale de l\\'animal, cela signifie que pour un éléphant de 7 tonnes, le squelette pèse 1,155 tonne. Les os de l\\'éléphant sont spongieux. Sa cage thoracique, formée de vingt côtes, est arrimée le long de l\\'épine dorsale.\\nL\\'éléphant possède deux genoux à ses membres postérieurs, qui sont constitués d\\'un fémur, d\\'une rotule et de l\\'association tibia-fibula. Les membres antérieurs, quant à eux, comprennent une scapula, un humérus, et l\\'association radius-ulna.\\nL\\'éléphant marche sur le bout des doigts,. Les orteils sont insérés dans le pied, il y en a entre 2 et 5, on en voit seulement les ongles. Cependant on peut voir entre trois et cinq ongles en fonction des pieds. Les pieds antérieurs ont une forme arrondie, alors que les pieds postérieurs ont une forme ovale. Les pieds sont composés de tissus adipeux qui agissent comme des amortisseurs.\\nContrairement à la plupart des mammifères, il est impossible pour un éléphant de sauter, pour des raisons d\\'ordre biomécanique : il lui faut toujours un pied sur le sol. Cependant il peut courir à une vitesse maximale de 20 km/h (un éléphant ayant été chronométré à 24 km/h dans le cadre d\\'une étude scientifique).\\nMême si on emploie le terme « courir » pour un éléphant, il est à noter que le terme est inapproprié. Il serait plus logique de dire qu’il « marche vite ». En effet, il ne change pas son allure (sa façon de se déplacer) lorsqu’il accélère.\\nUn éléphant d\\'Afrique mâle adulte mesure 3,50 mètres au garrot et pèse 5 à 6 tonnes, une femelle adulte mesure 3 mètres de haut au garrot pour une masse de 4 tonnes environ. À la naissance, l\\'éléphant pèse environ 120 kg. Un éléphant vit en moyenne 60 ans. Le plus grand éléphant connu a été signalé en Angola en 1974 : il s’agissait d’un mâle de 12 tonnes mesurant 4,20 m au garrot, soit un mètre de plus que la moyenne des éléphants africains.\\nDes éléphants nains, de la taille d\\'un grand cochon, ont également peuplé les îles méditerranéennes au cours de la Préhistoire, ; certains sont signalés en Crète jusqu\\'en 5000 av. J.-C., voire jusqu’en 3000 av. J.-C.,.\\n\\n\\n=== Trompe ===\\nLa principale caractéristique des éléphants est leur trompe appelée proboscis. Il s\\'agit d\\'un organe nasal (avec une fonction de respiration et de perception des odeurs) allongé qui découle de la fusion de la lèvre supérieure et du nez. La trompe est un organe souple et préhensile leur servant à porter l\\'eau et la nourriture à leur bouche, à tirer ou transporter des objets et à pousser des cris.\\nLa trompe comporte entre 100 000 et 150 000 muscles ; elle est dépourvue d\\'os et pèse plus de 100 kg.\\n« La trompe se compose de deux longs tuyaux cylindriques, partant de l’ouverture antérieure des fosses nasales. Ces tubes se rétrécissent à la région de l’inter mâchoire, ce qui empêche l’eau pompée par la trompe de pénétrer dans la cavité nasale ; ils offrent ensuite une dilatation, puis se resserrent de nouveau à l’endroit où ils s’ouvrent dans les narines osseuses, et où ils sont couverts par un cartilage nasal ovale. (…) Les tubes sont entourés d’une multitude de faisceaux musculaires, les uns longitudinaux, les autres rayonnant vers la peau et servant à comprimer les premiers. Quelques-uns enfin, mais en moins grand nombre sont circulaires. Cependant il faut distinguer de ces muscles, propres à la trompe, ceux qui servent à mouvoir l’organe en entier. Ces derniers sont comparables aux muscles de la queue. On les distingue en élévateurs et abaisseurs supérieurs et latéraux, qui naissent du front, des os propres du nez et des cartilages, tant de l’os maxillaire supérieur que de l’intermaxillaire ».\\nLe bout de la trompe d\\'un éléphant d\\'Afrique est en forme d\\'amande, alors que celle d\\'un éléphant d\\'Asie est en forme de poire. L\\'excroissance à son extrémité a une fonction analogue à un doigt, leur permettant de décortiquer une cacahuète. Les éléphants ne boivent pas directement par leur trompe. L\\'effort nécessaire pour se pencher jusqu\\'au sol afin de boire l\\'eau par la bouche étant trop important et l\\'opération étant même impossible lorsque l\\'eau se trouve au-dessous du niveau du sol, ils boivent en remplissant leur trompe avec de l\\'eau qu\\'ils aspirent et gardent momentanément avant de la verser ensuite, par gravité, dans leur bouche.\\nL\\'allongement du museau des proboscidiens anciens à l\\'origine de l\\'éléphant serait lié à la croissance continue des incisives (les défenses) et leur augmentation de taille : herbivores concurrencés par les ruminants et les équidés, leur adaptation trophique se traduit alors par un régime de plantes plus fibreuses peu nutritives et une augmentation de taille corrélative, les proboscidiens fourrageant pendant des heures à la recherche aussi bien de végétaux au sol que de feuilles d\\'arbres.\\n\\n\\t\\t\\n\\t\\t\\n\\n\\n=== Denture et défenses ===\\n\\nLe plus souvent les éléphants ont des défenses, des dents très allongées utilisées par ces animaux comme outil, arme de défense et attribut sexuel. Les défenses sont des dents supérieures à croissance continue. L\\'éléphanteau possède des prémolaires de lait qui tombent lorsque les molaires apparaissent, l\\'adulte n\\'en possède pas. Chez les éléphants adultes il n\\'y a que 6 dents, 2 incisives, ce sont les défenses, et 4 molaires. La formule dentaire est i1/0 c0/0 m1/1.\\n\\n\\n==== Dents ====\\nLes dents sont essentiellement composées d’ivoire et d’émail qui forment la couronne des dents par de nombreuses crêtes transversales, qui sont plus ou moins lamellées. Les crêtes sont disjointes puis, au fur et à mesure, un cément se forme et s’intercale entre les dents pour former un tout. Un petit nombre de dents molaires sont présentes à chaque mâchoire, « parfois une paire (…), (…) une paire à l’une des mâchoires et deux à l’autre, (…) encore deux paires à chacune », de plus les dents correspondantes entre elles « n’ont ni la même apparence, ni le même nombre de lamelles ».\\n\\nSelon les études de Corse et de Blainville, « les éléphants (…) ont six paires de dents à chacune des mâchoires. Ces dents augmentent de volume depuis la première jusqu’à la dernière ou sixième, et le nombre de leurs lamelles (…) est aussi de plus en plus considérable. ». « La succession des dents molaires s’opère ainsi par flots d’une manière lente mais réglée, et l’on admet trois flots différents. Les dents se présentent deux par deux de chaque côté de l’une et de l’autre mâchoire. Le degré plus ou moins avancé de l’usure de chacune d’elles détermine les différences que l’on remarque dans le nombre total de lamelles (…) pour chaque flot ».\\nLes éléphants ont généralement 26 dents : les 2 incisives appelées défenses, 12 prémolaires déciduales et 12 molaires. Contrairement à la plupart des mammifères, qui font pousser des dents de lait, puis les remplacent par un seul ensemble permanent de dents adultes, les éléphants sont des polyphyodontes : ils ont des cycles de rotation dentaire tout au long de leur vie. Les molaires sont remplacées six fois au cours de la vie d\\'un éléphant typique. Les dents ne sont pas remplacées par de nouvelles dents émergeant des mâchoires verticalement comme chez la plupart des mammifères. Au lieu de cela, de nouvelles dents poussent à l\\'arrière de la bouche et avancent pour repousser les anciennes. La première molaire de chaque côté de la mâchoire tombe lorsque l\\'éléphant a 2 ou 3 ans. La deuxième série de molaires tombe à l\\'âge de 4 à 6 ans. La troisième série tombe entre 9 et 15 ans et la quatrième série dure jusqu\\'à 18-28 ans. La cinquième série de dents tombe vers la quarantaine. La sixième poussée — et généralement la dernière — doit durer à l\\'éléphant le reste de sa vie. Les dents d\\'éléphant ont des crêtes dentaires en forme de boucle, qui sont plus épaisses et plus en forme de losange chez les éléphants d\\'Afrique.\\n\\n\\n==== Défenses ====\\n\\nLes défenses d\\'un éléphant sont les deuxièmes incisives modifiées de la mâchoire supérieure. Elles remplacent les dents de lait à l\\'âge de 6 à 12 mois et poussent continuellement d\\'environ 17 cm par an. Une défense nouvellement développée a un capuchon en émail lisse qui finit par s\\'estomper. La dentine est connue sous le nom d\\'ivoire ; sa section transversale se compose de motifs de lignes entrecroisées qui créent des zones en forme de losange. Une grande partie des défenses est visible de l\\'extérieur ; le reste est enserré dans un logement du crâne. Au moins un tiers de la défense contient la pulpe et certains nerfs s\\'étendent jusqu\\'à la pointe. Il serait donc difficile de l\\'enlever sans nuire à l\\'animal. Une fois retiré, l\\'ivoire commence à se dessécher et à se fissurer s\\'il n\\'est pas conservé au frais et à l\\'humidité.\\nL\\'éléphant se sert de ses défenses à plusieurs fins. Il les utilise pour creuser dans l\\'eau, le sel ou parmi les racines; écorcer ou marquer les arbres ; déplacer des arbres et des branches pour dégager un chemin. Lors des combats, elles servent pour attaquer, se défendre, protéger le corps.\\n\\nComme les humains, qui sont généralement droitiers ou gauchers, les éléphants ont généralement une différenciation des défenses droite et gauche. La défense dominante, appelée défense principale, est généralement plus usée et plus courte, avec une pointe plus arrondie. Pour les éléphants d\\'Afrique, les défenses sont présentes chez les mâles et les femelles, et ont à peu près la même longueur pour les deux sexes, atteignant jusqu\\'à 3 m, mais celles des mâles ont tendance à être plus épaisses. Autrefois, les défenses d\\'éléphant pesant 100 kg et plus n\\'étaient pas rares, mais on n\\'en voit plus guère aujourd\\'hui dépassant 50 kg.\\nChez les espèces asiatiques, seuls les mâles ont de grandes défenses. Les femelles asiatiques ont de très petites défenses, voire aucune. Il existe des mâles dépourvus de défenses, particulièrement communs au Sri Lanka. Les mâles asiatiques peuvent avoir des défenses aussi longues que celles des africains, mais elles sont généralement plus minces et plus légères : les plus grandes enregistrées mesuraient 3,02 m de long et pesaient 39 kg. La chasse à l\\'ivoire d\\'éléphant en Afrique et en Asie a conduit à une sélection naturelle pour des défenses plus courtes, ou absentes,.\\n\\n\\n=== Peau ===\\nLa peau de l\\'éléphant est d\\'une épaisseur d\\'environ 2 cm. Cette peau est fragile du fait de la présence de plis où viennent se loger des parasites. Il n\\'y a pratiquement pas de poils, et il n\\'y a ni glande sudoripare, ni glande sébacée. De ce fait, leur peau est sèche, c\\'est pour cela qu\\'elle doit être souvent humectée à l\\'aide d\\'eau projetée par la trompe ou couverte de poussière ou de boue également projetée par leur trompe.\\nLa couleur de la peau est grisâtre ; cependant sa couleur apparente est liée au sol sur lequel évolue l\\'éléphant. Elle peut aussi être due aux bains de boues.\\nLa faible densité des poils (quelques centaines par mètre carré, chaque poil mesurant en moyenne 2 centimètres de longueur et 0,5 mm de diamètre) agit non plus comme une fourrure mais participe — à hauteur de 23 % — avec d\\'autres mécanismes de thermorégulation (battement des oreilles, bains, pulvérisation d\\'eau avec leurs trompes, respiration percutanée) à la thermolyse du mammifère, les poils agissant comme des ailettes qui augmentent la surface d\\'échange et donc les transferts thermiques.\\n\\n\\t\\t\\n\\t\\t\\n\\n\\n=== Oreille ===\\nLes oreilles de l\\'éléphant lui permettent de réguler sa température corporelle, grâce à une vascularisation très importante. Lorsqu\\'il mange des fruits fermentés ayant un degré d\\'alcool d\\'environ 7°, l\\'éléphant remue violemment ses oreilles, de même pour sa queue et sa trompe. Elles sont généralement plus petites chez l\\'éléphant d\\'Asie.\\n\\n\\n=== Cerveau ===\\nLe cerveau de l\\'éléphant, situé à l\\'arrière de son crâne, pèse entre 4 et 6 kg, ce qui est déjà considérable. Si l\\'on compare la taille du cerveau de l\\'éléphant à sa masse corporelle, il est alors le mammifère ayant le plus petit cerveau, alors que la souris possède le plus grand.\\n\\n\\n== Biologie et comportement ==\\n\\n\\n=== Reproduction ===\\n\\n\\n==== Maturité sexuelle ====\\nSi les fonctions reproductrices des éléphants mâles se mettent en place vers l\\'âge de 10-15 ans, ils commencent à se reproduire vers l\\'âge de 30 ans quand ils sont suffisamment imposants pour pouvoir se battre avec d\\'autres mâles pour conquérir les femelles.\\nLes fonctions reproductrices de l\\'éléphant femelle apparaissent de 9 ans jusqu\\'à 15 ans.\\nDans l\\'organisation matriarcale des éléphants, les mâles sont connus pour leur tempérament indépendant et ont tendance à vivre en solitaire, forgeant parfois une alliance provisoire avec un autre individu ou intégrant une bande de manière informelle. Tandis que les femelles entretiennent des liens familiaux étroits et solides.\\n\\n\\n==== Comportement sexuel ====\\n\\nLes mâles en rut, dont le taux sanguin de testostérone peut s\\'accroître cinquante fois, agitent les oreilles et secouent la tête, leur pénis devient vert. Il en dégouline une urine fortement odorante. Cela est dû à la libération d\\'un musc d’une phéromone, la frontaline, sécrétée sous deux formes chirales. Ces deux énantiomères (deux formes : (+)-frontaline et (-)-frontaline) ne sont pas sécrétés en mêmes proportions. Chez les jeunes mâles, la forme (+) domine. Au fur et à mesure de la maturité et de la période de rut, les deux isomères forment un racémique, qui attire les femelles en phase folliculaire et en œstrus. La frontaline est libérée par la glande temporale chez l’éléphant en période de rut, la sécrétion débute peu de temps avant la puberté, à l’âge de 15 ans. Cependant le rut ne se produit qu\\'à partir de 25 ans et ne durera que quelques jours. Puis vers 31-35 ans, celui-ci dure plusieurs semaines. Vers 36-40 ans, il dure de 1 à 2 mois. Pour finir, après 40 ans, le rut s’étend sur une période de 2 à 4 mois. La quantité de phéromones émises augmente avec l’âge de l’éléphant ainsi qu’en milieu de rut. La concentration et la proportion d’énantiomères de la frontaline constituent pour les animaux qui seront attentifs au message une source d’information sur l’âge et le stade du musth de l\\'éléphant qui émet. Une concentration de frontaline, en racémique, sera le synonyme d\\'un mâle mature ayant un statut social important.\\n\\n\\n==== Accouplement ====\\n\\nUne fois que la femelle et le mâle sont ensemble, l\\'accouplement peut commencer. L\\'éléphant mâle étant très lourd, la copulation est très rapide. En général, elle dure entre 20 et 30 secondes. La période de copulations dure environ trois jours.\\nLa jeune femelle est effrayée lors de sa première période de chaleur, le mâle peut la poursuivre. Pour avertir la femelle qu\\'il va la saillir, le mâle pose sa trompe sur son dos ; la femelle s\\'immobilise alors.\\nLes mâles passent dans les troupeaux de femelles lors de leur rut pour sentir les vulves des femelles.\\n\\n\\n==== Gestation et mise bas ====\\n\\nLa gestation d\\'une éléphante est la plus longue de tous les mammifères terrestres. Elle dure de 20 à 22 mois. La durée d\\'allaitement est comprise entre 36 et 48 mois. Les mises bas s\\'espacent d\\'environ 2 ans et demi à 5 ans. La gestation est plus longue pour un éléphanteau mâle que pour un éléphanteau femelle.\\nUne éléphante peut être en gestation jusqu\\'à l\\'âge de cinquante ans. Dans la plupart des cas, un seul éléphant est porté ; les cas de gémellité sont très rares.\\n\\n\\n=== Vie sociale ===\\n\\nLes éléphants vivent dans une société matriarcale. Cette structure matriarcale existe depuis plus de sept millions d\\'années, des empreintes d\\'une harde d\\'éléphants de cette époque ayant été découvertes sur une surface de 5 hectares sur le site de Mleisa 1 dans les Émirats arabes unis, faisant de cette piste de mammifères fossile la plus vieille de ce type et probablement la plus longue piste préservée dans le monde. Les troupeaux sont composés d\\'une dizaine d\\'éléphantes et de jeunes éléphanteaux, après la maturité sexuelle les mâles quittent le groupe. Ils errent jusqu\\'à ce qu\\'ils fassent alliance avec d\\'autres jeunes mâles.\\nUne étude, menée dans un zoo, montre que l\\'éléphant aime les fruits fermentés à un degré d\\'alcool de 7°. Lorsque l\\'éléphant est saoul, il perd de sa sociabilité (alors que sobre il est très sociable). Lorsqu\\'il est ivre, il reste à l\\'écart du troupeau. Un chercheur américain défendait l\\'idée que les animaux s\\'enivrent ou se droguent, volontairement, pour oublier les tourments de leur existence. Pour le prouver, il a fait vivre durant un mois des éléphants d\\'une réserve californienne sur un territoire plus restreint qu\\'à leur accoutumée. La surpopulation due au petit espace a angoissé les animaux qui, du coup, ont bu trois fois plus que d\\'habitude. Ils sont devenus si agressifs qu\\'il a été dangereux de les approcher.\\n\\n\\n=== Communication ===\\nLe cri de l\\'éléphant est le barrissement. De récentes études scientifiques ont montré que les éléphants, comme de nombreux animaux, sont sensibles aux infrasons. L\\'utilité de l\\'audition de ces infrasons reste cependant mystérieuse. Il semble qu\\'ils soient capables de communiquer entre eux par les ondes acoustiques de surface transmises par le sol.\\n\\n\\n=== Sommeil ===\\nLes éléphants peuvent dormir debout ou couchés. Le fait de se coucher indique qu\\'ils sont parfaitement détendus.\\n\\n\\n=== Alimentation ===\\n\\nL\\'éléphant est herbivore, il mange une grande variété d\\'éléments végétaux : herbes, plantes, feuilles, fruits, racines et tubercules, écorces et même du bois. Il apprécie par exemple le bois tendre et gorgé de sève du baobab.\\nLes besoins alimentaires de l\\'éléphant sont importants, surtout qualitativement. En fonction de son environnement, il consacre une grande partie de son temps à la recherche de nourriture (16 à 20 heures par jour), se déplaçant sur de longues distances et sélectionnant les aliments les plus riches. Il peut se dresser sur ses pattes arrière pour attraper avec sa trompe les rameaux les plus tendres jusqu\\'à cinq ou six mètres de hauteur.\\nQuotidiennement, il faut à l\\'éléphant entre 150 et 180 kilogrammes de nourriture en saison sèche, et entre 200 et 260 kilogrammes en saison des pluies. Ces quantités varient aussi en fonction des espèces et des milieux fréquentés.\\nUn éléphant adulte boit jusqu\\'à 140 L d\\'eau par jour. Il aspire dans sa trompe jusqu\\'à dix litres à la fois, puis se les verse dans la bouche. Il peut rester trois ou quatre jours sans boire. Il peut se servir de sa trompe pour reprendre de l\\'eau dans son estomac et s\\'en servir pour se rafraîchir la peau. Sa peau très épaisse est l\\'objet de soins constants : outre les aspersions, les baignades et les roulades dans la boue, le poudrage à la poussière est bienvenu pour protéger l\\'épiderme des insectes et du soleil.\\nMalgré la quarantaine de mètres d\\'intestin qu\\'il possède, sa digestion est peu efficace. Elle dure environ 12 heures après les 16 à 20 heures où il a cherché à se nourrir, 40 à 60 % de la nourriture n\\'étant pas digérée. Si son alimentation n\\'est pas suffisamment riche, son tonus, son humeur et sa santé en général sont rapidement affectés.\\nLe comportement alimentaire a en général un impact important sur le milieu. Le bilan de ces conséquences varie en fonction des espèces (Afrique, Asie), de la saison, du biotope et de la densité de la population. Ainsi, l\\'éléphant peut être considéré comme destructeur d\\'arbres en particulier dans la savane, alors qu\\'il participe ailleurs très activement à la régénération en limite des zones forestières. Certaines espèces d\\'arbres sont dépendantes de l\\'éléphant pour leur extension : celui-ci, friand de leurs fruits, en dissémine les graines avec l\\'excellent terreau que constitue son crottin, capable de contenir jusqu\\'à 35 % de graines.\\n\\n\\n=== Intelligence ===\\n\\nEn l’état actuel des connaissances, l’éléphant est, avec l\\'humain, le dauphin, le corbeau et certaines espèces de grands singes, l\\'une des rares espèces animales à réussir le test du miroir de Gallup : lorsqu’on marque d’une tache le front d’un éléphant en un point qu’il ne peut voir directement et qu’on lui présente un miroir, il passe sa trompe sur la tache ; démontrant ainsi qu’il a reconnu son image et donc qu’il a conscience de lui-même,,.\\nLes éléphants peuvent utiliser des outils de défense, telles des pierres saisies avec leur trompe et qu\\'ils lancent sur leurs ennemis. Ils peuvent également se toiletter en se grattant avec des branches ou des baguettes des parties de corps qu\\'ils ne peuvent atteindre avec leur trompe. Ils présentent ainsi un exemple d’utilisation d\\'outil par un animal.\\nLors d\\'une expérimentation de Preston Foerder, un éléphant (d\\'Asie, Elephas maximus) s\\'est montré capable d\\'un éclair de compréhension (insight). Il est allé chercher un cube pour monter dessus et atteindre de la nourriture,.\\n\\n\\n=== Perception ===\\nLes éléphants sont réputés pour leur capacité à anticiper l\\'arrivée des intempéries. il semblerait qu\\'ils soient capables d\\'entendre les sons provoqués par le déplacement des nuages.\\n\\n\\n== Systématique ==\\n\\n\\n=== Taxonomie ===\\n\\nL’éléphant d\\'Asie et l’éléphant d’Afrique ont longtemps été considérés comme les deux seules espèces représentant la famille des Éléphantidés à l’époque moderne. Depuis, de récentes études génétiques ont permis de distinguer deux sous-espèces africaines distinctes : Loxodonta africana africana (« éléphant de la savane ») et Loxodonta africana cyclotis (« éléphant des forêts »).\\nLes espèces d\\'Éléphantidés vivant à l’heure actuelle sont donc :\\n\\n\\n=== Histoire évolutive ===\\n\\nL’extinction Crétacé-Tertiaire est suivie d\\'une diversification très rapide des ongulés africains, notamment l\\'ordre des Proboscidiens dont les plus anciennes espèces découvertes à ce jour sont Eritherium azzouzorum et Phosphatherium escuilliei, datant de la fin du Paléocène il y a 60 millions d\\'années. Sans trompe mais avec une première incisive agrandie (rappelant la naissance d\\'une défense) et des orbites oculaires en position antérieure, ces premiers proboscidiens sont petits et graciles, ont un corps bas sur pattes et un mode de vie semi-aquatique, à l\\'instar de Moeritherium.\\nAprès un déclin à l\\'oligocène, les proboscidiens connaissent une diversification avec l\\'apparition des Deinotheriidae et des Mammutidae. La seconde radiation évolutive voit l\\'émergence au début du Miocène des Gomphotheriidae qui sont à l\\'origine des Elephantidae et des Stegodontidae, familles qui correspondent à la troisième radiation évolutive au miocène supérieur.\\nLes Proboscidiens présents sur le continent américain, tels Mammut americanum ou Haplomastodon, se sont éteints il y a une dizaine de milliers d\\'années.\\n\\n\\n== L\\'éléphant et l\\'homme ==\\n\\n\\n=== Menaces de disparition ===\\n\\n\\n==== Chasse et braconnage ====\\n\\nDurant des millénaires, l\\'homme chassa l\\'éléphant pour sa consommation et pour le commerce de l\\'ivoire tiré des défenses. Durant l\\'Antiquité, les éléphants de Nubie furent utilisés dans les armées des Carthaginois. Au XVe siècle av. J.-C., il y avait encore des éléphants sur les bords de l\\'Euphrate, où le pharaon Thoutmôsis Ier chassait l\\'éléphant.\\nLa population des éléphants africains et asiatiques a été décimée, passant de plusieurs millions d\\'individus au début des années 1970 à quelques centaines de milliers 30 ans plus tard. Si bien qu\\'en 1989, la CITES interdit le commerce de l\\'ivoire. Les éléphants sont désormais considérés comme des espèces protégées et la chasse aux éléphants est très réglementée.\\nLe braconnage s\\'intensifie malheureusement chaque année. En 2011, entre 25 000 et 30 000 éléphants ont été abattus sauvagement afin de récupérer leurs défenses et alimenter les commerces illégaux notamment en provenance d\\'Asie.\\nL\\'éléphant a peu de prédateurs naturels, c\\'est-à-dire d\\'autres espèces que l\\'Homme. De grands fauves tels que le lion ou le tigre du Bengale (dans le cas de l\\'éléphant d\\'Asie) peuvent exercer une prédation sur les individus jeunes ou faibles ; il est cependant peu probable que ces animaux attaquent un adulte, au vu du danger qu\\'il peut représenter.\\nSelon l’Union internationale pour la conservation de la nature (UICN), la population des éléphants d’Afrique a sensiblement diminué au cours des années 2010 : le continent compte en 2019 environ 415 000 spécimens, soit 111 000 de moins que lors de la précédente décennie.\\n\\n\\n==== L\\'éléphant des forêts africaines menacé d\\'extinction d\\'ici 2025 ====\\nAu terme de la conférence organisée à Bangkok du 3 au 14 mars 2013, par la CITES, à laquelle 178 pays ont participé, l\\'état d\\'esprit était au pessimisme concernant la protection des éléphants « victimes dans leurs pays d\\'origine d\\'un braconnage sans précédent et d\\'un commerce effréné en Asie ». Nombre d\\'ONG concernées par cette action pensent que « la communauté internationale a échoué à protéger les éléphants ». Depuis 2007 le trafic d\\'ivoire a doublé et plus que triplé par rapport à 1998. Le nombre d\\'éléphants africains, selon les enquêtes présentées à la conférence, est compris entre 420 000 et 650 000. 25 000 ont été tués en 2011 et probablement 30 000 en 2012. Publiée en mars 2013 dans la revue PLoS One, une autre étude révèle que 62 % des éléphants des forêts ont été abattus durant ces dix dernières années. Si ce rythme perdure, ils pourraient disparaitre d\\'Afrique centrale d\\'ici 2025. Les spécialistes affirment qu\\'à terme, si le braconnage ne cesse pas, tous les éléphants du continent seront menacés d\\'extinction.\\n\\nÀ Gembloux Agro-Bio Tech - Université de Liège en Belgique, plusieurs chercheurs avaient déjà fait le même constat pour la population des éléphants de l\\'Afrique de l\\'Ouest. En 40 ans, leur nombre a diminué de moitié.\\nL\\'ONG Save the Elephants estime que le commerce illégal de l\\'ivoire à Hong Kong menace la survie des éléphants, étant donné que le marché de l\\'ivoire en Chine et en Asie du Sud-Est passe en grande partie par Hong Kong.\\n\\n\\n=== Perte d\\'habitat ===\\n\\nL\\'augmentation des risques de conflits d\\'intérêt pour l\\'habitat avec des populations humaines menace la survie de l\\'éléphant. Ce conflit tue 150 éléphants et un peu plus de 100 personnes par an au Sri Lanka. Contrairement à son cousin d\\'Afrique, l\\'éléphant d\\'Asie, possède de petites défenses. La disparition de celui-ci est principalement attribuée à la perte de son habitat. De grands morceaux de forêt disparaissent, ce qui touche profondément leur écosystème. Les arbres contribuent à l\\'ancrage du sol et l\\'absorption des eaux de ruissellement. La déforestation entraine des inondations et une érosion massive. Lorsque la forêt est réduite, les éléphants deviennent une partie du problème, car ils détruisent rapidement la végétation de la zone où ils vivent et éliminent toutes les ressources en nourriture.\\n\\n\\n=== Parcs nationaux ===\\n\\nLa première réserve officielle, Parc national Kruger, est peut-être la plus connue des réserves et celle ayant obtenu le plus grand succès. Cependant, de nombreux problèmes sont apparus depuis sa création. Les clôtures de la réserve ont coupé de nombreux animaux de leur alimentation en hiver ou de leurs zones de reproduction au printemps. Certains animaux sont morts, alors que d\\'autres comme les éléphants ont démoli les clôtures, entraînant des ravages dans les champs voisins. Lorsque les éléphants sont limités à un petit territoire, les dégâts infligés au paysage peuvent être énormes.\\nDe ce fait, certaines réserves, comme le Parc national Kruger, de l\\'avis de certains gestionnaires de faune sauvage, ont souffert de la surpopulation des éléphants, au détriment d\\'autres espèces de la faune dans la réserve. Le 25 février 2008, l\\'Afrique du Sud a annoncé que l\\'abattage pour contrôler le nombre d\\'éléphants, arrêté depuis 1994, reprendrait. Les défenseurs des droits des animaux ont menacé d\\'un appel au boycott par les touristes et à d\\'autres formes d\\'oppositions.\\n\\n\\n=== Utilisation par l\\'Homme ===\\n\\nLes éléphants en captivité (en) sont utilisés ou exhibés dans les cirques, ménageries (tel Abul-Abbas, l\\'éléphant blanc de Charlemagne et Hanno, celui du pape Léon X) et zoos (tel le célèbre Jumbo). On ne peut pas parler à leur égard de domestication car le cycle de vie de l\\'éléphant est trop long pour que cela soit économiquement rentable par rapport à une capture d\\'individus sauvages, la phase précédant la maturité sexuelle de l\\'animal durant plus de 10 ans.\\n\\nUtilisé comme animal de trait par les humains, ainsi que lors de batailles en tant qu\\'éléphant de guerre, l\\'éléphant a occupé de nombreuses fonctions, notamment celle d\\'exécuteur lors d\\'exécutions par éléphant. En 1914-1918, des éléphants de cirque ont en Europe par exemple servi à débarder le bois en forêt (de Mormal, dans le Nord de la France), ou encore à labourer, ou à tirer des wagons dans les usines de munitions.\\nL\\'éléphant peut également être entrainé par anéantissement.\\nLe conducteur d\\'un éléphant est appelé cornac ou mahout.\\n\\n\\n=== Expression ===\\n“avoir une mémoire d’éléphant” veut dire que l’ont a une très bonne mémoire\\n\\n\\n=== Produits dérivés ===\\n\\nÀ l\\'origine, les éléphants étaient chassés par les hommes pour leur viande.\\nCertaines parties, comme les pieds d\\'éléphants, ou des animaux entiers étaient naturalisés. Les poils et les défenses d\\'ivoire, bien sûr, étaient aussi utilisés. On s\\'en servait pour fabriquer des objets de décoration et en bijouterie, ou bien ils étaient destinés, ainsi que les dents et les ossements, à des cabinets de curiosité ou des museums.\\nL\\'ivoire a longtemps fait l\\'objet d\\'un commerce important qui subsiste encore parfois sous forme de trafic illégal malgré le statut de protection dont bénéficient les éléphants survivants.\\n\\n\\n=== Culture ===\\n\\n\\n==== Symbolique ====\\nDans la symbolique occidentale comme orientale, l\\'éléphant est associé à la mémoire, la sagesse, la longévité, la prospérité, la bienveillance, le père. Pour beaucoup de peuples africains, l\\'éléphant tient le rôle du père, du chef des animaux, du roi.\\n\\n\\n===== Orient =====\\n\\nL\\'éléphant apparaît dans la panthéon hindouiste et bouddhiste à partir du troisième millénaire avant Jésus-Christ, époque de sa domestication.\\nDans la religion hindoue, Ganesh est un dieu à tête d’éléphant ; il est le dieu de la Sagesse et le patron des étudiants. Les rares éléphants blancs sont les plus sacrés en Inde, et les éléphants domestiqués et décorés aux couleurs des dieux bénissent les fidèles de leur trompe dans certains temples.\\nEn Inde, l’éléphant évoque la force, la puissance, l\\'orage (forme ronde et grise des nuages de pluie), et il est sacré. Chaque dieu hindou chevauche un animal : Indra, dieu des Orages et de la Bataille, et Agni, dieu du Feu, se déplacent à dos d’éléphant.\\nAu Laos, passer sous la trompe d\\'un éléphant permet d\\'acquérir ses attributs : force, longévité, fertilité et caractère sacré. Chaque année à l\\'occasion du Nouvel An bouddhique, les cornacs laotiens organisent un baci ou soukhouan, cérémonie de rappel des âmes, pour leur éléphant.\\n\\n\\n===== Islam =====\\nDans le Coran, la 105e sourate (la 19e dans l’ordre chronologique) s\\'intitule Al-Fîl (l’Éléphant). Elle comprend cinq versets révélés à la Mecque et doit son nom à l’expression « ashâb al-fîl » (les gens de l’éléphant) présente dans le tout premier verset. Cette expression désigne les Abyssins, qui occupaient le Yémen voisin, voulaient évangéliser l’Arabie tout entière, notamment en attaquant la Kaaba, à La Mecque. En raison des entraves qu’ils mettaient au pèlerinage, le « ministre du calendrier » dans le gouvernement mecquois se vengea en profanant l’église de Sana\\'a. C’est alors que le gouverneur abyssin fit venir un éléphant de taille gigantesque appelé Mahmoud et dirigea une expédition sur La Mecque.\\n\\n\\n===== Occident =====\\nDans la symbolique chrétienne, l\\'éléphant symbolise le baptême : la femelle met bas dans l\\'eau d\\'un étang à côté duquel le mâle monte la garde pour écarter le dragon, symbole de l\\'esprit du mal.[réf. nécessaire]Dans la symbolique chrétienne, il représente aussi la chasteté (de tempérament frigide, il ne peut engendrer qu\\'après avoir absorbé, en guise d\\'aphrodisiaque, une racine de mandragore), la constance, la maîtrise de soi, la bénignité des princes (il n\\'a pas de fiel), la tempérance, la circonspection et la prudence.[réf. nécessaire]En France, on dit de quelqu\\'un qui a une bonne mémoire qu\\'il a « une mémoire d\\'éléphant » ; effectivement, l\\'éléphant a une excellente mémoire pour se rappeler ses congénères ou retrouver les pistes qu\\'il emprunte chaque année pour chercher sa nourriture. Sa mémoire visuelle lui permet également de se rappeler très longtemps les visages humains[source insuffisante].\\nL\\'éléphant représente les quatre piliers du monde : il porte le monde sur son dos.\\nL\\'éléphant est le symbole de la ville de Catane, en Italie, depuis le Moyen Âge (mais le lien remonte peut-être à l\\'Antiquité). La Fontaine de l\\'éléphant s\\'y dresse sur la place de la cathédrale.\\n\\n\\n===== Afrique =====\\nL\\'éléphant est l\\'emblème de la Côte d\\'Ivoire.\\nL\\'éléphant est symbole de royauté, de puissance et de sagesse et ce en général pour les peuples de tout le continent africain.\\nSon image est utilisée dans les cérémonies et danses, pour la fabrication des masques ou encore de mobiliers, d\\'objets rituels, dans beaucoup de tribus notamment chez les Bamileke de l\\'ouest du Cameroun ou encore chez les Gurusi du Burkina Faso.\\nHors tribus, l\\'éléphant est un symbole important au même titre que le lion et son image est présente au quotidien dans le monde africain.\\n\\n\\n===== Politique =====\\nEn politique, l\\'image de l\\'éléphant a pu être utilisé dans différents pays pour caractériser des courants politiques ou des politiciens : ainsi, l\\'emblème du Parti républicain américain est un éléphant, et certains des membres les plus influents du Parti socialiste français sont surnommés les « éléphants ».\\n\\n\\n===== Art =====\\n\\nDes représentations picturales de l\\'éléphant sont retrouvées en Occident dès le XIIe siècle comme dans le quartier historique de Montferrand sur la « Maison de l\\'Éléphant » (12 rue Kléber).\\nL\\'ivoire des défenses de l\\'éléphant a longtemps servi à la réalisation d\\'œuvres d\\'art. Les œuvres en or et ivoire sont qualifiées de chryséléphantines — chrusos, or en grec. Ce nom a été déformé en olifant, pour désigner une corne (instrument de musique) en ivoire.\\n\\n\\n===== Sport =====\\nEn sport, certaines équipes nationales portent des surnoms à l\\'image de l\\'éléphant :\\n\\nLa Côte d\\'Ivoire : Les éléphants\\nLa Guinée : Le Sily national (L\\'éléphant national)\\nLa Thaïlande : Les éléphants de guerre\\n\\n\\n==== Fiction ====\\n\\nLes éléphants ont inspiré de nombreux artistes. La liste ci-après est loin d\\'être exhaustive.\\n\\nCinéma :\\nLes Racines du ciel (The Roots of Heaven) de John Huston (1958), tiré du roman de Romain Gary.\\nTusk d\\'Alejandro Jodorowsky (1980).\\nChasseur blanc, cœur noir (White Hunter Black Heart) de Clint Eastwood (1990, inspiré par John Huston, chasseur d\\'éléphant sur le tournage de the African Queen en 1950).\\nSunny et l\\'éléphant de Frédéric Lepage, 2008.\\nDe l\\'eau pour les éléphants de Francis Lawrence, 2011, tiré du roman de Sara Gruen.\\nElephant Boy de Robert J. Flaherty en 1937\\nGrimsby : Agent trop spécial de Louis Leterrier (2016), Norman \"Nobby\" Butcher (Sacha Baron Cohen) se cache dans le vagin d\\'une éléphante.\\nDocumentaire\\nL\\'Homme et l’Éléphant de Vijay Singh.\\nDessins animés :\\nDumbo.\\nWinnie l\\'ourson et l\\'Éfélant\\nBabar\\nLittérature :\\nLes Racines du ciel de Romain Gary, Prix Goncourt en 1956.\\nLes Annales du disque-monde de Terry Pratchett (le disque-monde est soutenu par quatre éléphants géants).\\nL\\'Éléphant et le Singe de Jupiter de Jean de La Fontaine.\\nLe Voyage de l\\'éléphant de José Saramago\\nLittérature jeunesse :\\nHistoires comme ça de Rudyard Kipling (L\\'Enfant d\\'éléphant)\\nPoo Lorn l\\'éléphant de Reginald Campbell\\nLe Livre de la jungle de Rudyard Kipling (personnages de Hathi et de Kala Nag).\\nBabar de Laurent de Brunhoff\\nUn éléphant ça compte énormément de Helme Heine\\nLe Mystère de l\\'éléphant bleu de Enid Blyton\\nLa Maison éléphant de Henriette Bichonnier\\n Elmer, l\\'éléphant multicolore de David McKee\\nPomelo, l\\'éléphant rose, texte de Ramona Bádescu, illustrations de Benjamin Chaud : une quinzaine de titres, depuis 2002. Plusieurs de ces titres font partie de la « Bibliothèque jeunesse idéale » du Centre national de la littérature pour la jeunesse (BnF).\\n\\t\\t\\n\\n\\n== Notes et références ==\\n\\n\\n== Annexes ==\\n\\n\\n=== Bibliographie ===\\nElephants: Majestic Creatures of the Wild, Checkmark Books, 2000 (ISBN 978-0-87596-143-9, OCLC 475147472)\\n\\n\\n=== Articles connexes ===\\nBouse d\\'éléphant\\nIntelligence animale\\nÉléphant de guerre\\nHanno\\nListe d\\'éléphants de fiction\\nOrdre de l’Éléphant\\nMammouphant\\nBraconnage\\nÉléphant rose\\n\\n\\n=== Références taxonomiques ===\\n(en) Référence Mammal Species of the World (3e éd., 2005) : Elephas maximus  \\n(fr+en) Référence ITIS : genre Loxodonta Cuvier, 1825\\n(en) Référence Animal Diversity Web : Elephas maximus\\n(en) Référence UICN : espèce Elephas maximus Linnaeus, 1758\\n(en) Référence NCBI : genre Loxodonta (taxons inclus)\\n(en) Référence Fonds documentaire ARKive : Loxodonta africana  \\n(en) Référence Fonds documentaire ARKive : Elephas maximus  \\n\\n\\n=== Liens externes ===\\n\\nAnalyse des instruments internationaux de lutte contre le trafic et le braconnage des espèces menacées en Afrique centrale : le cas de l\\'éléphant et du gorille\\n« Physiologie de l\\'éléphant », sur elephants.free.fr\\nUn dossier sur l\\'éléphant chez Futura-Sciences\\n« Chang Nam : La légende des éléphants nains aquatiques en Thaïlande », sur magiedubouddha.com\\n Portail des mammifères'"
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      "source": [
        "We need to clean this up a bit. Let us remove all the special characters and keep only 26 letters and space. Note that this will remove accented characters in French also. We are also removing all the numbers and spaces. So this is not an ideal solution."
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        "def cleanup(text):\n",
        "  text = text.lower()  # make it lowercase\n",
        "  text = re.sub('[^a-z]+', '', text) # only keep characters, i.e. if not a-z then replace with space.\n",
        "  return text"
      ],
      "execution_count": null,
      "outputs": []
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    {
      "cell_type": "code",
      "source": [
        "text1 = re.sub('[a-z]', '1', 'espèce d\\'« éléphant d\\?Afrique »,')\n",
        "text1"
      ],
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          "height": 36
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        "id": "Iawqez-f4oT5",
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          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "\"111è11 1'« é1é11111 1\\\\?A111111 »,\""
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        "id": "qrOjC32fRuTK"
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      "source": [
        "eng1 = cleanup(eng1)\n",
        "eng2 = cleanup(eng2)\n",
        "fr1 = cleanup(fr1)\n",
        "fr2 = cleanup(fr2)"
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      "execution_count": null,
      "outputs": []
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    {
      "cell_type": "code",
      "metadata": {
        "id": "rIdqvL2G-LqL",
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      "source": [
        "print(eng1)"
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        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "thegiraffeisalargeafricanhoofedmammalbelongingtothegenusgiraffaitisthetallestlivingterrestrialanimalandthelargestruminantonearthtraditionallygiraffeswerethoughttobeonespeciesgiraffacamelopardaliswithninesubspeciesmostrecentlyresearchersproposeddividingthemintouptoeightextantspeciesduetonewresearchintotheirmitochondrialandnucleardnaaswellasmorphologicalmeasurementssevenotherextinctspeciesofgiraffaareknownfromthefossilrecordthegiraffeschiefdistinguishingcharacteristicsareitsextremelylongneckandlegsitshornlikeossiconesanditsspottedcoatpatternsitisclassifiedunderthefamilygiraffidaealongwithitsclosestextantrelativetheokapiitsscatteredrangeextendsfromchadinthenorthtosouthafricainthesouthandfromnigerinthewesttosomaliaintheeastgiraffesusuallyinhabitsavannahsandwoodlandstheirfoodsourceisleavesfruitsandflowersofwoodyplantsprimarilyacaciaspecieswhichtheybrowseatheightsmostotherherbivorescannotreachlionsleopardsspottedhyenasandafricanwilddogsmaypreyupongiraffesgiraffesliveinherdsofrelatedfemalesandtheiroffspringorbachelorherdsofunrelatedadultmalesbutaregregariousandmaygatherinlargeaggregationsmalesestablishsocialhierarchiesthroughneckingcombatboutswheretheneckisusedasaweapondominantmalesgainmatingaccesstofemaleswhichbearsoleresponsibilityforraisingtheyoungthegiraffehasintriguedvariousancientandmodernculturesforitspeculiarappearanceandhasoftenbeenfeaturedinpaintingsbooksandcartoonsitisclassifiedbytheinternationalunionforconservationofnatureiucnasvulnerabletoextinctionandhasbeenextirpatedfrommanypartsofitsformerrangegiraffesarestillfoundinnumerousnationalparksandgamereservesbutestimatesasofindicatethereareapproximatelymembersofgiraffainthewildmorethanwerekeptinzoosinetymologythenamegiraffehasitsearliestknownoriginsinthearabicwordzarfahperhapsborrowedfromtheanimalssomalinamegerithearabnameistranslatedasfastwalkerinearlymodernenglishthespellingsjarrafandziraphwereusedprobablydirectlyfromthearabicandinmiddleenglishjarrafandziraphgerfauntztheitalianformgiraffaaroseinthesthemodernenglishformdevelopedaroundfromthefrenchgirafecamelopardisanarchaicenglishnameforthegiraffeitderivesfromtheancientgreekkamloprdalisfromkmloscamelandprdalisleopardreferringtoitscamellikeshapeandleopardlikecolourationtaxonomyevolutionthegiraffeisoneofonlytwolivinggeneraofthefamilygiraffidaeintheorderartiodactylatheotherbeingtheokapithefamilywasoncemuchmoreextensivewithoverfossilgeneradescribedtheelongationoftheneckappearstohavestartedearlyinthegiraffelineagecomparisonsbetweengiraffesandtheirancientrelativessuggestvertebraeclosetotheskulllengthenedearlierfollowedbylengtheningofvertebraefurtherdownoneearlygiraffidancestorwascanthumeryxwhichhasbeendatedvariouslytohavelivedmillionyearsagomyamyaormyaandwhosedepositshavebeenfoundinlibyathisanimalresembledanantelopeandhadamediumsizedlightlybuiltbodygiraffokeryxappearedmyaontheindiansubcontinentandresembledanokapiorasmallgiraffeandhadalongerneckandsimilarossiconesgiraffokeryxmayhavesharedacladewithmoremassivelybuiltgiraffidslikesivatheriumandbramatheriumgiraffidslikepalaeotragusshansitheriumandsamotheriumappearedmyaandlivedthroughoutafricaandeurasiatheseanimalshadbroaderskullwithreducedfrontalcavitiespaleotragusresembledtheokapiandmayhavebeenitsancestorothersfindthattheokapilineagedivergedearlierbeforegiraffokeryxsamotheriumwasaparticularlyimportanttransitionalfossilinthegiraffelineageasthelengthandstructureofitscervicalvertebraewerebetweenthoseofamoderngiraffeandanokapianditsneckposturewaslikelysimilartotheformerbohliniawhichfirstappearedinsoutheasterneuropeandlivedmyawaslikelyadirectancestorofthegiraffebohliniacloselyresembledmoderngiraffeshavingalongneckandlegsandsimilarossiconesanddentitionbohliniacolonisedchinaandnorthernindiaandproducedthegiraffawhicharoundmyareachedafricaclimatechangesleadtotheextinctionoftheasiangiraffeswhiletheafricangiraffessurvivedandradiatedintonewspecieslivinggiraffesappeartohavearisenaroundmyaineasternafricaduringthepleistocenesomebiologistssuggestthemoderngiraffesdescendedfromgjumaeothersfindggracilisamorelikelycandidategjumaewaslargerandmorerobustwhileggraciliswassmallerandmoreslenderthechangesfromextensiveforeststomoreopenhabitatswhichbeganmyaarebelievedtobethemaindriverfortheevolutionofgiraffesduringthistimetropicalplantsdisappearedandwerereplacedbyaridcplantsandadrysavannahemergedacrosseasternandnorthernafricaandwesternindiasomeresearchershavehypothesisedthatthisnewhabitatcoupledwithadifferentdietincludingacaciaspeciesmayhaveexposedgiraffeancestorstotoxinsthatcausedhighermutationratesandahigherrateofevolutionthecoatpatternsofmoderngiraffesmayalsohavecoincidedwiththesehabitatchangesasiangiraffesarehypothesisedtohavehadmoreokapilikecolourationsthegiraffegenomeisaroundbillionbasepairsinlengthcomparedtothebillionbasepairsoftheokapioftheproteinsingiraffeandokapigenesareidenticalthedivergenceofgiraffeandokapilineagesdatestoaroundmyaasmallgroupofregulatorygenesinthegiraffeappeartoberesponsiblefortheanimalsheightandassociatedcirculatoryadaptationsspeciesandsubspeciestheinternationalunionforconservationofnatureiucncurrentlyrecognisesonlyonespeciesofgiraffewithninesubspeciescarllinnaeusoriginallyclassifiedlivinggiraffesasonespeciesinhegaveitthebinomialnamecervuscamelopardalismathurinjacquesbrissoncoinedthegenusgiraffainduringthesvarioustaxonomieswithtwoorthreespecieswereproposedastudyonthegeneticsofgiraffesusingmitochondrialdnasuggestedatleastsixlineagescouldberecognisedasspeciesastudyusingdetailedanalysesofthemorphologyofgiraffesandapplicationofthephylogeneticspeciesconceptdescribedeightspeciesoflivinggiraffesastudyalsoconcludedthatlivinggiraffesconsistofmultiplespeciestheresearcherssuggestedtheexistenceoffourspecieswhichhavenotexchangedgeneticinformationbetweeneachotherfortomillionyearsastudyshowedthatdependingonthemethodchosendifferenttaxonomichypothesesrecognizingfromtwotosixspeciescanbeconsideredforthegenusgiraffathatstudyalsofoundthatmultispeciescoalescentmethodscanleadtotaxonomicoversplittingasthosemethodsdelimitgeographicstructuresratherthanspeciesthethreespecieshypothesiswhichrecognisesgcamelopardalisggiraffaandgtippelskirchiishighlysupportedbyphylogeneticanalysesandalsocorroboratedbymostpopulationgeneticandmultispeciescoalescentanalysesawholegenomesequencingstudysuggeststheexistenceoffourdistinctspeciesandsevensubspeciesthecladogrambelowshowsthephylogeneticrelationshipbetweenthefourproposedspeciesandsevensubspeciesbasedonthegenomeanalysisnotetheeightlineagescorrespondtoeightofthetraditionalsubspeciesintheonespecieshypothesistherothschildgiraffeissubsumedintogcamelopardaliscamelopardalisthefollowingtablecomparesthedifferenthypothesesforgiraffespeciesthedescriptioncolumnshowsthetraditionalninesubspeciesintheonespecieshypothesisthefirstextinctspeciestobedescribedwasgiraffasivalensisfalconerandcautleyareevaluationofavertebrathatwasinitiallydescribedasafossilofthelivinggiraffewhiletaxonomicopinionmaybelackingonsomenamestheextinctspeciesthathavebeenpublishedincludegiraffagracilisgiraffajumaegiraffapriscillagiraffapomeligiraffapunjabiensisgiraffapygmaeagiraffasivalensisgiraffastilleicharacteristicsfullygrowngiraffesstandmfttallwithmalestallerthanfemalestheaverageweightiskglbforanadultmaleandkglbforanadultfemaledespiteitslongneckandlegsitsbodyisrelativelyshorttheskinismostlygrayortanandcanreachathicknessofmminthecentimetresinlongtailendsinalongdarktuftofhairandisusedasadefenseagainstinsectsthecoathasdarkblotchesorpatcheswhichcanbeorangechestnutbrownornearlyblacksurroundedbylighthairusuallywhiteorcreamcolouredmalegiraffesbecomedarkerastheygrowoldthecoatpatternhasbeenclaimedtoserveascamouflageinthelightandshadepatternsofsavannahwoodlandswhenstandingamongtreesandbushestheyarehardtoseeatevenafewmetresdistancehoweveradultgiraffesmoveabouttogainthebestviewofanapproachingpredatorrelyingontheirsizeandabilitytodefendthemselvesratherthanoncamouflagewhichmaybemoreimportantforcalveseachgiraffehasauniquecoatpatterncalvesinheritsomecoatpatterntraitsfromtheirmothersandvariationinsomespottraitsiscorrelatedwithcalfsurvivaltheskinundertheblotchesmayregulatetheanimalsbodytemperaturebeingsitesforcomplexbloodvesselsystemsandlargesweatglandsthefurmaygivetheanimalchemicaldefenseasitsparasiterepellentsgiveitacharacteristicscentatleastmainaromaticchemicalsareinthefuralthoughindoleandmethylindoleareresponsibleformostofthesmellbecausemaleshaveastrongerodourthanfemalesitmayalsohaveasexualfunctionheadbothsexeshaveprominenthornlikestructurescalledossiconeswhichcanreachcmintheyareformedfromossifiedcartilagecoveredinskinandfusedtotheskullattheparietalbonesbeingvascularisedtheossiconesmayhavearoleinthermoregulationandareusedincombatbetweenmalesappearanceisareliableguidetothesexorageofagiraffetheossiconesoffemalesandyoungarethinanddisplaytuftsofhairontopwhereasthoseofadultmalestendtobebaldandknobedontopalumpwhichismoreprominentinmalesemergesinthemiddleoftheskullmalesdevelopcalciumdepositsthatformbumpsontheirskullsastheyagemultiplesinuseslightenagiraffesskullhoweverasmalesagetheirskullsbecomeheavierandmoreclublikehelpingthembecomemoredominantincombattheoccipitalcondylesbonesatthebottomoftheskullallowtheanimaltotipitsheadoverdegreesandgrabfoodonthebranchesdirectlyabovethemwiththetonguelocatedonthesidesoftheheadthegiraffehasabroadvisualfieldfromitsgreatheightcomparedtootherungulatesgiraffevisionismorebinocularandtheeyesarelargerwithagreaterretinalsurfaceareagiraffesmayseeincolourandtheirsensesofhearingandsmellaresharptheearsaremovableandthenostrilsareslitshapedpossiblytowithstandblowingsandthegiraffestongueisaboutcminlongitisblackperhapstoprotectagainstsunburnandcangraspfoliageanddelicatelypickoffleavestheupperlipisflexibleandhairytoprotectagainstsharppricklestheupperjawhasahardpalateinsteadoffrontteeththemolarsandpremolarsarewidewithlowcrownsonthesurfaceneckthegiraffehasanextremelyelongatedneckwhichcanbeuptomftinlengthalongtheneckisamanemadeofshorterecthairsthenecktypicallyrestsatanangleofdegreesthoughjuvenilesareclosertodegreesthelongneckresultsfromadisproportionatelengtheningofthecervicalvertebraenotfromtheadditionofmorevertebraeeachcervicalvertebraisovercminlongtheycomprisepercentofthelengthofthegiraffesvertebralcolumncomparedwiththepercenttypicalofsimilarlargeungulatesincludingthegiraffesclosestlivingrelativetheokapithiselongationlargelytakesplaceafterbirthperhapsbecausegiraffemotherswouldhaveadifficulttimegivingbirthtoyoungwiththesameneckproportionsasadultsthegiraffesheadandneckareheldupbylargemusclesandanuchalligamentwhichareanchoredbylongthoracicvertebraespinesgivingthemahumpthegiraffesneckvertebraehaveballandsocketjointsthepointofarticulationbetweenthecervicalandthoracicvertebraeofgiraffesisshiftedtoliebetweenthefirstandsecondthoracicvertebraetandtunlikemostotherruminantswherethearticulationisbetweentheseventhcervicalvertebracandtthisallowsctocontributedirectlytoincreasednecklengthandhasgivenrisetothesuggestionthattisactuallycandthatgiraffeshaveaddedanextracervicalvertebrahoweverthispropositionisnotgenerallyacceptedasthasothermorphologicalfeaturessuchasanarticulatingribdeemeddiagnosticofthoracicvertebraeandbecauseexceptionstothemammalianlimitofsevencervicalvertebraearegenerallycharacterisedbyincreasedneurologicalanomaliesandmaladiesthereareseveralhypothesesregardingtheevolutionaryoriginandmaintenanceofelongationingiraffeneckscharlesdarwinoriginallysuggestedthecompetingbrowsershypothesiswhichhasbeenchallengedonlyrecentlyitsuggeststhatcompetitivepressurefromsmallerbrowserslikekudusteenbokandimpalaencouragedtheelongationoftheneckasitenabledgiraffestoreachfoodthatcompetitorscouldnotthisadvantageisrealasgiraffescananddofeeduptomfthighwhileevenquitelargecompetitorssuchaskuducanfeeduptoonlyaboutmftinhighthereisalsoresearchsuggestingthatbrowsingcompetitionisintenseatlowerlevelsandgiraffesfeedmoreefficientlygainingmoreleafbiomasswitheachmouthfulhighinthecanopyhoweverscientistsdisagreeaboutjusthowmuchtimegiraffesspendfeedingatlevelsbeyondthereachofotherbrowsersandastudyfoundthatadultgiraffeswithlongernecksactuallysufferedhighermortalityratesunderdroughtconditionsthantheirshorterneckedcounterpartsthisstudysuggeststhatmaintainingalongerneckrequiresmorenutrientswhichputslongerneckedgiraffesatriskduringafoodshortageanothertheorythesexualselectionhypothesisproposesthelongnecksevolvedasasecondarysexualcharacteristicgivingmalesanadvantageinneckingcontestsseebelowtoestablishdominanceandobtainaccesstosexuallyreceptivefemalesinsupportofthistheorynecksarelongerandheavierformalesthanfemalesofthesameageandmalesdonotemployotherformsofcombathoweveroneobjectionisitfailstoexplainwhyfemalegiraffesalsohavelongnecksithasalsobeenproposedthattheneckservestogivetheanimalgreatervigilancelegslocomotionandpostureagiraffesfrontandbacklegsareaboutthesamelengththeradiusandulnaofthefrontlegsarearticulatedbythecarpuswhichwhilestructurallyequivalenttothehumanwristfunctionsasakneeitappearsthatasuspensoryligamentallowsthelankylegstosupporttheanimalsgreatweightthehoovesoflargemalegiraffesreachcmcmininindiameterthefetlockofthelegislowtothegroundallowingthehooftobettersupporttheanimalsweightgiraffeslackdewclawsandinterdigitalglandswhilethepelvisisrelativelyshorttheiliumhasstretchedoutcrestsagiraffehasonlytwogaitswalkingandgallopingwalkingisdonebymovingthelegsononesideofthebodythendoingthesameontheothersidewhengallopingthehindlegsmovearoundthefrontlegsbeforethelattermoveforwardandthetailwillcurlupthemovementsoftheheadandneckprovidebalanceandcontrolmomentumwhilegallopingthegiraffecanreachasprintspeedofuptokmhmphandcansustainkmhmphforseveralkilometresgiraffeswouldprobablynotbecompetentswimmersastheirlonglegswouldbehighlycumbersomeinthewateralthoughtheymightbeabletofloatwhenswimmingthethoraxwouldbeweigheddownbythefrontlegsmakingitdifficultfortheanimaltomoveitsneckandlegsinharmonyorkeepitsheadabovethewaterssurfaceagirafferestsbylyingwithitsbodyontopofitsfoldedlegstoliedowntheanimalkneelsonitsfrontlegsandthenlowerstherestofitsbodytogetbackupitfirstgetsonitsfrontkneesandpositionsitsbacksideontopofitshindlegsitthenpullsupthebacksideupwardsandthefrontlegsstandstraightupagainateachstagetheanimalswingsitsheadforbalanceifthegiraffewantstoreachdowntodrinkiteitherspreadsitsfrontlegsorbendsitskneesstudiesincaptivityfoundthegiraffesleepsintermittentlyaroundhoursperdaymostlyatnightitusuallysleepslyingdownhoweverstandingsleepshavebeenrecordedparticularlyinolderindividualsintermittentshortdeepsleepphaseswhilelyingarecharacterisedbythegiraffebendingitsneckbackwardsandrestingitsheadonthehiporthighapositionbelievedtoindicateparadoxicalsleepinternalsystemsinmammalstheleftrecurrentlaryngealnerveislongerthantherightinthegiraffeitisovercminlongerthesenervesarelongerinthegiraffethaninanyotherlivinganimaltheleftnerveisovermftinlongeachnervecellinthispathbeginsinthebrainstemandpassesdowntheneckalongthevagusnervethenbranchesoffintotherecurrentlaryngealnervewhichpassesbackupthenecktothelarynxthusthesenervecellshavealengthofnearlymftinthelargestgiraffesdespiteitslongneckandlargeskullthebrainofthegiraffeistypicalforanungulateevaporativeheatlossinthenasalpassageskeepthegiraffesbraincooltheshapeoftheskeletongivesthegiraffeasmalllungvolumerelativetoitsmassitslongneckgivesitalargeamountofdeadspaceinspiteofitsnarrowwindpipethegiraffealsohasahightidalvolumesothebalanceofdeadspaceandtidalvolumeismuchthesameasothermammalstheanimalcanstillprovideenoughoxygenforitstissuesanditcanincreaseitsrespiratoryrateandoxygendiffusionwhenrunningthecirculatorysystemofthegiraffehasseveraladaptationsforitsgreatheightitskglbandcmftheartmustgenerateapproximatelydoublethebloodpressurerequiredforahumantomaintainbloodflowtothebrainassuchthewalloftheheartcanbeasthickascmingiraffeshaverelativelyhighheartratesfortheirsizeatbeatsperminutewhentheanimallowersitsheadthebloodrushesdownfairlyunopposedandaretemirabileintheupperneckwithitslargecrosssectionalareapreventsexcessbloodflowtothebrainwhenitraisesagainthebloodvesselsconstrictandpushbloodintothebrainsotheanimaldoesnotfaintthejugularveinscontainseveralmostcommonlysevenvalvestopreventbloodflowingbackintotheheadfromtheinferiorvenacavaandrightatriumwhiletheheadisloweredconverselythebloodvesselsinthelowerlegsareundergreatpressurebecauseoftheweightoffluidpressingdownonthemtosolvethisproblemtheskinofthelowerlegsisthickandtightpreventingtoomuchbloodfrompouringintothemgiraffeshaveoesophagealmusclesthatarestrongenoughtoallowregurgitationoffoodfromthestomachuptheneckandintothemouthforruminationtheyhavefourchamberedstomachswhichareadaptedtotheirspecializeddiettheintestinesofanadultgiraffemeasuremorethanmftinlengthandhavearelativelysmallratioofsmalltolargeintestinethegiraffehasasmallcompactliverfetusesmaybeasmallgallbladderthatvanishesbeforebirthbehaviourandecologyhabitatandfeedinggiraffesusuallyinhabitsavannahsandopenwoodlandstheypreferbyareasdominatedbyacacieaecommiphoracombretumandterminaliatreeoverbrachystegiawhicharemoredenselyspacedtheangolangiraffecanbefoundindesertenvironmentsgiraffesbrowseonthetwigsoftreespreferringthoseofthesubfamilyacacieaeandthegeneracommiphoraandterminaliawhichareimportantsourcesofcalciumandproteintosustainthegiraffesgrowthratetheyalsofeedonshrubsgrassandfruitagiraffeeatsaroundkglbofplantmatterdailywhenstressedgiraffesmaychewonlargebranchesstrippingthemofbarkgiraffesarealsorecordedtochewoldbonesduringthewetseasonfoodisabundantandgiraffesaremorespreadoutwhileduringthedryseasontheygatheraroundtheremainingevergreentreesandbushesmotherstendtofeedinopenareaspresumablytomakeiteasiertodetectpredatorsalthoughthismayreducetheirfeedingefficiencyasaruminantthegiraffefirstchewsitsfoodthenswallowsitforprocessingandthenvisiblypassesthehalfdigestedcuduptheneckandbackintothemouthtochewagainthegirafferequireslessfoodthanmanyotherherbivoresbecausethefoliageiteatshasmoreconcentratednutrientsandithasamoreefficientdigestivesystemtheanimalsfaecescomeintheformofsmallpelletswhenithasaccesstowateragiraffewillgonomorethanthreedayswithoutdrinkinggiraffeshaveagreateffectonthetreesthattheyfeedondelayingthegrowthofyoungtreesforsomeyearsandgivingwaistlinestotootalltreesfeedingisatitshighestduringthefirstandlasthoursofdaytimebetweenthesehoursgiraffesmostlystandandruminateruminationisthedominantactivityduringthenightwhenitismostlydonelyingdownsociallifegiraffesareusuallyfoundingroupsthatvaryinsizeandcompositionaccordingtoecologicalanthropogenictemporalandsocialfactorstraditionallythecompositionofthesegroupshadbeendescribedasopenandeverchangingforresearchpurposesagrouphasbeendefinedasacollectionofindividualsthatarelessthanakilometreapartandmovinginthesamegeneraldirectionmorerecentstudieshavefoundthatgiraffeshavelonglastingsocialgroupsorcliquesbasedonkinshipsexorotherfactorsandthesegroupsregularlyassociatewithothergroupsinlargercommunitiesorsubcommunitieswithinafissionfusionsocietyproximitytohumanscandisruptsocialarrangementsmasaigiraffesintanzaniahavedifferentsubpopulationswithoverlappingrangeseachofwhichdifferinreproductiveratesandcalfmortalitythenumberofgiraffesinagroupcanrangefromoneuptoindividualsgiraffegroupstendtobesexsegregatedalthoughmixedsexgroupsmadeofadultfemalesandyoungmalesalsooccurfemalegroupsmaybematrilineallyrelatedgenerallyfemalesaremoreselectivethanmalesinwhotheyassociatewithregardingindividualsofthesamesexparticularlystablegiraffegroupsarethosemadeofmothersandtheiryoungwhichcanlastweeksormonthsyoungmalesalsoformgroupsandwillengageinplayfightshoweverastheygetoldermalesbecomemoresolitarybutmayalsoassociateinpairsorwithfemalegroupsgiraffesarenotterritorialbuttheyhavehomerangesthatvaryaccordingtorainfallandproximitytohumansettlementsmalegiraffesoccasionallyroamfarfromareasthattheynormallyfrequentearlybiologistssuggestedgiraffesweremuteandunabletocreateenoughairflowtovibratetheirvocalfoldstothecontrarytheyhavebeenrecordedtocommunicateusingsnortssneezescoughssnoreshissesburstsmoansgruntsgrowlsandflutelikesoundsduringcourtshipmalesemitloudcoughsfemalescalltheiryoungbybellowingcalveswillemitbleatsmooingandmewingsoundssnortingandhissingisassociatedwithvigilanceduringnighttimegiraffesappeartohumtoeachotherabovetheinfrasoundrangethepurposeisuncleardominantmalesdisplaytoothermaleswithanerectpostureholdingthechinandheadupwhilewalkingstifflyanddisplayingtheirsidethelessdominantshowsubmissivenessbydroppingtheheadandearsloweringthechinandfleeingreproductionandparentalcarereproductioningiraffesisbroadlypolygamousafewoldermalesmatewiththefertilefemalesfemalescanreproducethroughouttheyearandexperienceoestruscyclingapproximatelyeverydaysfemalegiraffesinoestrousaredispersedoverspaceandtimesoreproductiveadultmalesadoptastrategyofroamingamongfemalegroupstoseekmatingopportunitieswithperiodichormoneinducedruttingbehaviourapproximatelyeverytwoweeksmalespreferyoungadultfemalesoverjuvenilesandolderadultsmalegiraffesassessfemalefertilitybytastingthefemalesurinetodetectoestrusinamultistepprocessknownastheflehmenresponseonceanoestrousfemaleisdetectedthemalewillattempttocourtherwhencourtingdominantmaleswillkeepsubordinateonesatbayacourtingmalemaylickafemalestaillayhisheadandneckonherbodyornudgeherwithhisossiconesduringcopulationthemalestandsonhishindlegswithhisheadheldupandhisfrontlegsrestingonthefemalessidesgiraffegestationlastsdaysafterwhichasinglecalfisnormallybornalthoughtwinsoccuronrareoccasionsthemothergivesbirthstandingupthecalfemergesheadandfrontlegsfirsthavingbrokenthroughthefetalmembranesandfallstothegroundseveringtheumbilicalcordanewborngiraffeismfttallwithinafewhoursofbirththecalfcanrunaroundandisalmostindistinguishablefromaoneweekoldhoweverforthefirstonetothreeweeksitspendsmostofitstimehidingitscoatpatternprovidingcamouflagetheossiconeswhichhavelainflatwhileitwasinthewombraiseupinafewdaysmotherswithcalveswillgatherinnurseryherdsmovingorbrowsingtogethermothersinsuchagroupmaysometimesleavetheircalveswithonefemalewhiletheyforageanddrinkelsewherethisisknownasacalvingpoolcalvesareatriskofpredationandamothergiraffewillstandoverthemandkickatanapproachingpredatorfemaleswatchingcalvingpoolswillonlyalerttheirownyoungiftheydetectadisturbancealthoughtheotherswilltakenoticeandfollowcalvesfirstruminateatfourtosixmonthsandstopnursingatsixtoeightmonthsyoungmaynotreachindependenceuntiltheyaremonthsoldfemalesbecomesexuallymaturewhentheyarefouryearsoldwhilemalesbecomematureatfourorfiveyearsspermatogenesisinmalegiraffesbeginsatthreetofouryearsofagemalesmustwaituntiltheyareatleastsevenyearsoldtogaintheopportunitytomateneckingmalegiraffesusetheirnecksasweaponsincombatabehaviourknownasneckingneckingisusedtoestablishdominanceandmalesthatwinneckingboutshavegreaterreproductivesuccessthisbehaviouroccursatloworhighintensityinlowintensityneckingthecombatantsrubandleanoneachotherthemalethatcankeepitselfmoreuprightwinstheboutinhighintensityneckingthecombatantswillspreadtheirfrontlegsandswingtheirnecksateachotherattemptingtolandblowswiththeirossiconesthecontestantswilltrytododgeeachothersblowsandthenpreparetocounterthepowerofablowdependsontheweightoftheskullandthearcoftheswinganeckingduelcanlastmorethanhalfanhourdependingonhowwellmatchedthecombatantsarealthoughmostfightsdonotleadtoseriousinjurytherehavebeenrecordsofbrokenjawsbrokennecksandevendeathsafteraduelitiscommonfortwomalegiraffestocaressandcourteachothersuchinteractionsbetweenmaleshavebeenfoundtobemorefrequentthanheterosexualcouplinginonestudyuptopercentofobservedmountingincidentstookplacebetweenmalestheproportionofsamesexactivitiesvariedfromtopercentonlyonepercentofsamesexmountingincidentsoccurredbetweenfemalesmortalityandhealthgiraffeshavehighadultsurvivalprobabilityandanunusuallylonglifespancomparedtootherruminantsuptoyearsbecauseoftheirsizeeyesightandpowerfulkicksadultgiraffesareusuallynotsubjecttopredationalthoughlionsmayregularlypreyonindividualsuptokglbgiraffesarethemostcommonfoodsourceforthebigcatsinkrugernationalparkcomprisingnearlyathirdofthemeatconsumedalthoughonlyasmallportionofthegiraffeswereprobablykilledbypredatorsasamajorityoftheconsumedgiraffesappearedtobescavengedadultfemalesurvivalissignificantlycorrelatedwiththenumberofsocialassociationscalvesaremuchmorevulnerablethanadultsandarealsopreyedonbyleopardscheetahsnilecrocodilesspottedhyenasandwilddogsaquartertoahalfofgiraffecalvesreachadulthoodcalfsurvivalvariesaccordingtotheseasonofbirthwithcalvesbornduringthedryseasonhavinghighersurvivalratesthelocalseasonalpresenceoflargeherdsofmigratorywildebeestsandzebrasreducespredationpressureongiraffecalvesandincreasestheirsurvivalprobabilityinturnithasbeensuggestedthatotherungulatesmaybenefitfromassociatingwithgiraffesastheirheightallowsthemtospotpredatorsfromfurtherawayzebraswerefoundtoaccesspredationriskbywatchinggiraffesandspendlesstimelookingaroundwhengiraffesarepresentsomeparasitesfeedongiraffestheyareoftenhostsforticksespeciallyintheareaaroundthegenitalswhichhavethinnerskinthanotherareastickspeciesthatcommonlyfeedongiraffesarethoseofgenerahyalommaamblyommaandrhipicephalusgiraffesmayrelyonredbilledandyellowbilledoxpeckerstocleanthemofticksandalertthemtodangergiraffeshostnumerousspeciesofinternalparasitesandaresusceptibletovariousdiseasestheywerevictimsofthenoweradicatedviralillnessrinderpestgiraffescanalsosufferfromaskindisorderwhichcomesintheformofwrinkleslesionsorrawfissuresasmuchasofgiraffeshavesymptomsofthediseaseinruahanationalparkbutitdidnotcausemortalityintarangireandislessprevalentinareaswithfertilesoilsrelationshipwithhumansculturalsignificancewithitslankybuildandspottedcoatthegiraffehasbeenasourceoffascinationthroughouthumanhistoryanditsimageiswidespreadincultureithasrepresentedflexibilityfarsightednessfemininityfragilitypassivitygracebeautyandthecontinentofafricaitselfgiraffesweredepictedinartthroughouttheafricancontinentincludingthatofthekiffiansegyptiansandkushitesthekiffianswereresponsibleforalifesizerockengravingoftwogiraffesdatedyearsagothathasbeencalledtheworldslargestrockartpetroglyphhowthegiraffegotitsheighthasbeenthesubjectofvariousafricanfolktalesthetugenpeopleofmodernkenyausedthegiraffetodepicttheirgodmdatheegyptiansgavethegiraffeitsownhieroglyphsrinoldegyptianandmmyinlaterperiodsgiraffeshaveapresenceinmodernwesternculturesalvadordaldepictedthemwithburningmanesinsomeofhissurrealistpaintingsdaliconsideredthegiraffetobeamasculinesymbolandaflaminggiraffewasmeanttobeamasculinecosmicapocalypticmonsterseveralchildrensbooksfeaturethegiraffeincludingdavidaufersthegiraffewhowasafraidofheightsgilesandreaesgiraffescantdanceandroalddahlsthegiraffeandthepellyandmegiraffeshaveappearedinanimatedfilmsasminorcharactersindisneysthelionkinganddumboandinmoreprominentrolesinthewildandthemadagascarfilmssophiethegiraffehasbeenapopularteethersinceanotherfamousfictionalgiraffeisthetoysrusmascotgeoffreythegiraffethegiraffehasalsobeenusedforsomescientificexperimentsanddiscoveriesscientistshaveusedthepropertiesofgiraffeskinasamodelforastronautandfighterpilotsuitsbecausethepeopleintheseprofessionsareindangerofpassingoutifbloodrushestotheirlegscomputerscientistshavemodeledthecoatpatternsofseveralsubspeciesusingreactiondiffusionmechanismstheconstellationofcamelopardalisintroducedintheseventeenthcenturydepictsagiraffethetswanapeopleofbotswanatraditionallyseetheconstellationcruxastwogiraffesacruxandmimosaformingamaleandgacruxanddeltacrucisformingthefemalecaptivitytheegyptianswereamongtheearliestpeopletokeepgiraffesincaptivityshippedthemaroundthemediterraneanthegiraffewasamongthemanyanimalscollectedanddisplayedbytheromansthefirstoneinromewasbroughtinbyjuliuscaesarinbcwiththefallofthewesternromanempirethehousingofgiraffesineuropedeclinedduringthemiddleagesgiraffeswereknowntoeuropeansthroughcontactwiththearabswhoreveredthegiraffeforitspeculiarappearanceindividualcaptivegiraffesweregivencelebritystatusthroughouthistoryinagiraffefrommalindiwastakentochinabyexplorerzhengheandplacedinamingdynastyzootheanimalwasasourceoffascinationforthechinesepeoplewhoassociateditwiththemythicalqilinthemedicigiraffewasagiraffepresentedtolorenzodemediciinitcausedagreatstironitsarrivalinflorencezarafaanotherfamousgiraffewasbroughtfromegypttoparisintheearlythcenturyasagiftforcharlesxoffranceasensationthegiraffewasthesubjectofnumerousmemorabiliaorgiraffanaliagiraffeshavebecomepopularattractionsinmodernzoosthoughkeepingthemhealthyisdifficultastheyrequirevastareasandneedtoeatlargeamountsofbrowsecaptivegiraffesinnorthamericaandeuropeappeartohaveahighermortalityratethaninthewildthemostcommoncausesbeingpoorhusbandrynutritionandmanagementgiraffesinzoosdisplaystereotypicalbehavioursparticularlythelickingofinanimateobjectsandpacingzookeepersmayoffervariousactivitiestostimulategiraffesincludingtrainingthemtotakefoodfromvisitorsstablesforgiraffesarebuiltparticularlyhightoaccommodatetheirheightexploitationgiraffeswereprobablycommontargetsforhuntersthroughoutafricadifferentpartsoftheirbodieswereusedfordifferentpurposestheirmeatwasusedforfoodthetailhairsservedasflyswattersbraceletsnecklacesandthreadsshieldssandalsanddrumsweremadeusingtheskinandthestringsofmusicalinstrumentswerefromthetendonsinbugandathesmokeofburninggiraffeskinwastraditionallyusedtotreatnosebleedsthehumrpeopleofkordofanconsumethedrinkummnyolokhwhichispreparedfromtheliverandbonemarrowofgiraffesrichardrudgleyhypothesisedthatummnyolokhmightcontaindmtthedrinkissaidtocausehallucinationsofgiraffesbelievedtobethegiraffesghostsbythehumrconservationstatusingiraffeswereassessedasvulnerablefromaconservationperspectivebytheiucninitwasestimatedthereweregiraffesinthewildthisdeclinedtooverinestimatesasofindicatethereareapproximatelymembersofgiraffainthewildthemasaiandreticulatedsubspeciesareendangeredandtherothschildsubspeciesisnearthreatenedthenubiansubspeciesiscriticallyendangeredtheprimarycausesforgiraffepopulationdeclinesarehabitatlossanddirectkillingforbushmeatmarketsgiraffeshavebeenextirpatedfrommuchoftheirhistoricrangeincludingeritreaguineamauritaniaandsenegaltheymayalsohavedisappearedfromangolamaliandnigeriabuthavebeenintroducedtorwandaandeswatiniasofthereweremorethanincaptivityatspeciesregisteredzooshabitatdestructionhashurtthegiraffeinthesaheltheneedforfirewoodandgrazingroomforlivestockhasledtodeforestationnormallygiraffescancoexistwithlivestocksincetheyavoiddirectcompetitionbyfeedingabovetheminseveredroughtsinnorthernkenyaledtoincreasedtensionsoverlandandthekillingofwildlifebyherderswithgiraffepopulationsbeingparticularlyhitprotectedareaslikenationalparksprovideimportanthabitatandantipoachingprotectiontogiraffepopulationscommunitybasedconservationeffortsoutsidenationalparksarealsoeffectiveatprotectinggiraffesandtheirhabitatsprivategamereserveshavecontributedtothepreservationofgiraffepopulationsineasternandsouthernafricathegiraffeisaprotectedspeciesinmostofitsrangeitisthenationalanimaloftanzaniaandisprotectedbylawandunauthorisedkillingcanresultinimprisonmenttheunbackedconventionofmigratoryspeciesselectedgiraffesforprotectioniningiraffeswerelistedunderappendixiioftheconventiononinternationaltradeinendangeredspeciesciteswhichmeansinternationaltradeincludinginpartsderivativesisregulatedtranslocationsaresometimesusedtoaugmentorreestablishdiminishedorextirpatedpopulationsbuttheseactivitiesareriskyanddifficulttoundertakeusingthebestpracticesofextensivepreandposttranslocationstudiesandensuringaviablefoundingpopulationaerialsurveyisthemostcommonmethodofmonitoringgiraffepopulationtrendsinthevastroadlesstractsofafricanlandscapesbutaerialmethodsareknowntoundercountgiraffesgroundbasedsurveymethodsaremoreaccurateandcanbeusedinconjunctionwithaerialsurveystomakeaccurateestimatesofpopulationsizesandtrendsseealsofaunaofafricagiraffecentregiraffemanorhotelinnairobiwithgiraffesreferencesexternallinksgiraffeconservationfoundation\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Instead of directly using characters as the features, to understand a text better, we may consider group of tokens i.e. ngrams as features.\n",
        "\n",
        "For this example let us consider that each character is one word, and let us see how n-grams work."
      ],
      "metadata": {
        "id": "XAJNs7PD_cVM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "## nltk library provides many tools for text processing, please explore them."
      ],
      "metadata": {
        "id": "E1pXE4sK_0kl"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jXFTWwd0rk63"
      },
      "source": [
        "Now let us calculate the frequency of the character n-grams. N-grams are groups of characters of size n. A unigram is a single character and a bigram is a group of two characters and so on.\n",
        "\n",
        "Let us count the frequency of each character in a text and plot it in a histogram."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g3Lz3YUjN0L5"
      },
      "source": [
        "## Dont worry if you do not understand these functions right away, you can revisit them and follow step-by-step.\n",
        "\n",
        "# convert a tuple of characters to a string\n",
        "def tuple2string(tup):\n",
        "  st = ''\n",
        "  for ii in tup:\n",
        "    st = st + ii\n",
        "  return st\n",
        "\n",
        "# convert a tuple of tuples to a list of strings\n",
        "def key2string(keys):\n",
        "  return [tuple2string(i) for i in keys]\n",
        "\n",
        "# plot the histogram\n",
        "def plothistogram(ngram):\n",
        "  keys = key2string(ngram.keys())\n",
        "  values = list(ngram.values())\n",
        "\n",
        "  # sort the keys in alphabetic order\n",
        "  combined = zip(keys, values) ## keys i.e. characters on x axis and their count in the given doc as values.\n",
        "  zipped_sorted = sorted(combined, key=lambda x: x[0]) ## sorting based on keys, to get a to z order.\n",
        "  keys, values = map(list, zip(*zipped_sorted))\n",
        "  plt.bar(keys, values)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zHD62zbZcwAB"
      },
      "source": [
        "Let us compare the histograms of English pages and French pages. Can you spot a difference?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LKcGRgH6b0KP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 551
        },
        "outputId": "a61a6f80-18ae-4e09-9de1-708537055aeb"
      },
      "source": [
        "## we passed ngrams 'n' as 1 to get unigrams. Unigram is nothing but single token (in this case character).\n",
        "## ngrams imported from nltk, it returns ngrams from given string. Counter returns dictionary with keys as elements and counts as values.\n",
        "unigram_eng1 = Counter(ngrams(eng1,1)) ##just to get count of each element.\n",
        "plothistogram(unigram_eng1)\n",
        "plt.title('English 1')\n",
        "plt.show()\n",
        "unigram_eng2 = Counter(ngrams(eng2,1))\n",
        "plothistogram(unigram_eng2)\n",
        "plt.title('English 2')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAELCAYAAADURYGZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAebUlEQVR4nO3de1BTZ/4G8IeEAl6AmIgarVtvK8W6ipqKi+tsi12xDgreFsuqW606dr1gra5ULeCNKaDuWJWl1q4zdTtesAWEVnHVemnXdrX1xlKtwyrVglyCqCgXSc7vD8f8qpLLibnh+3xmnJG83/Pme5IDT3JOco6XJEkSiIhIWAp3N0BERO7FICAiEhyDgIhIcAwCIiLBMQiIiATHICAiEhyDgOgJXLt2DcHBwWhqagIAzJgxA9nZ2VaXCw4ORklJibPbI7KJt7sbIHKFiIgIVFVVQalUmm4bO3YsEhMTHXo/W7dudeh8AJCdnY3t27fjypUraNu2LaKiorBw4UJ4e/PXlxyDWxIJIzMzE+Hh4e5uQ7a6ujosXboU/fr1w40bN/Dmm2/iH//4B2bNmuXu1ugpwV1DJLzPPvsMr732GlJTU/Hiiy8iIiICR48eNY1fvXoVf/rTnzBgwAC8/vrrWLFiBRYtWtTsXFOmTEFWVhYAoKSkBJMnT8agQYMQFhaGBQsWPFT773//GyNGjIBOp8OKFStg7kv+cXFx0Ol08PHxQceOHTF69Gh8//33Dlp7IgYBEQDg3Llz6N69O7755hvMmDEDy5YtM/1hXrRoEfr164dvv/0Wc+fORW5urk1zbtiwAUOHDsXJkydx7NgxTJ48+aHxI0eOYM+ePdi7dy/27duH48eP2zTvyZMn0atXL3krSGQBg4CEMWfOHOh0OtO/3bt3m8Y6d+6MP/7xj1AqlRg7diwqKytRVVWF0tJSnD9/HvPnz4ePjw90Oh0iIiJsuj9vb2+UlpaioqICvr6+0Ol0D43PnDkTAQEB6Ny5M8LCwnDhwgWrc+7ZsweFhYWYPn26vJUnsoDHCEgYmzdvNnuMoH379qb/t2rVCgBw9+5d3LhxA4GBgabbAECr1aKsrMzq/S1evBgbNmzAhAkTEBgYiGnTpmHChAmm8aCgoIfu886dOxbnO3jwINavX49t27ZBrVZbvX8iWzEIiCwICgrCzZs3UVdXZwoDW0LgwbKrV68GAJw6dQrTpk3Diy++iOeee052H8eOHcPy5cuxZcsWBAcHy16eyBLuGiKyoEuXLujbty82btyIxsZGnD59Gl9++aVNy+7btw/Xr18HAAQGBsLLywsKhfxfuRMnTmDx4sXYuHEj+vXrJ3t5Imv4joCEMXv27Ie+RxAeHo7NmzdbXW7t2rVISEhAWFgY+vXrh1GjRsFgMFhd7vz580hJSUFtbS00Gg2WLVuGrl27yu47IyMDt2/ffujjooMGDXLKdxZITF68MA2RPAsWLECPHj0wf/58d7dC5BDcNURkxblz5/DTTz/BaDTi2LFjOHToEF555RV3t0XkMNw1RGRFVVUV5s2bh5qaGnTq1AnJycno06ePu9sichjuGiIiEhx3DRERCY5BQEQkOAYBEZHgWuzB4hs37sBodMzhDY2mLfT6WofXtvR6T+rF2fWe1Iuz6z2pF2fXe1Ivrqi3RKHwQrt2bZoda7FBYDRKDguCB/M5o7al13tSL86u96RenF3vSb04u96TenFFvT24a4iISHAMAiIiwTEIiIgExyAgIhIcg4CISHAMAiIiwTEIiIgE12K/RyAi/4BW8PN9/CkLCvJ/6Of6hibcvlXnqraIqIVjELQgfr7eGP12rtW6vHXRuO2Cfojo6cBdQ0REgmMQEBEJjkFARCQ4BgERkeAYBEREgmMQEBEJjkFARCQ4BgERkeAYBEREgmMQEBEJjkFARCQ4m4KgoaEBSUlJGDFiBEaPHo13330XAHD58mXExsYiMjISsbGxuHLlimkZe8eIiMi1bAqC9PR0+Pr6oqCgAHl5eYiPjwcAJCUlIS4uDgUFBYiLi0NiYqJpGXvHiIjItawGwZ07d5CTk4P4+Hh4eXkBANq3bw+9Xo+ioiJERUUBAKKiolBUVITq6mq7x4iIyPWsnob66tWrUKlU2LRpE7799lu0adMG8fHx8PPzQ8eOHaFUKgEASqUSHTp0QFlZGSRJsmtMrVY7cVWJiKg5VoPAYDDg6tWr6NOnD5YsWYKzZ89i9uzZ2LBhgyv6M0ujaevQ+R69uIujal1RL3eOlryuzqz3pF6cXe9JvTi73pN6cUW9PawGgVarhbe3t2lXTv/+/dGuXTv4+fmhvLwcBoMBSqUSBoMBFRUV0Gq1kCTJrjE59PpaGI2SfWv9iKAgf1RW2nYpFzm1jq6Xs0FYmqMlrKur6z2pF2fXe1Ivzq73pF5cUW+JQuFl9gW01WMEarUaYWFh+PrrrwHc/8SPXq9Ht27dEBISgvz8fABAfn4+QkJCoFarodFo7BojIiLXs+lSlStWrMDSpUuRmpoKb29vpKWlISAgAMnJyUhISEBGRgYCAgKQmppqWsbeMSIici2bgqBr167Yvn37Y7f37NkTWVlZzS5j7xgREbkWv1lMRCQ4BgERkeAYBEREgmMQEBEJjkFARCQ4BgERkeAYBEREgmMQEBEJjkFARCQ4BgERkeAYBEREgmMQEBEJjkFARCQ4BgERkeAYBEREgmMQEBEJjkFARCQ4BgERkeAYBEREgmMQEBEJjkFARCQ4BgERkeAYBEREgvO2pSgiIgI+Pj7w9fUFACxatAjDhg3DmTNnkJiYiIaGBnTp0gXp6enQaDQAYPcYERG5ls3vCN5//33k5uYiNzcXw4YNg9FoxOLFi5GYmIiCggLodDqsXbsWAOweIyIi17N711BhYSF8fX2h0+kAAJMmTcL+/fufaIyIiFzPpl1DwP3dQZIkYdCgQVi4cCHKysrQuXNn07harYbRaERNTY3dYyqVykGrRUREtrIpCD755BNotVo0NjZizZo1WLlyJf7whz84uzeLNJq2Dp0vKMjfKbWuqJc7R0teV2fWe1Ivzq73pF6cXe9Jvbii3h42BYFWqwUA+Pj4IC4uDm+++SamTp2K0tJSU011dTUUCgVUKhW0Wq1dY3Lo9bUwGiVZy5gTFOSPysrbDq91dL2cDcLSHC1hXV1d70m9OLvek3pxdr0n9eKKeksUCi+zL6CtHiO4e/cubt++34gkSfjiiy8QEhKCvn37or6+HqdOnQIA7Ny5EyNHjgQAu8eIiMj1rL4j0Ov1mDdvHgwGA4xGI3r27ImkpCQoFAqkpaUhKSnpoY+BArB7zBX8A1rBz/fx1f7lq+36hibcvlXnsp6IiNzJahB07doVOTk5zY4NHDgQeXl5Dh1zNj9fb4x+O9diTd66aDjmzRgRkefjN4uJiATHICAiEhyDgIhIcAwCIiLBMQiIiATHICAiEhyDgIhIcAwCIiLBMQiIiARn82moiYieFE/x4pkYBETkMjzFi2firiEiIsExCIiIBMcgICISHIOAiEhwDAIiIsExCIiIBMcgICISHIOAiEhwDAIiIsExCIiIBMcgICISHIOAiEhwsoJg06ZNCA4Oxo8//ggAOHPmDMaMGYPIyEhMnz4der3eVGvvGBERuZbNQfDf//4XZ86cQZcuXQAARqMRixcvRmJiIgoKCqDT6bB27donGiMiItezKQgaGxuxcuVKJCcnm24rLCyEr68vdDodAGDSpEnYv3//E40REZHr2XQ9gg0bNmDMmDF49tlnTbeVlZWhc+fOpp/VajWMRiNqamrsHlOpVDY3rtG0tbnWHr+8UIacMXfUy51Dzvyetq7OrHfU3I33DPB5Rmm13lydo/tx9dz21MtdviWvqzv+HlhjNQhOnz6NwsJCLFq0yOnNyKHX18JolGQvZ+uDWlnZ/KUxgoL8zY45u17OBuGI/t25rq6ud/TzZO3iK8D9C7C4YztrCduwpftrKevqjnpLFAovsy+grQbByZMnUVxcjOHDhwMArl+/jjfeeANTpkxBaWmpqa66uhoKhQIqlQpardauMSIicj2rxwhmzZqFr776CocPH8bhw4fRqVMnfPTRR5gxYwbq6+tx6tQpAMDOnTsxcuRIAEDfvn3tGiMiItez+5rFCoUCaWlpSEpKQkNDA7p06YL09PQnGiMiIteTHQSHDx82/X/gwIHIy8trts7eMSIici1+s5iISHAMAiIiwTEIiIgExyAgIhIcg4CISHB2f3yUSA7/gFbw8318c3v0m6b1DU24favOVW3RE+Lz+nRgEJBL+Pl623zaBcd8oZ5cgc/r04G7hoiIBMcgICISHIOAiEhwDAIiIsExCIiIBMcgICISHIOAiEhw/B4BkZvxS1nkbgwCIjfjl7LI3bhriIhIcAwCIiLBMQiIiATHICAiEhyDgIhIcPzUEBGZ8KOsYrIpCP7yl7/g2rVrUCgUaN26Nd59912EhITg8uXLSEhIQE1NDVQqFVJTU9GtWzcAsHuMiNyHH2UVk027hlJTU7F3717k5ORg+vTpWLp0KQAgKSkJcXFxKCgoQFxcHBITE03L2DtGRESuZVMQ+Pv//9vC2tpaeHl5Qa/Xo6ioCFFRUQCAqKgoFBUVobq62u4xIiJyPZuPESxbtgxff/01JEnC1q1bUVZWho4dO0KpVAIAlEolOnTogLKyMkiSZNeYWq12wioSEZElNgfBmjVrAAA5OTlIS0tDfHy805qyhUbT1qnzP3pwzNYxd9TLnUPO/C25d7n1nraucuudua6OmMOR/XnS8+pp9faQ/amhmJgYJCYmolOnTigvL4fBYIBSqYTBYEBFRQW0Wi0kSbJrTA69vhZGoyS3fZsf1MrK5g+FBQX5mx1zdr2cDcIR/bfk3uXWu3NdPel5dXbvT/r7B7jveW0J9ZYoFF5mX0BbPUZw584dlJWVmX4+fPgwAgMDodFoEBISgvz8fABAfn4+QkJCoFar7R4jIiLXs/qOoK6uDvHx8airq4NCoUBgYCAyMzPh5eWF5ORkJCQkICMjAwEBAUhNTTUtZ+8YERG5ltUgaN++PXbv3t3sWM+ePZGVleXQMSIici2eYoKISHAMAiIiwTEIiIgEx5POkV14cjKipweDgOzCk5MRPT24a4iISHAMAiIiwTEIiIgExyAgIhIcDxaTkJr71BM/8USiYhCQkGz51BM/8USi4K4hIiLBMQiIiATHICAiEhyDgIhIcAwCIiLBMQiIiATHICAiEhyDgIhIcAwCIiLBMQiIiATHICAiEhyDgIhIcFaD4MaNG5g5cyYiIyMxevRozJ07F9XV1QCAM2fOYMyYMYiMjMT06dOh1+tNy9k7RkRErmU1CLy8vDBjxgwUFBQgLy8PXbt2xdq1a2E0GrF48WIkJiaioKAAOp0Oa9euBQC7x4iIyPWsBoFKpUJYWJjp59DQUJSWlqKwsBC+vr7Q6XQAgEmTJmH//v0AYPcYERG5nqxjBEajETt27EBERATKysrQuXNn05harYbRaERNTY3dY0RE5HqyLkyzatUqtG7dGpMnT8a//vUvZ/VkE42mrVPnf/RqVbaOuaNe7hxy5nd2L3LrXf1YOrIXR8zxtD6vcmudua4tvd4eNgdBamoqSkpKkJmZCYVCAa1Wi9LSUtN4dXU1FAoFVCqV3WNy6PW1MBolWcsAtj+olZXNX5sqKMjf7Jiz6+VsEI7o35G9uLp3a/XO3A48/bFxZ+9P+rgDjlvXp7HeEoXCy+wLaJt2Da1fvx6FhYXYvHkzfHx8AAB9+/ZFfX09Tp06BQDYuXMnRo4c+URjRETkelbfEVy6dAkffPABunXrhkmTJgEAnn32WWzevBlpaWlISkpCQ0MDunTpgvT0dACAQqGwa0w0zV1AHeBF1InItawGwa9//WtcvHix2bGBAwciLy/PoWMiseUC6gAvok5EzsVvFhMRCY5BQEQkOAYBEZHgGARERIJjEBARCY5BQEQkOAYBEZHgGARERIJjEBARCY5BQEQkOFmnoSbrmjt/EM8dRESejEHgYLacP4jnDiIiT8IgICKPZcsZevkO+8kxCIjIY/EdtmvwYDERkeAYBEREguOuISIrPO1KctxvTo7GICCywtOuJMf95uRo3DVERCQ4BgERkeAYBEREgmMQEBEJjkFARCQ4q0GQmpqKiIgIBAcH48cffzTdfvnyZcTGxiIyMhKxsbG4cuXKE48REZHrWQ2C4cOH45NPPkGXLl0euj0pKQlxcXEoKChAXFwcEhMTn3iMiIhcz2oQ6HQ6aLXah27T6/UoKipCVFQUACAqKgpFRUWorq62e4wczz+gFYKC/B/6B+Chn/0DWrm5SyJyN7u+UFZWVoaOHTtCqVQCAJRKJTp06ICysjJIkmTXmFqtdtAq0QP84hER2aLFfrNYo2nr1PkfPX2ArWOOmN/V9Q9qG+8Z4POM0uI8zdU4shdr9c5+3Fx9f654Xh1xv46Yw1G9y633pOfEFfX2sCsItFotysvLYTAYoFQqYTAYUFFRAa1WC0mS7BqTS6+vhdEoyV7O1ge1srL518lBQf5mx+TOL+cJdmb9g/UJCvK36R2EK3pvjrXHXk59S3ye5Nbb8zh6Wu/O/n192uotUSi8zL6AtuvjoxqNBiEhIcjPzwcA5OfnIyQkBGq12u4xIiJyD6vvCFavXo0DBw6gqqoK06ZNg0qlwueff47k5GQkJCQgIyMDAQEBSE1NNS1j7xgREbme1SBYvnw5li9f/tjtPXv2RFZWVrPL2DtGRESux28WExEJjkFARCS4FvvxUSIiT9aSriTHILCiuSfTXZcoJKKWoyV9oZNBYEVLejKJyHaedi1qd2IQEJGQPO1a1O7Eg8VERIJjEBARCY67hojoqcEPd9iHQUBETw1+uMM+3DVERCQ4BgERkeAYBEREgmMQEBEJjgeL6anQks7rQuRpGAT0VOCnRYjsx11DRESCYxAQEQmOQUBEJDgGARGR4BgERESCYxAQEQmOHx8lIrLB03xFM7cFweXLl5GQkICamhqoVCqkpqaiW7du7mqHiMiip/mKZm7bNZSUlIS4uDgUFBQgLi4OiYmJ7mqFiEhobnlHoNfrUVRUhG3btgEAoqKisGrVKlRXV0OtVts0h0LhZff9d2jXStb8zqy3pdbZ9Z7Ye9u2fvC14W14Q0MTamvrbZ7fE9fVWfUPapt7LJ/0cZTbi9x6EX//bNnmf/k8yWXpb6aXJEmSXbM+gcLCQixZsgSff/656bZRo0YhPT0dL7zwgqvbISISGj81REQkOLcEgVarRXl5OQwGAwDAYDCgoqICWq3WHe0QEQnNLUGg0WgQEhKC/Px8AEB+fj5CQkJsPj5ARESO45ZjBABQXFyMhIQE3Lp1CwEBAUhNTUWPHj3c0QoRkdDcFgREROQZeLCYiEhwDAIiIsExCIiIBMcgICISHIPARsHBwbhz506Lvr+DBw/i1VdfRUxMDP73v/85bF57eo2OjkZ9vbyvytuyjL2Pm6ufX7pv48aNaGxsdHcbwmMQCGTnzp2YP38+cnJy3P5R3dzcXPj5+Tl9GXKcpqYmh8+5adMm3Lt3z+HzkjxCB8Hbb7+NcePGYfTo0ZgzZw5u3rxpsf6jjz5CdHQ0IiMjUVBQYHX+06dP47XXXsOYMWMwZswYfPXVV2ZrDxw4gJEjRyI6OhqbN2+2OvfZs2cxZcoUjBs3DuPGjcORI0cs1qekpOC7777D2rVrMWXKFKvzFxQUYOTIkYiJiUFmZqbVV8zbt2/H+PHjMXz4cJseG3tegctZxmg0IiUlBQsXLnTIK87g4GD8/e9/N63jiRMnsG7dOsTExCAqKgrFxcXNLpOZmSnrcTl27BhiYmIwevRo/PnPf0ZJSYnFnt5//31Z2+Sj25m1xzQ4OBgbN27E+PHjsWnTJotz19XVYf78+Rg1ahTGjBmD+Ph4i/UrVqwAAEyaNAnR0dG4deuW2dpr164hLCzM7M+/lJGRgZSUFNPPN27cQFhYGO7evftY7c6dO019nDt3DsHBwTh37hwAIDk5Gbt27XpsmeLiYvz+97/Hzz//DOB+mL311ltme9+6davpPgCgqqoK4eHhqKtr/poFR48eRXR0tOlf3759cfDgQbPzO4QkML1eb/r/+vXrpfT0dLO1vXv3ljZu3ChJkiQVFxdLgwcPlqqqqszW37hxQwoPD5e+++47SZIkqampSaqpqWm2trKyUho8eLBUXFwsSZIkbdmyRerdu7dUW1vbbP3Nmzel6Ohoqby8XJIkSSovL5eGDRsm3bx508LaStLkyZOlw4cPW6z5ZT+XL1+WJEmStm3bZrGf3r17S9u3b5ckSZJOnTol/e53v7N6H5bme5JlevfuLen1emnevHnSe++9JxmNRofM3bt3b+mf//ynJEmS9MUXX0ihoaGmx3LLli3S22+/3ewych6XqqoqKSwsTLp06ZIkSZK0e/duacKECRZ7krNNyt3OHtzHBx98YLHvBw4cOCBNnz7d9LO57f3R+W3ZDq5evSoNHjzY7M+/9PPPP0tDhw6V7t27J0mSJH388cdSQkJCs7VXrlyRIiMjJUmSpMzMTCk2Nta0viNGjJBKSkqaXS47O1uaOHGidPz4cWnEiBHS7du3zfb+4G/Bg/XctGmTtGbNGitrfN+uXbuk2NhYqb6+3qZ6ewn9jiA3N9f0jiA/Px8//PCDxfqJEycCAHr06IE+ffrgzJkzZmvPnDmDnj17YuDAgQAApVKJwMDAZmvPnj2LPn36mHbXxMbGWuzj9OnTuHbtGmbOnIno6GjMnDkTXl5eFl89yvGgnwcXCho/frzVZUaNGgUACA0NRUVFBRoaGhzSiz1mzJiB/v37Y8mSJfDysv905Y969dVXAcB0htyXX34ZANC3b1/89NNPzS4j53E5e/Ysnn/+efTq1QvA/cf9hx9+QG1trdll5GyTcrezB8aOHWtT3fPPP4/i4mKsWLEC+/btg4+Pj03LOVrnzp3Rq1cvHD16FACQnZ2NcePGNVv73HPPoaGhAdevX8eJEyfw1ltv4cSJEygrK8O9e/fwq1/9qtnlYmJi0KNHD8yZMwfr1q1D27ZtzfajUqkQERGB3NxcNDU1ISsrC3FxcVbX4/jx49i2bRsyMjLg6+trw5rbT9ggOHXqFHbs2IGtW7ciLy8PCxYsaDEHrSRJQnBwMHJzc03/jh49it/85jdu6+nBhqpUKgE4Z3+yrcLCwnD8+HGzb73t9WAdFQrFQ3/kFAqF2fX1pMfFXq1bt7aprmvXrsjPz8fQoUNx4sQJREdHO+wFgbe3N6RfnATB2rxjx45FTk4OLl68iNu3b0On05mtHTJkCL788kvo9XqEhYWhsrISR44cMbvrCQAaGxtx6dIl+Pv7Q6/XW+1/8uTJ2LFjBw4dOoSePXtavRrjhQsXkJSUhIyMDJecg03YILh16xbatm0LlUqFxsZGfPrpp1aXeVBz5coVFBUVITQ01GxtaGgoiouLcfr0aQD3z7Bq7hhEaGgoioqKcOXKFQBAVlaWxT4GDBiAkpISfPPNN6bbzp0799AvypPo378/ioqKTK9ys7OzHTKvq8ydOxfh4eF44403LL6a9jShoaG4cOGC6XhDdnY2+vTpY/HVptxtUs52Jtf169ehVCrxyiuv4J133kF1dTVqamosLtOmTRubnqP27dvj3r17pne9D05Yac6IESNw8uRJbNu2DWPHjrX4znDIkCH48MMPMWDAAADAwIED8eGHH+K3v/2t2WXS0tLwwgsvYNu2bUhKSsL169ct9hMcHAyVSoWUlBSr7wbKy8sxb948pKeno3v37hZrHUXYi9cPGzYMe/fuRWRkJNq1awedTofz589bXMZgMCAmJgZ1dXVYuXIlNBqN2VqVSoWNGzfivffew927d6FQKLBkyRKEh4c/VqvRaLBq1SrMnj0bfn5+GDFihMU+AgMDkZGRgfT0dKSkpODevXvo2rUrMjMzHbIrpH379khOTsbMmTPRqlUrvPTSS3jmmWfQqpVtV2dyJlvXb9asWfDz88Prr7+OrVu3QqVSObmzJ6dWq5GWloZFixahqakJarUa6enpFpeRs03K3c7kunjxItatWwfg/sH6WbNmoWPHjhaXmT59OqZOnQo/Pz9s374dAQEBzdZ5e3tj2bJlmDZtGtRqNV566SWL87Zq1QrDhw/HZ599hkOHDlmsHTJkCP7617+a/vAPGTIEu3btwpAhQ5qtP3jwIP7zn/8gKysLvr6+mDNnDhYuXIiPP/4Y3t7m/6ROnDgRf/vb30y7FM3JyspCdXU1Vq5cabrtnXfeMduPI/Ckc9Ss2tpa0yvRTz/9FHv27MGOHTvc1o9er8fLL7+Ms2fPOnS/f0sWHByM77//Hm3atHHrHGSbZcuWoXv37pgxY4a7W3mMsO8IyLLt27dj//79MBgMCAwMxOrVq93WS1FREebNm4c5c+YwBKjFKS8vx9SpUxEUFITly5e7u51m8R0BEZHghD1YTERE9zEIiIgExyAgIhIcg4CISHAMAiIiwTEIiIgE939AdR/aUIrdyQAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fDM_UhCL2QLt",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 551
        },
        "outputId": "ba2d380c-139d-4fc2-919e-ccbcb412ade2"
      },
      "source": [
        "unigram_fr1 = Counter(ngrams(fr1,1))\n",
        "plothistogram(unigram_eng1)\n",
        "plt.title('French 1')\n",
        "plt.show()\n",
        "unigram_fr2 = Counter(ngrams(fr2,1))\n",
        "plothistogram(unigram_fr2)\n",
        "plt.title('French 2')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## A good feature is one that helps in easy prediction and classification.\n",
        "## for ex : if you wish to differentiate between grapes and apples, size can be one of the useful features."
      ],
      "metadata": {
        "id": "VUEys9KoA0L0"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kxgrdZLKdkAB"
      },
      "source": [
        "We can see that the unigrams for French and English are very similar. So this is not a good feature if we want to distinguish between English and French. Let us look at bigrams."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OmRCxItx2T9W",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "3fe2b937-d361-4f45-c7a6-fe53b3ab15a6"
      },
      "source": [
        "## Now instead of unigram, we will use bigrams as features, and see how useful bigrams are as features.\n",
        "\n",
        "bigram_eng1 = Counter(ngrams(eng1,2)) # bigrams\n",
        "plothistogram(bigram_eng1)\n",
        "plt.title('English 1')\n",
        "plt.show()\n",
        "\n",
        "bigram_eng2 = Counter(ngrams(eng2,2))\n",
        "plothistogram(bigram_eng2)\n",
        "plt.title('English 2')\n",
        "plt.show()\n",
        "\n",
        "bigram_fr1 = Counter(ngrams(fr1,2))\n",
        "plothistogram(bigram_eng1)\n",
        "plt.title('French 1')\n",
        "plt.show()\n",
        "\n",
        "bigram_fr2 = Counter(ngrams(fr2,2))\n",
        "plothistogram(bigram_fr2)\n",
        "plt.title('French 2')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O-egsHMIg5Rp"
      },
      "source": [
        "Another way to visualize bigrams is to use a 2-dimensional graph."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## lets have a lot at bigrams.\n",
        "\n",
        "bigram_eng1\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7LYSVe02dG59",
        "outputId": "3aebbfa3-8a2b-48dd-8764-03f6b5587a24"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Counter({('t', 'h'): 836,\n",
              "         ('h', 'e'): 694,\n",
              "         ('e', 'g'): 164,\n",
              "         ('g', 'i'): 279,\n",
              "         ('i', 'r'): 315,\n",
              "         ('r', 'a'): 441,\n",
              "         ('a', 'f'): 258,\n",
              "         ('f', 'f'): 262,\n",
              "         ('f', 'e'): 286,\n",
              "         ('e', 'i'): 145,\n",
              "         ('i', 's'): 212,\n",
              "         ('s', 'a'): 240,\n",
              "         ('a', 'l'): 398,\n",
              "         ('l', 'a'): 180,\n",
              "         ('a', 'r'): 323,\n",
              "         ('r', 'g'): 39,\n",
              "         ('g', 'e'): 151,\n",
              "         ('e', 'a'): 347,\n",
              "         ('f', 'r'): 77,\n",
              "         ('r', 'i'): 161,\n",
              "         ('i', 'c'): 161,\n",
              "         ('c', 'a'): 168,\n",
              "         ('a', 'n'): 523,\n",
              "         ('n', 'h'): 25,\n",
              "         ('h', 'o'): 110,\n",
              "         ('o', 'o'): 58,\n",
              "         ('o', 'f'): 194,\n",
              "         ('e', 'd'): 280,\n",
              "         ('d', 'm'): 35,\n",
              "         ('m', 'a'): 243,\n",
              "         ('a', 'm'): 77,\n",
              "         ('m', 'm'): 29,\n",
              "         ('l', 'b'): 11,\n",
              "         ('b', 'e'): 121,\n",
              "         ('e', 'l'): 155,\n",
              "         ('l', 'o'): 147,\n",
              "         ('o', 'n'): 368,\n",
              "         ('n', 'g'): 329,\n",
              "         ('i', 'n'): 587,\n",
              "         ('g', 't'): 75,\n",
              "         ('t', 'o'): 246,\n",
              "         ('o', 't'): 138,\n",
              "         ('e', 'n'): 322,\n",
              "         ('n', 'u'): 25,\n",
              "         ('u', 's'): 101,\n",
              "         ('s', 'g'): 42,\n",
              "         ('f', 'a'): 65,\n",
              "         ('a', 'i'): 79,\n",
              "         ('i', 't'): 262,\n",
              "         ('t', 'i'): 317,\n",
              "         ('s', 't'): 365,\n",
              "         ('e', 't'): 175,\n",
              "         ('t', 'a'): 145,\n",
              "         ('l', 'l'): 134,\n",
              "         ('l', 'e'): 266,\n",
              "         ('e', 's'): 659,\n",
              "         ('t', 'l'): 45,\n",
              "         ('l', 'i'): 161,\n",
              "         ('i', 'v'): 92,\n",
              "         ('v', 'i'): 78,\n",
              "         ('t', 'e'): 283,\n",
              "         ('e', 'r'): 467,\n",
              "         ('r', 'r'): 34,\n",
              "         ('r', 'e'): 450,\n",
              "         ('t', 'r'): 91,\n",
              "         ('i', 'a'): 70,\n",
              "         ('n', 'i'): 112,\n",
              "         ('i', 'm'): 70,\n",
              "         ('n', 'd'): 384,\n",
              "         ('d', 't'): 125,\n",
              "         ('r', 'u'): 39,\n",
              "         ('u', 'm'): 58,\n",
              "         ('m', 'i'): 83,\n",
              "         ('n', 'a'): 169,\n",
              "         ('n', 't'): 303,\n",
              "         ('n', 'e'): 193,\n",
              "         ('r', 't'): 139,\n",
              "         ('h', 't'): 74,\n",
              "         ('a', 'd'): 96,\n",
              "         ('d', 'i'): 158,\n",
              "         ('i', 'o'): 162,\n",
              "         ('l', 'y'): 127,\n",
              "         ('y', 'g'): 20,\n",
              "         ('s', 'w'): 81,\n",
              "         ('w', 'e'): 77,\n",
              "         ('o', 'u'): 190,\n",
              "         ('u', 'g'): 47,\n",
              "         ('g', 'h'): 89,\n",
              "         ('t', 't'): 83,\n",
              "         ('o', 'b'): 29,\n",
              "         ('e', 'o'): 86,\n",
              "         ('s', 'p'): 115,\n",
              "         ('p', 'e'): 136,\n",
              "         ('e', 'c'): 238,\n",
              "         ('c', 'i'): 101,\n",
              "         ('i', 'e'): 106,\n",
              "         ('a', 'c'): 127,\n",
              "         ('m', 'e'): 134,\n",
              "         ('o', 'p'): 79,\n",
              "         ('p', 'a'): 80,\n",
              "         ('r', 'd'): 53,\n",
              "         ('d', 'a'): 131,\n",
              "         ('w', 'i'): 92,\n",
              "         ('h', 'n'): 5,\n",
              "         ('s', 'u'): 106,\n",
              "         ('u', 'b'): 27,\n",
              "         ('b', 's'): 15,\n",
              "         ('s', 'm'): 68,\n",
              "         ('m', 'o'): 141,\n",
              "         ('o', 's'): 100,\n",
              "         ('c', 'e'): 108,\n",
              "         ('y', 'r'): 16,\n",
              "         ('s', 'e'): 232,\n",
              "         ('r', 'c'): 38,\n",
              "         ('c', 'h'): 134,\n",
              "         ('r', 's'): 113,\n",
              "         ('p', 'r'): 106,\n",
              "         ('r', 'o'): 236,\n",
              "         ('p', 'o'): 92,\n",
              "         ('d', 'd'): 28,\n",
              "         ('i', 'd'): 47,\n",
              "         ('e', 'm'): 149,\n",
              "         ('u', 'p'): 50,\n",
              "         ('p', 't'): 45,\n",
              "         ('o', 'e'): 19,\n",
              "         ('i', 'g'): 80,\n",
              "         ('e', 'x'): 47,\n",
              "         ('x', 't'): 20,\n",
              "         ('t', 's'): 177,\n",
              "         ('s', 'd'): 33,\n",
              "         ('d', 'u'): 66,\n",
              "         ('u', 'e'): 13,\n",
              "         ('e', 'w'): 70,\n",
              "         ('w', 'r'): 4,\n",
              "         ('h', 'i'): 146,\n",
              "         ('r', 'm'): 44,\n",
              "         ('o', 'c'): 55,\n",
              "         ('d', 'r'): 33,\n",
              "         ('d', 'n'): 17,\n",
              "         ('u', 'c'): 39,\n",
              "         ('c', 'l'): 33,\n",
              "         ('a', 'a'): 22,\n",
              "         ('a', 's'): 231,\n",
              "         ('o', 'r'): 258,\n",
              "         ('r', 'p'): 21,\n",
              "         ('p', 'h'): 20,\n",
              "         ('o', 'l'): 72,\n",
              "         ('o', 'g'): 34,\n",
              "         ('l', 'm'): 11,\n",
              "         ('u', 'r'): 129,\n",
              "         ('s', 's'): 129,\n",
              "         ('e', 'v'): 57,\n",
              "         ('v', 'e'): 228,\n",
              "         ('n', 'o'): 99,\n",
              "         ('n', 'c'): 103,\n",
              "         ('c', 't'): 87,\n",
              "         ('s', 'o'): 168,\n",
              "         ('f', 'g'): 19,\n",
              "         ('e', 'k'): 14,\n",
              "         ('k', 'n'): 13,\n",
              "         ('o', 'w'): 92,\n",
              "         ('w', 'n'): 21,\n",
              "         ('n', 'f'): 27,\n",
              "         ('o', 'm'): 156,\n",
              "         ('m', 't'): 21,\n",
              "         ('e', 'f'): 82,\n",
              "         ('f', 'o'): 118,\n",
              "         ('s', 'i'): 215,\n",
              "         ('i', 'l'): 115,\n",
              "         ('l', 'r'): 4,\n",
              "         ('c', 'o'): 169,\n",
              "         ('s', 'c'): 82,\n",
              "         ('f', 'd'): 6,\n",
              "         ('g', 'u'): 23,\n",
              "         ('u', 'i'): 18,\n",
              "         ('s', 'h'): 98,\n",
              "         ('g', 'c'): 13,\n",
              "         ('h', 'a'): 237,\n",
              "         ('c', 's'): 6,\n",
              "         ('y', 'l'): 18,\n",
              "         ('g', 'n'): 18,\n",
              "         ('c', 'k'): 82,\n",
              "         ('k', 'a'): 30,\n",
              "         ('d', 'l'): 28,\n",
              "         ('g', 's'): 41,\n",
              "         ('r', 'n'): 56,\n",
              "         ('n', 'l'): 35,\n",
              "         ('i', 'k'): 15,\n",
              "         ('k', 'e'): 50,\n",
              "         ('d', 'c'): 25,\n",
              "         ('o', 'a'): 32,\n",
              "         ('a', 't'): 339,\n",
              "         ('t', 'p'): 22,\n",
              "         ('n', 's'): 140,\n",
              "         ('i', 'f'): 32,\n",
              "         ('f', 'i'): 61,\n",
              "         ('u', 'n'): 93,\n",
              "         ('d', 'e'): 137,\n",
              "         ('a', 'e'): 28,\n",
              "         ('g', 'w'): 7,\n",
              "         ('o', 'k'): 29,\n",
              "         ('a', 'p'): 72,\n",
              "         ('p', 'i'): 47,\n",
              "         ('i', 'i'): 4,\n",
              "         ('e', 'e'): 142,\n",
              "         ('d', 's'): 71,\n",
              "         ('s', 'f'): 50,\n",
              "         ('m', 'c'): 3,\n",
              "         ('u', 't'): 55,\n",
              "         ('d', 'f'): 41,\n",
              "         ('m', 'n'): 5,\n",
              "         ('t', 'g'): 20,\n",
              "         ('u', 'a'): 25,\n",
              "         ('y', 'i'): 24,\n",
              "         ('a', 'b'): 58,\n",
              "         ('b', 'i'): 41,\n",
              "         ('a', 'v'): 77,\n",
              "         ('v', 'a'): 49,\n",
              "         ('n', 'n'): 17,\n",
              "         ('a', 'h'): 19,\n",
              "         ('h', 's'): 20,\n",
              "         ('d', 'w'): 15,\n",
              "         ('w', 'o'): 27,\n",
              "         ('o', 'd'): 81,\n",
              "         ('r', 'f'): 29,\n",
              "         ('s', 'l'): 44,\n",
              "         ('f', 'l'): 24,\n",
              "         ('f', 'w'): 4,\n",
              "         ('d', 'y'): 23,\n",
              "         ('y', 'p'): 35,\n",
              "         ('p', 'l'): 32,\n",
              "         ('y', 'a'): 60,\n",
              "         ('w', 'h'): 70,\n",
              "         ('e', 'y'): 44,\n",
              "         ('y', 'b'): 16,\n",
              "         ('b', 'r'): 53,\n",
              "         ('w', 's'): 22,\n",
              "         ('r', 'h'): 15,\n",
              "         ('r', 'b'): 18,\n",
              "         ('v', 'o'): 12,\n",
              "         ('h', 'l'): 11,\n",
              "         ('d', 'h'): 20,\n",
              "         ('h', 'y'): 21,\n",
              "         ('y', 'e'): 24,\n",
              "         ('n', 'w'): 11,\n",
              "         ('l', 'd'): 45,\n",
              "         ('d', 'o'): 69,\n",
              "         ('a', 'y'): 43,\n",
              "         ('y', 'u'): 5,\n",
              "         ('f', 's'): 13,\n",
              "         ('g', 'o'): 22,\n",
              "         ('b', 'a'): 41,\n",
              "         ('f', 'u'): 15,\n",
              "         ('n', 'r'): 22,\n",
              "         ('u', 'l'): 101,\n",
              "         ('l', 't'): 65,\n",
              "         ('t', 'm'): 19,\n",
              "         ('s', 'b'): 65,\n",
              "         ('b', 'u'): 25,\n",
              "         ('g', 'r'): 63,\n",
              "         ('g', 'a'): 67,\n",
              "         ('a', 'g'): 70,\n",
              "         ('g', 'g'): 29,\n",
              "         ('b', 'l'): 60,\n",
              "         ('l', 'h'): 5,\n",
              "         ('h', 'r'): 22,\n",
              "         ('k', 'i'): 45,\n",
              "         ('m', 'b'): 28,\n",
              "         ('t', 'b'): 12,\n",
              "         ('b', 'o'): 42,\n",
              "         ('a', 'w'): 13,\n",
              "         ('n', 'm'): 22,\n",
              "         ('c', 'c'): 20,\n",
              "         ('h', 'b'): 7,\n",
              "         ('i', 'b'): 19,\n",
              "         ('t', 'y'): 37,\n",
              "         ('y', 'f'): 15,\n",
              "         ('y', 'o'): 32,\n",
              "         ('e', 'h'): 54,\n",
              "         ('d', 'v'): 10,\n",
              "         ('c', 'u'): 39,\n",
              "         ('t', 'u'): 52,\n",
              "         ('p', 'p'): 43,\n",
              "         ('f', 't'): 75,\n",
              "         ('n', 'b'): 24,\n",
              "         ('n', 'p'): 12,\n",
              "         ('k', 's'): 26,\n",
              "         ('d', 'b'): 34,\n",
              "         ('b', 'y'): 31,\n",
              "         ('y', 't'): 40,\n",
              "         ('l', 'u'): 29,\n",
              "         ('r', 'v'): 43,\n",
              "         ('f', 'n'): 4,\n",
              "         ('i', 'u'): 15,\n",
              "         ('c', 'n'): 3,\n",
              "         ('s', 'v'): 5,\n",
              "         ('v', 'u'): 4,\n",
              "         ('l', 'n'): 9,\n",
              "         ('n', 'y'): 13,\n",
              "         ('l', 'f'): 20,\n",
              "         ('s', 'n'): 21,\n",
              "         ('l', 'p'): 15,\n",
              "         ('r', 'k'): 12,\n",
              "         ('d', 'g'): 23,\n",
              "         ('o', 'x'): 12,\n",
              "         ('x', 'i'): 15,\n",
              "         ('y', 'm'): 14,\n",
              "         ('e', 'p'): 84,\n",
              "         ('n', 'z'): 6,\n",
              "         ('z', 'o'): 7,\n",
              "         ('g', 'y'): 9,\n",
              "         ('r', 'l'): 37,\n",
              "         ('t', 'k'): 3,\n",
              "         ('c', 'w'): 2,\n",
              "         ('d', 'z'): 5,\n",
              "         ('z', 'a'): 4,\n",
              "         ('h', 'p'): 6,\n",
              "         ('p', 's'): 22,\n",
              "         ('l', 's'): 70,\n",
              "         ('b', 'n'): 1,\n",
              "         ('t', 'w'): 41,\n",
              "         ('w', 'a'): 47,\n",
              "         ('l', 'k'): 9,\n",
              "         ('g', 'l'): 19,\n",
              "         ('s', 'j'): 1,\n",
              "         ('j', 'a'): 6,\n",
              "         ('z', 'i'): 4,\n",
              "         ('h', 'w'): 6,\n",
              "         ('e', 'u'): 30,\n",
              "         ('d', 'p'): 23,\n",
              "         ('y', 'd'): 9,\n",
              "         ('h', 'j'): 2,\n",
              "         ('h', 'g'): 7,\n",
              "         ('a', 'u'): 24,\n",
              "         ('t', 'z'): 1,\n",
              "         ('z', 't'): 1,\n",
              "         ('m', 'g'): 5,\n",
              "         ('h', 'f'): 8,\n",
              "         ('m', 'd'): 3,\n",
              "         ('t', 'd'): 12,\n",
              "         ('k', 'k'): 1,\n",
              "         ('m', 'l'): 2,\n",
              "         ('m', 'k'): 1,\n",
              "         ('k', 'm'): 4,\n",
              "         ('o', 'i'): 15,\n",
              "         ('a', 'x'): 6,\n",
              "         ('x', 'o'): 8,\n",
              "         ('m', 'y'): 13,\n",
              "         ('a', 'o'): 7,\n",
              "         ('y', 'w'): 6,\n",
              "         ('m', 'u'): 24,\n",
              "         ('h', 'm'): 14,\n",
              "         ('o', 'v'): 35,\n",
              "         ('l', 'g'): 10,\n",
              "         ('c', 'r'): 25,\n",
              "         ('o', 'h'): 16,\n",
              "         ('m', 'p'): 39,\n",
              "         ('t', 'v'): 5,\n",
              "         ('e', 'b'): 74,\n",
              "         ('s', 'k'): 32,\n",
              "         ('k', 'u'): 16,\n",
              "         ('f', 'v'): 2,\n",
              "         ('r', 'w'): 10,\n",
              "         ('h', 'u'): 17,\n",
              "         ('r', 'y'): 42,\n",
              "         ('y', 'x'): 4,\n",
              "         ('x', 'w'): 2,\n",
              "         ('h', 'h'): 10,\n",
              "         ('m', 's'): 12,\n",
              "         ('i', 'z'): 9,\n",
              "         ('z', 'e'): 11,\n",
              "         ('x', 'a'): 5,\n",
              "         ('b', 'c'): 3,\n",
              "         ('x', 'm'): 3,\n",
              "         ('y', 'h'): 16,\n",
              "         ('l', 'w'): 5,\n",
              "         ('l', 'c'): 18,\n",
              "         ('s', 'r'): 26,\n",
              "         ('x', 's'): 3,\n",
              "         ('m', 'w'): 5,\n",
              "         ('l', 'v'): 28,\n",
              "         ('k', 'p'): 5,\n",
              "         ('y', 's'): 44,\n",
              "         ('g', 'j'): 2,\n",
              "         ('j', 'u'): 10,\n",
              "         ('y', 'c'): 11,\n",
              "         ('c', 'p'): 1,\n",
              "         ('t', 'c'): 30,\n",
              "         ('u', 'd'): 27,\n",
              "         ('x', 'p'): 8,\n",
              "         ('f', 'm'): 12,\n",
              "         ('h', 'c'): 16,\n",
              "         ('n', 'j'): 5,\n",
              "         ('c', 'q'): 1,\n",
              "         ('q', 'u'): 13,\n",
              "         ('g', 'm'): 11,\n",
              "         ('i', 'x'): 6,\n",
              "         ('x', 'l'): 1,\n",
              "         ('g', 'd'): 9,\n",
              "         ('i', 'p'): 19,\n",
              "         ('x', 'c'): 3,\n",
              "         ('g', 'f'): 4,\n",
              "         ('p', 'u'): 23,\n",
              "         ('e', 'q'): 8,\n",
              "         ('p', 'b'): 2,\n",
              "         ('a', 'j'): 2,\n",
              "         ('p', 'y'): 2,\n",
              "         ('m', 'f'): 12,\n",
              "         ('k', 'g'): 7,\n",
              "         ('b', 'f'): 4,\n",
              "         ('d', 'k'): 6,\n",
              "         ('t', 'f'): 19,\n",
              "         ('k', 't'): 5,\n",
              "         ('u', 'f'): 8,\n",
              "         ('f', 'h'): 5,\n",
              "         ('k', 'b'): 4,\n",
              "         ('t', 'n'): 5,\n",
              "         ('w', 'm'): 2,\n",
              "         ('g', 'p'): 8,\n",
              "         ('i', 'q'): 2,\n",
              "         ('x', 'b'): 1,\n",
              "         ('s', 'y'): 8,\n",
              "         ('x', 'u'): 6,\n",
              "         ('x', 'e'): 2,\n",
              "         ('c', 'm'): 9,\n",
              "         ('g', 'v'): 2,\n",
              "         ('p', 'w'): 5,\n",
              "         ('p', 'c'): 2,\n",
              "         ('w', 't'): 9,\n",
              "         ('p', 'f'): 1,\n",
              "         ('k', 'o'): 6,\n",
              "         ('k', 'l'): 5,\n",
              "         ('r', 'j'): 2,\n",
              "         ('w', 'c'): 3,\n",
              "         ('k', 'w'): 3,\n",
              "         ('u', 'v'): 2,\n",
              "         ('k', 'r'): 3,\n",
              "         ('a', 'k'): 10,\n",
              "         ('g', 'b'): 7,\n",
              "         ('o', 'y'): 4,\n",
              "         ('c', 'v'): 4,\n",
              "         ('k', 'v'): 1,\n",
              "         ('t', 'j'): 2,\n",
              "         ('j', 'o'): 2,\n",
              "         ('b', 'd'): 1,\n",
              "         ('n', 'q'): 1,\n",
              "         ('f', 'b'): 9,\n",
              "         ('k', 'd'): 2,\n",
              "         ('c', 'g'): 1,\n",
              "         ('h', 'd'): 5,\n",
              "         ('b', 't'): 1,\n",
              "         ('y', 'n'): 12,\n",
              "         ('f', 'c'): 4,\n",
              "         ('b', 'j'): 5,\n",
              "         ('j', 'e'): 5,\n",
              "         ('n', 'k'): 16,\n",
              "         ('k', 'y'): 3,\n",
              "         ('m', 'h'): 4,\n",
              "         ('n', 'x'): 1,\n",
              "         ('w', 'w'): 2,\n",
              "         ('x', 'y'): 2,\n",
              "         ('e', 'j'): 1,\n",
              "         ('n', 'v'): 6,\n",
              "         ('f', 'p'): 4,\n",
              "         ('c', 'y'): 2,\n",
              "         ('f', 'y'): 1,\n",
              "         ('b', 'p'): 1,\n",
              "         ('x', 'g'): 1,\n",
              "         ('e', 'z'): 2,\n",
              "         ('w', 'l'): 1,\n",
              "         ('p', 'm'): 2,\n",
              "         ('h', 'v'): 1,\n",
              "         ('b', 'm'): 1,\n",
              "         ('w', 'b'): 2,\n",
              "         ('w', 'd'): 2,\n",
              "         ('p', 'n'): 1,\n",
              "         ('b', 'g'): 1,\n",
              "         ('k', 'c'): 1,\n",
              "         ('y', 'k'): 1,\n",
              "         ('a', 'q'): 1,\n",
              "         ('y', 'z'): 2,\n",
              "         ('w', 'f'): 1,\n",
              "         ('u', 'x'): 3,\n",
              "         ('p', 'g'): 1,\n",
              "         ('y', 'j'): 1,\n",
              "         ('i', 'w'): 2,\n",
              "         ('r', 'z'): 1,\n",
              "         ('z', 'h'): 1,\n",
              "         ('l', 'q'): 1,\n",
              "         ('q', 'i'): 1,\n",
              "         ('s', 'x'): 1,\n",
              "         ('h', 'k'): 1,\n",
              "         ('g', 'z'): 1,\n",
              "         ('m', 'v'): 1,\n",
              "         ('m', 'r'): 2,\n",
              "         ('f', 'k'): 1,\n",
              "         ('k', 'h'): 3,\n",
              "         ('a', 'z'): 1})"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3EaPJgtaVxZM"
      },
      "source": [
        "## a function to plot 2-D histogram. The values are color mapped.\n",
        "\n",
        "def plotbihistogram(ngram):\n",
        "  freq = np.zeros((26,26))\n",
        "  for ii in range(26):\n",
        "    for jj in range(26):\n",
        "      freq[ii,jj] = ngram[(chr(ord('a')+ii), chr(ord('a')+jj))] #ord converts char to code\n",
        "  plt.imshow(freq, cmap = 'jet')\n",
        "  plt.colorbar()\n",
        "  return freq"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "ord"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4IFVtO8q8TJB",
        "outputId": "920b2b7e-2210-4d2f-b6ff-e706589cad39"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<function ord(c, /)>"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M7jq3AwnVzQT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 519
        },
        "outputId": "94aab872-694c-47c0-a7ca-8982b6f03d92"
      },
      "source": [
        "bieng1 = plotbihistogram(bigram_eng1)\n",
        "plt.show()\n",
        "bieng2 = plotbihistogram(bigram_eng2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UXPTOj67WsPT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 519
        },
        "outputId": "1d89b657-a19e-477c-fdfc-d07ad1177220"
      },
      "source": [
        "bifr1 = plotbihistogram(bigram_fr1)\n",
        "plt.show()\n",
        "bifr2 = plotbihistogram(bigram_fr2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": 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wDouOtcQkR0Si4SSXmaNmMskRkUilJsckF5eG6MEIjQMTTgTpXoLUYVMa+DAVxxjrxNCR61QmqJY+C+kYmdG5VY1xoFNp4NPsFYJdTHJWbV0VS+X3+1FWVoY5c+bggw8+CK/v7OxEZWUlysvLUVlZiUAgMJ7lJKI0GkQOBoTXoEWn6xKT3MKFC9HU1ISiouhHXBoaGlBVVYW2tjZUVVWhvr5+3ApJROk1ck/O/GXNy1UxyZWWlo4aOqW3txcdHR2oqKgAAFRUVKCjowN9fRYZj56IUmrknpz0sqIxXUQHg0EUFhbC4Rj+oxwOBwoKChAMBlNaOCKyhpF7cmavkEXvyaW94SEQqI5a1vX1aSpJYnTdl+4iKMmEzzNzPktfuougZDzKOQQHhoSamt2iNbkxJTm3242enh5omgaHwwFN03D27FnlEUEjeTzb0dX1CYDhf5A2W+Q0cCqtgakgDQ8UPTSQrvtgs/ki1lizdXVsn2eyrasqvd6vH2P0Z2lNmVjOkhIXAoHHU3LckEI/uZBFk9yY6pf5+fnwer1obW0FALS2tsLr9SIvT2WeVCLKNIPXWk+llxWJNblNmzbh8OHDOHfuHB555BG4XC4cOHAAPp8PtbW12LlzJ5xOJ/x+/9hKcLA6unJwIuLy6i6fwgGkGpBcy/qT/m+m8a/YlsVYm+hzekJt8ZY15vHLPoVzxKplRazzKBwjYJxQ2Uj4PCc9KZ9jyPhbUakJG0k1W+OAl0Yq5/yaYXmVYfk3wv5q0/CZG8sgpKmn0k8uY+/J1dXVoa6ubtT6mTNnYu/eveNSKCKyFpV7clI8XdLe8EBE1pfJ9+SY5IhIpNIPLqv6yRHRjWUQkxUe6xrbeHLbt2+Pemz0xIkTWLx4McrLy7Fy5Ur09vaGtzWLxcMkR0Qi+ZGuSQpDMY3217/+FSdOnAg/NhoKhbBu3TrU19ejra0NpaWl2Lp1qxgzwyRHRKLxeOJhcHAQGzZsgM/nC69rb29Hbm4uSktLAQDLli3DoUOHxJgZ3pMjIlEi9+SCwSA0TYuKOZ1OOJ3R3WGef/55LF68GMXFxeF1wWAQM2bMCC/n5eUhFArhwoULpjGXyxW3XExyRCRKpAvJ8uXLcfp09Nh71dXVqKmpCS//+c9/Rnt7O9auXZv6whqkP8l9Kwh0Xcv6ejFwV3dE0KtwgFNC/JJ4hK/seE/Ywhdj3dU47+MROq9ePqlwjCQFdits9E9CXOgAO/R7hXP8g7D8R4VjSJ15zya5PwBEztT+Q8MyMBGdcCfmHLJEupA0NTXFrMlFOnr0KD788EMsXLgQAPC3v/0N3//+97FixQqcOXMmvF1fXx/sdjtcLhfcbnfcmJn0JzkisryrmCw+tnX1WuuqyjPsjz32GB577LHwcllZGXbt2oVZs2bhN7/5DY4dO4bS0lLs2bMHixYtAgDMnTsX/f39MWNmmOSISDRR/eTsdjsaGxvR0NCAgYEBFBUVYcuWLWLMDJMcEYnG+7GuN998M/x+3rx5aGkx3hqQY/EwyRGRiI91EVFWy+THupjkiEiU1UMtERENIBcDyBW3sSILJDljc3NxxHupDxyAW1Iwh8HnpA1iDcAYue6/K5xkl3Jxxo/K131EiH9PiBcLcQD4nWHZ2BdMZaDIWebhBxebhpe8/Kp4hv02Y80k0ZGvexLcPhaV/nzGCdlHHpRP3T9v1uSIKKvxnhwRZTXW5Igoq3H4cyLKaleRg0GhYeFqps7WRUTEe3JElNU02MXLUY335IgoU6kMbz6W4c8nggVK9RyAC9fe+xA9dptCv6TLu4UNFP7E70j98WL124ocp+41+RzimHPSZMgqYk0kErlOpc/VctPoY/o20/iLtvMK5zD2KzSOG6jQPxLm/eDwyhum4f2vyMMBYc/XDMuV0cvLxjihekKMfeBiMf62RpZV9lXDy1UiymrsQkJEWW1kSkJpGytikiMiEe/JEVFW4z05IspqvCdHRFmNj3URUVbj8OdElNUGkYNBaOI2VpT+JOd5PLq/6izf9fenfJB9QYgfVziGdJ5Y8Ytx3sdTKMR/pXAMSawOx5HrjJM4x/KMafRFm7S/T+EcuyPe/wNGf0cqk3XrQlzqUKzQ+XrZ7uvvKx+OXgYgThieEiqfxfgbj8e6fvSjH6G7uxt2ux1Tp07F008/Da/Xi87OTtTW1uLChQtwuVzw+/3weDwAYBqLR6lUfr8fZWVlmDNnDj744IPw+rKyMixatAhLlizBkiVL8M477yT0RxJRZhjpQiK9EuH3+/HGG2+gubkZK1euxFNPPQUAaGhoQFVVFdra2lBVVYX6+vrwPmaxeJSS3MKFC9HU1ISiotH/+23btg379+/H/v37sWDBAtW/j4gyyEjrqtkr0dbVadOmhd9fvnwZNpsNvb296OjoQEVFBQCgoqICHR0d6OvrM42ZUUq9paWlCRWeiLJLIv3kgsEgNC36/p3T6YTTOfoZ8PXr1+PIkSPQdR2//OUvEQwGUVhYCIdj+FgOhwMFBQUIBoPQdT1uLC8v/nPuSd+TW7t2LXRdx9133401a9bE/EPMBN6KXtZPRi75kiwdAHwzBcfwjVqj66PXWVHi5Ux0+7F4OGpJ1x+OuVVy1qT8iONTztQbj9/m8GNd5vdBRx7rWr58OU6fPh0Vq66uRk1Nzah9Nm/eDABobm5GY2MjVq9enaISX5dUkmtqaoLb7cbg4CA2b96MDRs2YOvWrQkdw/M1oOva56GfBGyR7QhKDQ/3CHGVhgdpxq/ocui6DzabL+aW8UkND5LEZ34aXU7zEUaGNSV8nmg+cYvIhgddfxg2225DPKBwjAYh/gshrjLqy/WGhbGXc2JFfuclJS4EAo+n5LjD99xC4jbAcF6IVZMz8+1vfxv19fX43Oc+h56eHmiaBofDAU3TcPbsWbjdbui6HjdmJqkuyiMHz8nJQVVVFY4fV0koRJRpErkn53a7UVxcHPUyJrlPP/0UwWAwvPzmm2/i1ltvRX5+PrxeL1pbWwEAra2t8Hq9yMvLM42ZGXNN7sqVK9A0DdOmTYOu6zh48CC8XuO4YESUDYYTmVSTU+8M/Nlnn2H16tX47LPPYLfbceutt2LXrl2w2Wzw+Xyora3Fzp074XQ64fdfH7fPLBaPTdd1qcMRNm3ahMOHD+PcuXOYPn06XC4Xdu3ahZqaGmiahlAohJkzZ6Kurg4FBQXKfygAeDzPoatreNDMsV0GTjyWM3UsXca1vvBbfQtgW2eIb/XBasbrcnU+PkS30GevGJPxLmam5HyppFSTq6urQ11d3aj1zc3NKS8QEVnPcE3OvD7EUUiIKGNdxWQMCrfwrzLJEVGm0kIO4cnVazU5C462xCRHRCJtyCFOi6PBASs+o88kR0QiTXNA081HZ9BsFqzGgUmOiBRoQ0xyRJTFQpodWsg8yYXs4jhcacEkR0SiwYEcDAotD4PWbFy1QJI7+Hj0uIAnfNff36UyQ7k0EOQi8Qhf1dtM42/b/hZjrSfivcqgmZfMw7cIz89e9imcQ7JKYZsjQlwaxPFBhXP8m2HZ+BzpWYVjzBLi3xPiCrPLb33l+vstD0YvAwC+JBzgPfkcIpW5TCdgYM0hB8TmVfGxgvRIf5IjIuvTHEr/L1gRkxwRyYZsTHJElMU0yEnOmu0OTHJEpGAAwKCwjfkgJWnDJEdEsquQ2zdYkyOijBWC3LrKmhwRZawhyPfk2E8ujv+J692iWgBEDVun0kdImKhmrnyEt7sWCltI8x78o3wSvG0eviztf5PCOYTJjouL5UN0S3NRdJuHVSZ2u/Bo9PIsw/Kp3ykcpNc8/G3h2umcwm/r3fsNK4zL0u8iBd+ZVag0PKQ/m8Rk0WIRkaWo1OQs2sWESY6IZAMA+oVt2PBARBlL5XJVaphIE2uOjUJE1nJV8aXo/PnzePTRR1FeXo4HHngA1dXV6OvrAwCcOHECixcvRnl5OVauXIne3uv3X81i8TDJEZFspAuJ2SuBLiQ2mw2rVq1CW1sbWlpacPvtt2Pr1q0IhUJYt24d6uvr0dbWhtLS0vCE9WYxM0xyRCQbUnwpcrlcuOeee8LLd911F86cOYP29nbk5uaitHS4mX7ZsmU4dOgQAJjGzPCeHBHJVBoermWTYDAITYu+Qed0OuF0OmPuFgqF8Oqrr6KsrAzBYBAzZswIx/Ly8hAKhXDhwgXTmMvlkoqVRn0AzkUsR75X6kP0hnn4wmL5EG9JfaZ6hHUq48kJk26PntY22qYUtM8LXdyGnRTifebhY28pnCPy5s39wKnfG+IKBf1vj5rHm6V7NSrfmbHP4DTDsvT7TMU4byr/RCdgPLkEGh6WL1+O06dPR4Wqq6tRU1MTc7eNGzdi6tSpePDBB/H73xt/C8lLf5IjIutLoJ9cU1NTzJpcLH6/H11dXdi1axfsdjvcbjfOnDkTjvf19cFut8PlcpnGzDDJEZEsgZqc2+1WOuSzzz6L9vZ2vPjii8jJGZ7LcO7cuejv78exY8dQWlqKPXv2YNGiRWLMDJMcEclUuogkcNV88uRJvPDCC/B4PFi2bBkAoLi4GDt27EBjYyMaGhowMDCAoqIibNmyBQBgt9vjxswwyRGRLMWjkHzhC1/A+++/HzM2b948tLS0JByLh0mOiGQqratTJqIgiWOSIyIZH9Anoqw2BPmeG5McEWWskUe3pG0sKP1J7s+/BbpGRox8GPjD7ohgnsIBhIEJuxUGYOwWBt6MOXhn5DqVwRFPmYc3KRxCFKsvUuS6sXSANSgVOuEe26xwjr83LBvLpTC5tNRz4HK+ebxdiAMAIic3fxLAvxriJcL+wncOALhPiP+HwjEmQAaPQiImufPnz+OJJ57ARx99hJycHJSUlGDDhg3Iy8vDiRMnUF9fH9Wcm5+v8uMhooySwffkxAf0xzJaABFlmZHWVbPXQNpKZ0pMcmMZLYCIsszI5arZy6KXqzZd13XVjUOhEFauXImysjIUFhZi3759ePHFF8PxO++8E2+//bb4LBkRZRbPvwBd58y3KbkNCGybmPIkIqGGh/EYLcDj+S26rjU86PrDsNl2R0RVRiGZJcQVbhRsEhoe6p6NWtT1NbDZItcZR6eI5bQQ9wlxlRv60Q0go8u5SuEYb5mHS4VRXRJseND1pbDZ9hni/yUfwrfePP5bYf92+RSRDQ+6/iRsNr8hXiTsP/END7rug83mAwCUlLgQCDye0P5x3QhdSBIZLYCIskwGdyFRGhl4ZLSAHTt2xBwtAIDyiABElIEyuOFBrMmNZbSAxJQg+tOJvPxUqarHGtAyQXVSco7Vv+yiEE/UfwpxlSEeYm0TWbZnY8QTdOy4sIFK38b3It4vNSwr8kl/Syq+E6n/o8rlqMQi/eAk2Xy5OtbRAogoi2Tw5Wr6n3ggIuvL5iceiIgy+YkHJjkikmXzPTkiIgxCbj0dnIiCJI5JjohkvFwloqzGy9VkHMP1Pk3zARxJQxl+loZzGmXL4AbC5NMpk4p+cBLjY4UqjxlmqQzuQqL0xAMR3eBSPAqJ3+9HWVkZ5syZgw8++CC8vrOzE5WVlSgvL0dlZSUCgYBSzAyTHBHJpASncs8uwsKFC9HU1ISiouhBDhoaGlBVVYW2tjZUVVWhvr5eKWaGSY6IZCl+drW0tBRutztqXW9vLzo6OlBRUQEAqKioQEdHB/r6+kxjEgvckyMiy0vgiYdgMAhNi752dTqdcDpjzUFyXTAYRGFhIRwOBwDA4XCgoKAAwWAQuq7HjeXlmT8vzSRHRLIEupAsX74cp09Hj59YXV2NmpqacSmahEmOiGQJdCFpamqKWZOTuN1u9PT0QNM0OBwOaJqGs2fPwu12Q9f1uDEJ78kRkUxTfGE4WRUXF0e9VJJcfn4+vF4vWltbAQCtra3wer3Iy8szjUlYkyMimX7tJW2jaNOmTTh8+DDOnTuHRx55BC6XCwcOHIDP50NtbS127twJp9MJv//6kPNmMTNZkORUJnaWxJo8OpJUT5f2VzmG9FWoDJopUSmnRCqH/D/26L/V+L/xRHQoVvndGG9CGT+/VHwnN6a6ujrU1dWNWj9z5kzs3bs35j5mMTO8XCWirJYFNTkiGn+qtdZUXC2kFpMcEUvv6cEAAAa0SURBVCnQIN90s4FJjogy1FWoJbkpE1CWxDDJEZGCfgAhYRs71CZan1hMckSkQGWYEcdEFCRhTHJEpEDl4VVrskCSm4zom5WR71UGKZS2mYgboanoL2WVARmT/VtU/o6JuKSR+uuNZdDNG7lf3FXISS6B3sATyAJJjoisT6UmZ5uIgiSMSY6IFFxFptZkmeSISEE/5DkHrTnJA5McESlQuVxl6yoRZSyVAeWY5IgoY2Xu7NJMckSkQKUmZ810Ys1SEZHF9EPuA5mhXUjOnz+PJ554Ah999BFycnJQUlKCDRs2IC8vD3PmzMHs2bNhtw8PS9fY2Ig5c+YkWASHoRipzrsqzd5WaBpPduBOq1D5/oyDYo7HIJlj6exL8al0IbHmb1T8RdpsNqxatQr33HMPgOGZr7du3Yqf/exnAIA9e/bg5ptvHt9SElGaJTAnocWIIwO7XK5wggOAu+66C2fOnBnXQhGR1YzckzN7ZUHDQygUwquvvoqysrLwuhUrVkDTNNx7772oqalBTk5OygtJROmWua2rNl3XlZ+qfeaZZ9DT04Pt27fDbrcjGAzC7Xbj8uXLWLduHWbPno2f/OQn41leIkoDj+cVdHVdMt2mpGQaAoEHJ6hE6pRrcn6/H11dXdi1a1e4oWFkYtdbbrkF3/3ud/HSSy8lXACP56Xwh6fr/wKbbVtEdCJmbUqcrvtgs/lSfNTUNzyMLmcqZhWTqMyCdb2Vbnw+y9TLxHKWlLgQCDyeoiOrtK4mNuJPZ2cnamtrceHCBbhcLvj9fng8nrEWMC6l2bqeffZZtLe3Y8eOHeHL0U8++QT9/f0AgKGhIbS1tcHr9aa8gERkBUOKL3UNDQ2oqqpCW1sbqqqqUF9fn9oiXyPW5E6ePIkXXngBHo8Hy5YtAwAUFxdj1apVqK+vh81mw9DQEL785S9j9erVCReguPiWqOWSksixxqThltOnpMSV4iNKX8XY7ndEl1Ol4p7sfZXchLdJ/Wc5PjKtnMXFKnPgqikuvgnSb2N4GyAYDELToltanU4nnM7r5ent7UVHR0f46q+iogIbN25EX18f8vKM8/AmJ6F7ckREZvr7+3Hvvffik08+iVpfXV2Nmpqa8HJ7ezuefPJJHDhwILzuW9/6FrZs2YI77rgjpWXiEw9ElDKDg4N47bXXRq2PrMVNNCY5IkoZ42VpPG63Gz09PdA0DQ6HA5qm4ezZs+HGzFRSanggIkql/Px8eL1etLa2AgBaW1vh9XpTfj8O4D05IkqTDz/8ELW1tbh48SKcTif8fj8+//nPp/w8THJElNV4uUpEWY1JjoiyGpMcEWU1JjkiymqW6Cc3UQ/qJqusrAw5OTnIzR1+LGnt2rVYsGBBmks1PHhCW1sbTp8+jZaWFsyePRuA9T7XeOW00udqNhL2iRMnUF9fj4GBARQVFWHLli3Iz8+3XDlTM2J3FtEtYMWKFXpzc7Ou67re3Nysr1ixIs0liu3rX/+6/v7776e7GKMcPXpUP3PmzKjyWe1zjVdOK32u58+f1//whz+El3/+85/rP/3pT3VN0/T77rtPP3r0qK7rur5jxw69trY2XcWMW05d1/XZs2frly9fTlfRLCftl6sjD+pWVFQAGH5Qt6OjA3191hxmyYpKS0tH9RS34ucaq5xWE28k7Pb2duTm5qK0tBQAsGzZMhw6dChdxeSI3QlI++VqMBhEYWEhHI7hiWkdDgcKCgoQDAbHpfdzstauXQtd13H33XdjzZo1aX0mzww/1+RFjoQdDAYxY8aMcCwvLw+hUCh8KyCdOGK3ubTX5DJJU1MT3njjDezbtw+6rmPDhg3pLlJWsOrnunHjRkydOhUPPmi90W4jGcv51ltv4bXXXkNTUxNOnTqFHTt2pLmE6ZX2JBf5oC6AcX1QN1kjZcrJyUFVVRWOHz+e5hLFx881OSMjYT/33HOw2+1wu91Rl4N9fX2w2+1pr8UZywmMHrHbCp9nOqU9yU3kg7rJuHLlCi5dGhmmXcfBgwctPRIyP9exizUS9ty5c9Hf349jx44BGJ6Kc9GiReksJkfsVmSJZ1cn6kHdZHz88ceoqamBpmkIhUKYOXMm6urqUFBQkO6iYdOmTTh8+DDOnTuH6dOnw+Vy4cCBA5b7XGOVc9euXZb6XE+ePImKigp4PB5MmTIFwPBI2Dt27MDx48fR0NAQ1YXktttus1Q5Y43Y/dRTT93QcyNbIskREY2XtF+uEhGNJyY5IspqTHJElNWY5IgoqzHJEVFWY5IjoqzGJEdEWY1Jjoiy2v8HeKFLy5MSWkwAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": 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SjW6nPavA6fB5pkMbgfRsZ0GBd9QBRrzCCv0AwzEmwHXr1iEzMxPNzc1wuVw4ceIEgIv1hXvvvRdvvvkmamtr8dJLL4mxeMR1zJqTk4OioiI0NTUBAJqamlBUVITsbOP4aUQ0GQxcqPJKL2DoEllnZ2fU69Sp6O5RZ8+eRUNDA5YuXQqXa2gUwauuusq0vjARtQfxCHDNmjXYtWsXTpw4gQceeABerxfbt29HIBBAdXU1Nm/ejKysLASDwfha8MYyYCBi+v3AxfffDkB2SYJxoEU3H+VztuvHY8yNPGIzDpQ5lq/Mw1NWmscHAwr7EPyrwjYanhYWkI5EH1Foh2HYTGO7GowPJI/HrUJceAA8AOBfDNPG38H/Eda3ou+m/PsVf1sWUOkHOHwNsKKiAl1dXVGxyspKVFVVjUwfOXIEXq8XGzduxAcffIDLLrsMS5cuxbRp08atL+i6Pm4s3oMvMQHW1NSgpqZm1PyZM2fitddei2unRJReVK4BDsfr6+uhaVpULCsreqRwTdNw5MgR3HTTTVi5ciU+/vhjPPjgg3jmmWesbbgg5UUQIrK/WK4BqtQCfD4fpkyZMnI6e/PNN+PKK6/EtGnTxq0v6LpuWe1hWPrVrYko6azuB5idnY05c+bgvffeAzBU3e3u7obf7x+3vjARtQceARKRaABT0S/c6uaJcTzAxx9/HI8++iiCwSCmTJmCtWvXIisry7S+YFnt4QImQCISDd/uJi0Ti2uvvRYvv/zyqPlm9QWraw9MgEQkiqUKnE6YAIlIpHKNLx3vBWYCJCJRLN1g0knqE+C/Aei48F4H8O3I4DcVNnBQiJ8WtzD7f/5VWCIwxrzITq4WjIIz+GHi25A0/C+Fhf5NiL8oxP+s0I7IjuPXAQ2HDQuodCCWLrjvF+IqP/23I97/zDANJGeQ2onv5KxiIm6Fs4PUJ0Aisr3zmCoOeHqeT4UjosmI1wCJyLF4DZCIHIvXAInIsXgKTESOxY7QRORY/chEPzLFZdKNzRPgp/Ii0x4zj/sVdjMoLTBDmPcdhZ00CnGVgS8Tla+wzE4h/u8WtCNyHw+Nsc8syMb6TiJUzzcN61e4TOMA4Hpss2GO8YcijUJixVMSrXjcQuJ4BEhEjsVrgETkWDwCJCLHYj9AInKs88jAgFDkOC/cKmdHTIBEJOI1QCJyLA1u8RRX4zVAIpqMJmJIfDuwQYs3AOi98D6A6LH3hL5eANAnjHH3qUI/qup2YYGxtnE84r3Uxw8Qx3WbdpN5vE9hFyKFvobTHjIN//ir35jGX3SdUmiHsf+c8WeoMAbeLPN+fnjqLdOwC/9P3kfNfYZpw2ezxooHuKfHEFI8BSYix2I3GCJyLJXHYg6kydFsJCZAIhLxGiARORavARKRY/EaIBE5Fm+FIyLH4pD4RORYA8jAADRxmXST+gSYtQzwRkx7Axff9wYgyxPix4U4gMuF/ZwZK35+nPfjWCDsY6vKQ8sTVSQv0hcwDb8ojSMa+f2Np1f6WxU+z4PSAp8IcYXO1mteufh+9cLoaQDWDESajIerJ87Rt8IFg0E0Nzejq6sLjY2NKCwsBACUlpYiIyMDmZlDo0SsWLECt99++8S1lohSwtHdYObOnYvFixejoqJiVOzZZ58dSYhENDk5ugpcUlIy0e0gIhubrP0AXbqu66oLl5aWYsuWLVGnwJdffjl0XUdxcTGWL1+OrCyVB9oQUTq5Gx/jKAZMl5mODDTj5iS1yBoJnbTX19fD5/NhYGAATzzxBFatWoX169fHtA3/PwAdR4be6ycB15URQUuKIApP5rpceLKcoQii6wG4XIExFx1XwkWQrtj2h7HaaT7SyxDz0V5EMRZBdP1ncLmMf7vC3zpN2E/fs8IGFIogEaMR6fpCuFzGIohYiUm6yO+8oMCL9vZllmx36BpgWFwmHhs3bsSvf/3rkfpCS0sLamtr0d/fjxkzZmDdunXIyckBANNYPBI6aff5fACAjIwMlJeXY//+/YlsjohsavgaoNkrnmuAf/nLX9DS0oIZM4b+ZxMOh/Hwww+jtrYWzc3NKCkpGTmoMovFK+4EeO7cOZw+fRoAoOs6duzYgaIihW4WRJR2pOQXeY0wFAqhs7Mz6nXq1OhxIgcGBrBq1SoEAoGRea2trcjMzBypOyxYsAA7d+4UY/FSOmZds2YNdu3ahRMnTuCBBx6A1+vFli1bUFVVBU3TEA6HMXPmTNTV1cXeglMbgN6IAVGVTnsjHYt9n0Zj9vOz2NYk7EOU4Omtipi/PyCe03upv6IlnlpoPl2dhDbYhAYPBsVT4KEEWFFRga6u6O+0srISVVVVUfOeeeYZ3HPPPcjPzx+ZFwqFMH369JHp7OxshMNh9Pb2msa8Xi/ioZQAa2pqUFNTM2p+Q0NDXDslovQydIRnXi8dToD19fXQtOi7RozF0Y8++gitra1YsWKFtQ2NUfr1XCSipDuPqRgQrpidv5AAh2sDZvbu3YtDhw5h7ty5AIAvvvgCP/3pT7Fo0SIcPXp0ZLmenh643W54vV74fL5xY/FKv56LRJR0Wtij9FL185//HHv27MHu3buxe/duXHPNNfjtb3+LJUuWoK+vD/v27QMAbN26FfPmzQMAzJo1a9xYvHgESEQibdCDQWkZeJDoeAhutxtr165FXV1dVFcXKRYvJkAiEmmaB5puPhKG5or/hHL37t0j72+99VY0No79pEWzWDyYAIlIpA1ObAJMFSZAIhKFNTe0sHkCDLulsdLshwmQiEQD/RkYMB8PFQPpNxaCDRLg3GXRY5aWBS6+b5Lu5wSAOUL8EnELP9bfM42PPQho5D3IKoNanjYPf1u4H/n9JxT2MZbIZ7U+qLC8NJCoEL/+Z/IuDho7ZBvv51a5T1e46+jr/2we/1RhF9XvXHy/8s7oaQDA9cIGrLhXWOVZu0kYVHXQA2FAaAjdBG0p9QmQiOxP80AsA6chJkAikg26mACJyKE0yAkw/WogTIBEpKAfEMZDhTBWgi0xARKR7DzkWguPAIloUgpDrgLzCJCIJqVByNcA2Q8wDh5DK2JukdAPUGG4sR2QhtPZO8a83Ij3HfJOpD+s1zysZqxzlIh5CxWenfCK1O9M6KP3dXkXo55Ncr1h+uCfFLbRnlg7pC58ANBk7GtonFZpZ6LkfqxJ6QeoUgRJfTaJWRo2mYiSTuUIMA27yTABEpGsH0CfsAyLIEQ0KamcAktFEhtiAiQimUo3mCRcirQaEyARydgNhogci0UQInIslSJIGmaT1DfZeHE16v8iKuPC/ad5+H1hXDgAf//gvwlLvDzGvMgB5bLFfQBXmIfXCKv/QGEXY44dFzFvq8o2pPEAhe+kaY/CPmZEvL8OOHjYEH9b3sSC5eZxqV/lzgPyPpAlxJNxyHMqCftQwCIIETkWT4GJyLF4BEhEjsVuMETkWOwGQ0SOpVIFnpaMhliLCZCIZCyCEJFjDUK+xscESESTkgb5GiCrwHH4rzeAjrMXJhYCTa9EBFUGgzxnHt7zlryJLf8kLDDWxxQ5T6XDttChVezoHG+JLWK9QZUBPIUO27PvN4+3qDzA/TsR76/D6AFlFT7PfxXiUsdy3CDvAwHDe+MD3aVRVVU6Md8lxBU6hSeDU7vBnDx5Eo888gg+//xzZGRkoKCgAKtWrUJ2djZaWlpQW1uL/v5+zJgxA+vWrUNOjsKow0SUXibpNUC3tIDL5cKSJUvQ3NyMxsZGXHvttVi/fj3C4TAefvhh1NbWorm5GSUlJVi/fn0y2kxEyTZcBTZ79aesdXETE6DX68WcORefuzF79mwcPXoUra2tyMzMRElJCQBgwYIF2Llz58S1lIhSZ/gU2OyVhqfALl3XddWFw+EwfvKTn6C0tBR5eXnYtm0bnn/++ZH4zTffjHfffRder/SQISJKJ/7/ADpOmC9TcBXQ/mxy2mOVmIogq1evxqWXXoqFCxfirbcUigsK/P430HGhCKLrC+FyRRZBehS2MEOISyN6ALhfKIL8Lhg1qesr4XJFzpOepAbIF8QDCcZH0/UAXK7I9f5dYS1hlJTZ95nHYyyC6PqdcLneMcTfkzex9THzuFQEaZV3EfmZj/4sAbkIclBhH9YWQSLbWVDgRXv7spjWH5fF3WDirS1YXXcQT4GHBYNBdHR0YMOGDXC73fD5fDh69OhIvKenB263m0d/RJORpvhSFE9tYSLqDkoJ8Omnn0Zrays2bdqEjIwMAMCsWbPQ19eHffv2AQC2bt2KefPmJdQYIrKpGIogoVAInZ2dUa9Tp6LPgOKpLUxE3UE8BT5w4ACee+45+P1+LFiwAACQn5+PTZs2Ye3atairq4s6HLWWyimwyjKC30mnIWP1S/tKiMdKZSDRRL2e+CZa/iws8E2FjbwT8f5Ow7SiBUFhASu+E+OlDeO0yimuxCb9/CQxnAJXVFSgq6srKlRZWYmqqqoxVwuHw3j11VdRWlqKUCiE6dOnj8Sys7MRDofR29trGov3zFNMgDfccAM+++yzMWO33norGhsb49oxEaWRGO4Eqa+vh6ZFL5yVNf61+ImoLahK/Z0gRGR/MdwJ4vP5lDc7XFvYsmWLWFuYiLqDchGEiBxM6gOocqeIQay1hYmoO/AIkIhkFneDiae24Ha7La87MAESkWwA8q1uA+qbi7e2YHXdgQmQiGSTdDAEJkAiknFA1InSgeinWFvRtypWj6dgn0Zp0h9MJPUTtIoV/fwkxn/xafjYM6twQFQiciynDohKRMRrgETkXCqPxUzDAVGZAIlIxlNgInIsngITkWOxGwwRORa7wRCRY+kXXtIyacYGCXAKogeajHyv0vFU5eHpiUpGp9tsIW7BwK9Kzy5JtLNvPN+HcR2VcympnVb8LoztMH5+Du4YPUlwOCwiciwbHAESkf2pHu2qnGXYBxMgESnQIF/kc4EJkIgmofNQS4DTktAW6zABEpGCPgBhYRk3gCuS0BbrMAESkYJByB39PMloiKWYAIlIgcrNwOnHBgnwMkQfWkceQqv0fZO+FJXqlR0u3FrRz09iRb9KqU+kSp9J4+dt/A6t6F8nfaen4timk/v9nYf8by39ekLbIAESkf2pHAG6ktEQSzEBEpGC85iMR8BMgESkoA/ycy/TbzQEJkAiUqByCswqMBFNSioDAjIBEtGkNDmHhGYCJCIFKkeA6ZdO0q/FRJQCfZD7eE7CbjAnT57EI488gs8//xwZGRkoKCjAqlWrkJ2djRtvvBGFhYVwu4eGFVy7di1uvPHGGJvwJYDeiOlYOwRbUZqffOX9sakMEpro4K/xDLo6EZ9/PB2daXwq3WDS79+RmABdLheWLFmCOXPmAACCwSDWr1+PJ598EgCwdetWXHbZZRPbSiJKscn5XExxRGiv1zuS/ABg9uzZOHr06IQ2iojsZvgaoNlrkhdBwuEwXn31VZSWlo7MW7RoETRNwx133IGqqipkZGRY3kgiSrXJWQV26bqufAfz448/jmPHjmHjxo1wu90IhULw+Xw4c+YMHn74YRQWFuKXv/zlRLaXiFLA738FHR2nTZcpKLgC7e0Lk9QiaygfAQaDQXR0dGDLli0jRQ+fzwcAuPzyy/HDH/4QL7zwQswN8Ps3oKNjqAii6wG4XIGYt5Fs6dtO+xVB0veztKfIdhYUeNHevsyiLatUgWMbVenw4cOorq5Gb28vvF4vgsEg/H5/vA2Mi9JT4Z5++mm0trZi06ZNI6e4X375Jfr6+gAAg4ODaG5uRlFR0cS1lIhSaFDxpa6urg7l5eVobm5GeXk5amtrrW2yAvEI8MCBA3juuefg9/uxYMECAEB+fj6WLFmC2tpauFwuDA4O4pZbbsHSpUtjbkB+flbUdEGBN+ZtpEJ6tjNTYQ2VZcyonFRE/0NJz8/Svobbafy3lYj8/EsgJbihZYBQKARNi64IZ2VlISvrYnu6u7vR1tY2ctZYVlaG1atXo6enB9nZ0jOyrRPTNUAiIjN9fX2444478OWXX0bNr6ysRFVV1ch0a2srVq5cie3bt4/M+/73v49169bhG9/4RtLayztBiMgyAwMDeP3110fNjzz6sxMmQCKyjPFUdzw+nw/Hjh2DpmnweDzQNA3Hjx8fKdtqYV4AAAMhSURBVKwmi1IRhIjISjk5OSgqKkJTUxMAoKmpCUVFRUm9/gfwGiARpcihQ4dQXV2NU6dOISsrC8FgEF/72teS2gYmQCJyLJ4CE5FjMQESkWMxARKRYzEBEpFj2aIfoB1uilZRWlqKjIwMZGYO3S62YsUK3H777Slu1dBAFc3Nzejq6kJjYyMKCwsB2O9zHa+ddvpczUZAb2lpQW1tLfr7+zFjxgysW7cOOTk5tmunNSO1O4RuA4sWLdIbGhp0Xdf1hoYGfdGiRSlu0di++93v6p999lmqmzHK3r179aNHj45qn90+1/HaaafP9eTJk/r7778/Mv3UU0/pv/rVr3RN0/S77rpL37t3r67rur5p0ya9uro6Vc0ct526ruuFhYX6mTNnUtW0tJLyU+Dhm6LLysoADN0U3dbWhp6eWJ8N4lwlJSWjetDb8XMdq512M94I6K2trcjMzERJSQkAYMGCBdi5c2eqmsmR2i2S8lPgUCiEvLw8eDxDD1X2eDzIzc1FKBRKeq9wFStWrICu6yguLsby5ctte48jP9fERY6AHgqFMH369JFYdnY2wuHwyOWFVOJI7fFL+RFgOqmvr8fvf/97bNu2DbquY9WqValu0qRg18919erVuPTSS7Fwob1HOTa285133sHrr7+O+vp6HDx4EJs2bUpxC+0r5Qkw8qZoACm7KVrFcJsyMjJQXl6O/fv3p7hF4+PnmpjhEdA3bNgAt9sNn88XdYrZ09MDt9ud8qM/YzuB0SO12+HztKuUJ0C73BQtOXfuHE6fHnomgq7r2LFjh61HwObnGr+xRkCfNWsW+vr6sG/fPgBDj4OdN29eKpvJkdotYIt7ge1wU7TkyJEjqKqqgqZpCIfDmDlzJmpqapCbm5vqpmHNmjXYtWsXTpw4gSuvvBJerxfbt2+33ec6Vju3bNliq8/1wIEDKCsrg9/vx7Rp0wAMjYC+adMm7N+/H3V1dVHdYK666ipbtXOskdofffRRPrt7HLZIgEREqZDyU2AiolRhAiQix2ICJCLHYgIkIsdiAiQix2ICJCLHYgIkIsdiAiQix/r/y2shHE23DgUAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rGOEHcyGokD0"
      },
      "source": [
        "Let us look at the top 10 ngrams for each text."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dk2TkzTno8vb"
      },
      "source": [
        "from IPython.core.debugger import set_trace\n",
        "\n",
        "def ind2tup(ind):\n",
        "  ind = int(ind)\n",
        "  i = int(ind/26)\n",
        "  j = int(ind%26)\n",
        "  return (chr(ord('a')+i), chr(ord('a')+j))\n",
        "\n",
        "def ShowTopN(bifreq, n=10):\n",
        "  f = bifreq.flatten()\n",
        "  arg = np.argsort(-f)\n",
        "  for ii in range(n):\n",
        "    print(f'{ind2tup(arg[ii])} : {f[arg[ii]]}')\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_HeWNh_q0QZ1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6ec1a483-b059-49d7-ce52-8b9ffc34cd52"
      },
      "source": [
        "print('\\nEnglish 1:')\n",
        "ShowTopN(bieng1)\n",
        "print('\\nEnglish 2:')\n",
        "ShowTopN(bieng2)\n",
        "print('\\nFrench 1:')\n",
        "ShowTopN(bifr1)\n",
        "print('\\nFrench 2:')\n",
        "ShowTopN(bifr2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "English 1:\n",
            "('t', 'h') : 836.0\n",
            "('h', 'e') : 694.0\n",
            "('e', 's') : 659.0\n",
            "('i', 'n') : 587.0\n",
            "('a', 'n') : 523.0\n",
            "('e', 'r') : 467.0\n",
            "('r', 'e') : 450.0\n",
            "('r', 'a') : 441.0\n",
            "('a', 'l') : 398.0\n",
            "('n', 'd') : 384.0\n",
            "\n",
            "English 2:\n",
            "('t', 'h') : 1482.0\n",
            "('a', 'n') : 1366.0\n",
            "('h', 'e') : 1194.0\n",
            "('i', 'n') : 1013.0\n",
            "('n', 't') : 828.0\n",
            "('e', 'r') : 803.0\n",
            "('e', 's') : 759.0\n",
            "('r', 'e') : 755.0\n",
            "('l', 'e') : 720.0\n",
            "('h', 'a') : 715.0\n",
            "\n",
            "French 1:\n",
            "('e', 's') : 735.0\n",
            "('l', 'e') : 437.0\n",
            "('e', 'n') : 410.0\n",
            "('d', 'e') : 388.0\n",
            "('o', 'n') : 349.0\n",
            "('n', 't') : 328.0\n",
            "('r', 'e') : 314.0\n",
            "('e', 'l') : 302.0\n",
            "('s', 'e') : 254.0\n",
            "('l', 'a') : 244.0\n",
            "\n",
            "French 2:\n",
            "('e', 's') : 1036.0\n",
            "('n', 't') : 795.0\n",
            "('d', 'e') : 657.0\n",
            "('e', 'n') : 650.0\n",
            "('l', 'e') : 625.0\n",
            "('a', 'n') : 557.0\n",
            "('r', 'e') : 485.0\n",
            "('o', 'n') : 484.0\n",
            "('e', 'l') : 442.0\n",
            "('s', 'e') : 390.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## At times, we need to reduce the number of features. We will discuss this more in the upcoming sessions, but a small example has been discussed here. Instead of using each unique token (a word) as a feature, we reduced the number of features by using 1-gram and 2-gram of characters as features."
      ],
      "metadata": {
        "id": "RfwwQj_4CyBA"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6kDovOP4l98z"
      },
      "source": [
        "We observe that the bigrams are similar across different topics but different across languages. Thus, the bigram frequency is a good feature for distinguishing languages, but not for distinguishing topics.\n",
        "\n",
        "Thus, we were able to convert a many-dimensional input (the text) to 26 dimesions (unigrams) or 26*26 dimensions (bigrams).\n",
        "\n",
        "\n",
        "A few ways to explore:\n",
        "1. Try with different languages.\n",
        "2. The topics we used are quite similar, wikipedia articles of 'elephant' and 'giraffe'. What happens if we use very different topics? What if we use text from another source than Wikipedia?\n",
        "3. How can we use and visualize trigrams and higher n-grams?"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Features of Images.\n",
        "### Images in digital format are stored as numeric values, and hence we can use these values as features. for ex : a black and white (binary) image is stored as an array of 0  and 255 or 0 and 1."
      ],
      "metadata": {
        "id": "CpA1eKZiDjTm"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2ZJfjIHk-oHV"
      },
      "source": [
        "# Part 2: Written numbers\n",
        "\n",
        "We will use a subset of the MNIST dataset. Each input character is represented in a 28*28 array. Let us see if we can extract some simple features from these images which can help us distinguish between the digits.\n",
        "\n",
        "Load the dataset:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yNsLJSr6wGY0",
        "outputId": "abb82824-82ce-4b1f-e65c-ac3c3381051d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "from keras.datasets import mnist\n",
        "\n",
        "#loading the dataset\n",
        "(train_X, train_y), (test_X, test_y) = mnist.load_data()\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
            "11493376/11490434 [==============================] - 0s 0us/step\n",
            "11501568/11490434 [==============================] - 0s 0us/step\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jVNr144WAUZO"
      },
      "source": [
        "Extract a subset of the data for our experiment:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P3MN8ddxAASZ"
      },
      "source": [
        "no1 = train_X[train_y==1,:,:] ## dataset corresponding to number = 1.\n",
        "no0 = train_X[train_y==0,:,:] ## dataset corresponding to number = 0."
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ePXCs0qyCLpc"
      },
      "source": [
        "Let us visualize a few images here:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BQeyZSh-Arpc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 205
        },
        "outputId": "4dbc3a94-3663-4a93-ecf0-b8eb7f208910"
      },
      "source": [
        "for ii in range(5):\n",
        "  plt.subplot(1, 5, ii+1)\n",
        "  plt.imshow(no1[ii,:,:])\n",
        "plt.show()\n",
        "for ii in range(5):\n",
        "  plt.subplot(1, 5, ii+1)\n",
        "  plt.imshow(no0[ii,:,:])\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 5 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a = no1>0\n",
        "a.shape, no1.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "n2UFfFWhCYzT",
        "outputId": "7bfdb9d0-2119-4a7c-c46f-99dec0ca9bdd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((6742, 28, 28), (6742, 28, 28))"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## to help you understand how the np.sum is working to find count of pixels that are not zero.\n",
        "\n",
        "mtx = np.arange(8).reshape(2,2,2)\n",
        "a = mtx>1\n",
        "a[0][0][0]\n",
        "type(a[0][0][0])\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LHjttKNkDK29",
        "outputId": "518bf4fb-f8c1-44f8-ded2-e5bb7c9f42d9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "numpy.bool_"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## We can even use value of each pixel as a feature. But let us see how to derive other features."
      ],
      "metadata": {
        "id": "2_1n_KXkE3zg"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1g-Tg7EKDz96"
      },
      "source": [
        "Now, let us start with a simple feature: the sum of all pixels and see how good this feature is."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I8SztDk7CyZc"
      },
      "source": [
        "## sum of pixel values.\n",
        "\n",
        "sum1 = np.sum(no1>0, (1,2)) # threshold before adding up\n",
        "sum0 = np.sum(no0>0, (1,2))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8oW3XCOCE7Zv"
      },
      "source": [
        "Let us visualize how good this feature is: (X-axis is mean, y-axis is the digit)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "sum1.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LDz2vOp_GAZr",
        "outputId": "29c82f59-420d-4022-8152-a58b5e825b74"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(6742,)"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i8PIe8o_DPpU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        },
        "outputId": "5c8e1ac8-96dd-4e5c-e609-bf6b8c8d4540"
      },
      "source": [
        "plt.hist(sum1, alpha=0.7);\n",
        "plt.hist(sum0, alpha=0.7);\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7_hToEepFtl2"
      },
      "source": [
        "We can already see that this feature separates the two classes quite well.\n",
        "\n",
        "Let us look at another, more complicated feature. We will count the number black pixels that are surrounded on four sides by non-black pixels, or \"hole pixels\"."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HwEnlm6RFFej"
      },
      "source": [
        "def cumArray(img):\n",
        "  img2 = img.copy()\n",
        "  for ii in range(1, img2.shape[1]):\n",
        "    img2[ii,:] = img2[ii,:] + img2[ii-1,:]  # for every row, add up all the rows above it.\n",
        "  #print(img2)\n",
        "  img2 = img2>0\n",
        "  #print(img2)\n",
        "  return img2\n",
        "\n",
        "def getHolePixels(img):\n",
        "  im1 = cumArray(img)\n",
        "  im2 = np.rot90(cumArray(np.rot90(img)), 3) # rotate and cumulate it again for differnt direction\n",
        "  im3 = np.rot90(cumArray(np.rot90(img, 2)), 2)\n",
        "  im4 = np.rot90(cumArray(np.rot90(img, 3)), 1)\n",
        "  hull =  im1 & im2 & im3 & im4 # this will create a binary image with all the holes filled in.\n",
        "  hole = hull & ~ (img>0) # remove the original digit to leave behind the holes\n",
        "  return hole\n",
        "\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iw3HjgnupUEI"
      },
      "source": [
        "Visualize a few:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H0sjr23NYEFe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 391
        },
        "outputId": "02ed8df4-2d0a-45ca-a738-bcbd881ce3d9"
      },
      "source": [
        "imgs = [no1[456,:,:],  no0[456,:,:]]\n",
        "for img in imgs:\n",
        "  plt.subplot(1,2,1)\n",
        "  plt.imshow(getHolePixels(img))\n",
        "  plt.subplot(1,2,2)\n",
        "  plt.imshow(img)\n",
        "  plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAC7CAYAAAB1qmWGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAT7ElEQVR4nO3da1BUZ5oH8D/d6UbRkBYU0oCBcLN6yp0lQmHVpkxWTIIzwaQykywU0SRmTHbMhslqoYVbLBgv2bRS1sQRC7OXzE7GkayZXbKgscllkrKypWgSk2WdJRCwHekOhItR46Bw+uwHxw7sOdhN92n6nNf/70u6n355fd7uJw+Hc+sYWZZlEBGR4ZminQAREWmDDZ2ISBBs6EREgmBDJyISBBs6EZEg2NCJiAQRdkPv6elBaWkpiouLUVpaijNnzmiQFlH0sbbJaMJu6LW1tSgvL4fL5UJ5eTlqamq0yIso6ljbZDQx4VxYNDg4iOLiYhw/fhxmsxmSJGHx4sVobW1FQkJCUHMsufdhHP3wLWRmF4aahq51d7UJuTa9rys11Y6jH74V8s+HW9tL7n0Yvb1e3b9PoRJ1XYC+1xaorm8JZ3Kv14vk5GSYzWYAgNlsRlJSErxeb9ANvbfXCwBwu8+Fk4quibo2UdcFhF/bvb1e//sj6vsk6roA464trIauhe6uNgCANOqJciaRI+raRF2XFq7XNSDu+yTqugDjri2shm6329HX1wdJkvx/lvb398Nutwc9R2Z2Ibq72mC2pISTim5Jox4h16b3daWnp01oqlMVbm1nZhfC7T6n+/cpVKKuC9D32gLVdVgHRRMTE+FwONDS0gIAaGlpgcPhCHp3C5FesbbJiMLe5bJ582ZUVVVh7969iI+Ph9Pp1CIvoqhjbZPRhN3Qs7KycPDgQS1yIdIV1jYZDa8UJSISBBs6EZEg2NCJiATBhk5EJAg2dCIiQbChExEJgg2diEgQbOhERIJgQyciEgQbOhGRINjQiYgEwYZORCQINnQiIkGwoRMRCYINnYhIEGzoRESCYEMnIhIEGzoRkSDC/gq6oqIiWK1WxMbGAgAqKyuxZMmSsBMjijbWNhlN2A0dAHbv3o3c3FwtpiLSFdY2GQl3uRARCUKTLfTKykrIsoz8/HysX78e8fHxWkxLFHWsbTKSGFmW5XAm8Hq9sNvtuHr1KrZv345vv/0WdXV1WuVHFDWsbTKasBv6eB0dHVi7di3ef//9oH8mM7sQ3V1tMFtStEpDV6RRj5Br0/u60tPT0N3Vptl8U63tzOxCuN3ndP8+hUrUdQH6Xlugug5rH/rly5dx8eJFAIAsyzh8+DAcDkc4UxLpAmubjCisfeiDg4OoqKiAJEnw+XzIyspCbW2tVrkRRQ1rm4worIY+f/58NDU1aZULkW6wtsmIeNoiEZEg2NCJiAShyXnoRHTzmht3m2r88Tl/HtTPvzDna9X4rJRRRez1z+9QHfsfPq8i9lH/74P690XCLXQiIkGwoRMRCYINnYhIEGzoRESCYEMnIhIEz3IhusnZZycoYutuzVMd+9xvH/E/vvRfvwAAmGy3q4413ZakQXYTPT9J/Lk/XlTEpPcOqI49uumsIvbDoaPhpKUb3EInIhIEGzoRkSDY0ImIBMGGTkQkCB4UJbrJvZeUpohlHg18q+Bb0r8fiXRCYpp5qzJW8qzq2KU/9CliF5v3TXy+twwA8M2/fqIY29E5T3XeZUMfBcwz0riFTkQkCDZ0IiJBsKETEQmCDZ2ISBBs6EREggh4lovT6YTL5UJvby+am5uRm5sLAOjp6UFVVRXOnz8Pm80Gp9OJjIyMSOdLpJmbrbZ/PXepavzOD6rDmlcaOKceb3ldETMXrVCOe79Z9edj4pVnrlz94HPVse9+YFfEHnhoUHWs9fl1ipjl4bWqz+c+rPz5RGlMdd6eEuWNCe78fHq/ZCPgFvqyZcuwf/9+pKamTojX1taivLwcLpcL5eXlqKmpiViSRJHA2ibRBGzoBQUFsNsn/vYbHBzE6dOnUVJSAgAoKSnB6dOnMTQ0FJksiSKAtU2iCenCIq/Xi+TkZJjNZgCA2WxGUlISvF4vEhKUd267ke6uNgCANOoJJRVDEHVtIq5Lq9q+XteAmO8TAFiScib8V+F76rt4FAoeCTzmT+J+qh5/NOgZgjPpmm7gjo/fU8QkLZKZgqhfKZqZXYjurjaYLSnRTiUipFGPkGvT+7rS09MmNNXplpldCLf7nK7ep8n2of/4E+U+9BjzjVuDJSkHo/2dAMTYh26+Pcv/ePza1MiT7EP/ahr2oQeq65Aaut1uR19fHyRJgtlshiRJ6O/vV/z5Stoa8ajfs3lGypKw5wh3XlGIUttb7crm/ePj6gc/AzXv8cZOvQMAsDyQ439cuOpXqmNPDynvO26frWxG3kvqu7MsKnmZYtT3El8Z61AGX1MdijLXPkXsn1u+OyhqScqB1NcDADAn36mcYJIc4h2yMqj++ydiQjptMTExEQ6HAy0tLQCAlpYWOByOKe9uIdIb1jYZWcBfzdu2bUNraysGBgawevVq2Gw2HDp0CJs3b0ZVVRX27t2L+Ph4OJ3O6ciXSDOsbRJNwIZeXV2N6mrln2pZWVk4ePBgRJIimg6sbRINrxQlIhIEGzoRkSCiftoihW8qZ66EO+/NeOaLnu2wF6nG/+btpxSxqZzNMhlTTqHi8euxR1TH5kN5lstkZ7SoGZ3k9MBwNXqOK2KP3j/T//iRrx7A2/f/EgBQ8vmLirHSp+rrTXzjfzXJLxzcQiciEgQbOhGRINjQiYgEwYZORCQIHhQlMogFc9IUMbWDnwBgnpeuiF167hnVsfd9pDz4uNWn/LcAwDXz2uXtr5x5AxuX7gQA/NuFLtWxRvJp7HePHxn3/AdfuxVjzXkPqM5RlvKBIqZ2ADaSuIVORCQINnQiIkGwoRMRCYINnYhIEDwoOgW8l/jE92D8Y1HXqyfzLPGKmCkhVWWkuqNH1e/pfmroQ0VsBbpvONcrAPb0RuYK5WjY7vnA/3jLuOcbf3lZMTZ2w07VOervPq+INU7zPd64hU5EJAg2dCIiQbChExEJgg2diEgQbOhERIII6iwXp9MJl8uF3t5eNDc3Izc3FwBQVFQEq9WK2Nhr18lWVlZiyRKe7UDGYLS6LrolWRGb7B7nY8feUsR+NnZa85xE987rcYpYyQb1sTM2bVIGDz6lbUIBBNXQly1bhieeeAKPP/644rXdu3f7/0cgMhLWNYkmqIZeUFAQ6TyIph3rmkQT9oVFlZWVkGUZ+fn5WL9+PeLjlRc/3Eh3VxsAQBr1hJuKroxfj2hru84yL8v/WLQ1alXXQHTeG8tDlYrYmUFlLByifebjhbI2S1KOJvOEI6yGvn//ftjtdly9ehXbt2/Hli1bUFdXN6U5MrML0d3VBrMlJZxUpkUoV4pKox7N1hap7w4NhWVeFka//tL/XG9Xiqanp01oqlOhVV273ec0/fxrUpYqYn93YrPqWLV96I7Vr6uO/cOFr6eci5br0pvxa3sz8S8Vr6t9zygASH09itisRU9pmVrAug6rodvt1y4ltlqtKC8vx9q1a8OZTjf01Dj1ZvwvKr01ca3ota6fvaM36LFjHyprOJTGfbOYaYlVfV5ckxj0HL7fH9M0p1CEfNri5cuXcfHiRQCALMs4fPgwHA6HZokRRQPrmowsqC30bdu2obW1FQMDA1i9ejVsNhsaGhpQUVEBSZLg8/mQlZWF2traSOdLpBnWNYkmqIZeXV2N6upqRbypqUnzhIimC+uaRMMrRYmIBMGGTkQkCH7BBZFBzF40O+ixvsFvI5iJeB6dt0j1ueXRnynGyj6f6hzHKv5b+8SmiFvoRESCYEMnIhIEGzoRkSDY0ImIBMGDojQpUS/tN6oZ1a8og7L6Abpfv3u7SpT3QweAEvsiRayh5a9v+Hy8kRrlgVIAuH+IB0WJiEgjbOhERIJgQyciEgQbOhGRINjQiYgEwbNcVEx2doeoX3zBs1mMYeBHP1HE5v72H1XHPr3n+4rYf1YMqI5996vPw0tMp0wx6turuxP/qIiZk+9UfS5fVY790WFZg+wig1voRESCYEMnIhIEGzoRkSDY0ImIBBHwoOjw8DA2btyIs2fPwmq1Ij09HVu2bEFCQgJOnTqFmpoaXLlyBampqdi5cycSE4P/lmyjUTt4aLQDpTwA+h2j1fbPz9oVsa2T3Jv7lr94RBF7Y8nbqmPnvancrvNNcksBvcq4LVkR+/Sv1G5/AMzcvDvoecdcv1LEftfXHnxi0yzgFnpMTAzWrFkDl8uF5uZmzJ8/H3V1dfD5fNiwYQNqamrgcrlQUFCAurq66ciZSBOsbRJNwIZus9mwePFi//O8vDx4PB60t7cjNjYWBQUFAICysjIcOXIkcpkSaYy1TaKZ0j50n8+HAwcOoKioCF6vFykpKf7XEhIS4PP5cP78ec2TJIo01jaJYEoXFm3duhVxcXFYuXIl3nnnHU0S6O5qAwBIox5N5tOL8evR09q0zEVP6wqX1rV9va4B/bxPtt/8TjU++pvQ5tPLuiLBkpRz7b8/Ue5qk1RiehF0Q3c6nXC73WhoaIDJZILdbofH890HOjQ0BJPJBJvNNqUEMrML0d3VBrMlJfBgHZrsoOj1g4/SqEeztWlxAFarg6JarisS0tPTJjTVG4lEbWdmF8LtPqfp+1SZcq8itvX4ZtWxMSblH9/f/u2zqmPnvdmpiAU6KKq3z1/Lg6KWpByM9l97T0ab9ylev/WnIf4G1ECgug6qoe/atQvt7e149dVXYbVaAQALFy7EyMgITp48iYKCAjQ2NmL58uXaZG0g03nWCM9Q0Z6RarvO86Eitq5UvUknHvwnRWzWz19VHdv+cYUitrT/D6pj+y4N3yjFkMy0xKrGi+f+mSL2D3FXVcfecXC9Ivb/L+e/Eelrt/+xJSnH/9yxoTXoOfQgYEPv7OzEvn37kJGRgbKyMgBAWloa6uvrsWPHDtTW1k44tYvIKFjbJJqADT0nJwcdHR2qry1atAjNzc2aJ0U0HVjbJBpeKUpEJAg2dCIiQfB+6EQGdvf/XFCNryj8+ynMojx75+5b1Q9U/vulE1OYNzjfu22+any+KU4R2zuijAEAVvxLWDm0jw35H7977j6UFO8AAJy7qH4Peb3iFjoRkSDY0ImIBMGGTkQkCDZ0IiJBsKETEQmCZ7kQGdiZb/pU47+YJK5HHw90qcehHp8Oev4SixvhFjoRkSDY0ImIBMGGTkQkCDZ0IiJBsKETEQmCDZ2ISBBs6EREgmBDJyISBBs6EZEgAl4pOjw8jI0bN+Ls2bOwWq1IT0/Hli1bkJCQgAULFiA3NxemP33D+I4dO7BgwYKIJ02kBdY2iSZgQ4+JicGaNWuwePFiAIDT6URdXR1eeuklAEBjYyNmzZoV2SyJIoC1TaIJuMvFZrP5Cx4A8vLy4PF4IpoU0XRgbZNopnRzLp/PhwMHDqCoqMgfW7VqFSRJwj333IOKigpYrVbNkySKNNY2iSBGlmU52MEvvvgi+vr6sGfPHphMJni9Xtjtdly6dAkbNmxAbm4u1q1bF8l8iSKCtU0iCHoL3el0wu12o6GhwX+gyG63AwBmz56Nxx57DK+99tqUE8jMLkR3VxvMlpQp/6wRSKMeIdem93Wlp6ehu6stqLGRqO3M7EK43ed0/z6FStR1AfpeW6C6Duq0xV27dqG9vR319fX+Pzu/+eYbjIyMAADGxsbgcrngcDg0SJlo+rC2SSQBt9A7Ozuxb98+ZGRkoKysDACQlpaGNWvWoKamBjExMRgbG8Ndd92FF154IeIJE2mFtU2iCdjQc3Jy0NHRofpac3Oz5gkRTRfWNomGV4oSEQmCDZ2ISBBs6EREgmBDJyISBBs6EZEg2NCJiATBhk5EJIgp3ZwrElJTr11inZ6eFuVMIkfUtel5XdfrSg//vp7fp3CIui5Av2sLVNdTujkXERHpF3e5EBEJgg2diEgQbOhERIJgQyciEgQbOhGRINjQiYgEwYZORCQINnQiIkGwoRMRCSLqDb2npwelpaUoLi5GaWkpzpw5E+2UQuJ0OlFUVIQFCxbgiy++8MeNvr7h4WE888wzKC4uxooVK/D8889jaGgIAHDq1Ck89NBDKC4uxtNPP43BwcEoZ6sfRv/cx2NtG6i25ShbtWqV3NTUJMuyLDc1NcmrVq2KckahOXHihOzxeOSlS5fKHR0d/rjR1zc8PCwfO3bM//zll1+WN23aJEuSJN93333yiRMnZFmW5fr6ermqqipaaeqO0T/38VjbxqntqDb0gYEBOT8/Xx4bG5NlWZbHxsbk/Px8eXBwMJpphWV80Yu4viNHjshPPvmk/Nlnn8kPPvigPz44OCjn5eVFMTP9EPFzl2XWthFEdZeL1+tFcnIyzGYzAMBsNiMpKQlerzeaaWlGtPX5fD4cOHAARUVF8Hq9SElJ8b+WkJAAn8+H8+fPRzFDfRDtc1cj2hpFqe2o70Mn49i6dSvi4uKwcuXKaKdCpClRajuq90O32+3o6+uDJEkwm82QJAn9/f2w26N7L2utiLQ+p9MJt9uNhoYGmEwm2O12eDwe/+tDQ0MwmUyw2WxRzFIfRPrcJyPSGkWq7ahuoScmJsLhcKClpQUA0NLSAofDgYSEhGimpRlR1rdr1y60t7ejvr4eVqsVALBw4UKMjIzg5MmTAIDGxkYsX748mmnqhiif+42IskbRajvqX3Dx5ZdfoqqqChcuXEB8fDycTicyMzOjmVJItm3bhtbWVgwMDGDOnDmw2Ww4dOiQ4dfX2dmJkpISZGRkYMaMGQCAtLQ01NfX45NPPkFtbS2uXLmC1NRU7Ny5E3Pnzo1yxvpg9M99PNa2cWo76g2diIi0wYOiRESCYEMnIhIEGzoRkSDY0ImIBMGGTkQkCDZ0IiJBsKETEQmCDZ2ISBD/B4mURkWJh7VvAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vS-4erNXtxMi"
      },
      "source": [
        "Now let us plot the number of hole pixels and see how this feature behaves"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Dpm1dRgsety8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        },
        "outputId": "db88e6ba-b246-4d6b-bff6-f50b30764c85"
      },
      "source": [
        "hole1 = np.array([getHolePixels(i).sum() for i in no1])\n",
        "hole0 = np.array([getHolePixels(i).sum() for i in no0])\n",
        "\n",
        "plt.hist(hole1, alpha=0.7);\n",
        "plt.hist(hole0, alpha=0.7);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8UjCBHpJ31yq"
      },
      "source": [
        "This feature works even better to distinguish between one and zero.\n",
        "\n",
        "\n",
        "Now let us try the number of pixels in the 'hull' or the number with the holes filled in:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OSzH26ElXNri"
      },
      "source": [
        "Let us try one more feature, where we look at the number of boundary pixels in each image."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h-2czBypXMwT"
      },
      "source": [
        "def minus(a, b):\n",
        "  return a & ~ b\n",
        "\n",
        "def getBoundaryPixels(img):\n",
        "  img = img.copy()>0  # binarize the image\n",
        "  rshift = np.roll(img, 1, 1)\n",
        "  lshift = np.roll(img, -1 ,1)\n",
        "  ushift = np.roll(img, -1, 0)\n",
        "  dshift = np.roll(img, 1, 0)\n",
        "  boundary = minus(img, rshift) | minus(img, lshift) | minus(img, ushift) | minus(img, dshift)\n",
        "  return boundary"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u-V688jFerXh",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 391
        },
        "outputId": "8f23d86f-df4e-4b5d-9dea-c87c4077dfb0"
      },
      "source": [
        "imgs = [no1[456,:,:],  no0[456,:,:]]\n",
        "for img in imgs:\n",
        "  plt.subplot(1,2,1)\n",
        "  plt.imshow(getBoundaryPixels(img))\n",
        "  plt.subplot(1,2,2)\n",
        "  plt.imshow(img)\n",
        "  plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kSsxsbCNXcNh",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        },
        "outputId": "8bdc8787-9288-4be6-efb8-0bc5b70c8fcb"
      },
      "source": [
        "bound1 = np.array([getBoundaryPixels(i).sum() for i in no1])\n",
        "bound0= np.array([getBoundaryPixels(i).sum() for i in no0])\n",
        "\n",
        "plt.hist(bound1, alpha=0.7);\n",
        "plt.hist(bound0, alpha=0.7);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WuP04Ao_R0Yz"
      },
      "source": [
        "What will happen if we plot two features together?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "paDGHlFSd5Fu"
      },
      "source": [
        "Feel free to explore the above graph with your mouse.\n",
        "\n",
        "\n",
        "We have seen that we extracted four features from a 28*28 dimensional image.\n",
        "\n",
        "\n",
        "Some questions to explore:\n",
        "1. Which is the best combination of features?\n",
        "2. How would you test or visualize four or more features?\n",
        "3. Can you come up with your own features?\n",
        "4. Will these features work for different classes other than 0 and 1?\n",
        "5. What will happen if we take more that two classes at a time?"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Features from CSV file"
      ],
      "metadata": {
        "id": "gIJdT3tYIMyN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "\n",
        "df = pd.read_csv('/content/sample_data/california_housing_train.csv')"
      ],
      "metadata": {
        "id": "SfR0jKjRI9fx"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df.head()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "9VU02WsOJLs_",
        "outputId": "4d964d36-b399-440a-9b59-9517e870fc9d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   longitude  latitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
              "0    -114.31     34.19                15.0       5612.0          1283.0   \n",
              "1    -114.47     34.40                19.0       7650.0          1901.0   \n",
              "2    -114.56     33.69                17.0        720.0           174.0   \n",
              "3    -114.57     33.64                14.0       1501.0           337.0   \n",
              "4    -114.57     33.57                20.0       1454.0           326.0   \n",
              "\n",
              "   population  households  median_income  median_house_value  \n",
              "0      1015.0       472.0         1.4936             66900.0  \n",
              "1      1129.0       463.0         1.8200             80100.0  \n",
              "2       333.0       117.0         1.6509             85700.0  \n",
              "3       515.0       226.0         3.1917             73400.0  \n",
              "4       624.0       262.0         1.9250             65500.0  "
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-8513b64e-14ff-4ec1-81d6-c714795afa99\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "\n",
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              "\n",
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>longitude</th>\n",
              "      <th>latitude</th>\n",
              "      <th>housing_median_age</th>\n",
              "      <th>total_rooms</th>\n",
              "      <th>total_bedrooms</th>\n",
              "      <th>population</th>\n",
              "      <th>households</th>\n",
              "      <th>median_income</th>\n",
              "      <th>median_house_value</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-114.31</td>\n",
              "      <td>34.19</td>\n",
              "      <td>15.0</td>\n",
              "      <td>5612.0</td>\n",
              "      <td>1283.0</td>\n",
              "      <td>1015.0</td>\n",
              "      <td>472.0</td>\n",
              "      <td>1.4936</td>\n",
              "      <td>66900.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-114.47</td>\n",
              "      <td>34.40</td>\n",
              "      <td>19.0</td>\n",
              "      <td>7650.0</td>\n",
              "      <td>1901.0</td>\n",
              "      <td>1129.0</td>\n",
              "      <td>463.0</td>\n",
              "      <td>1.8200</td>\n",
              "      <td>80100.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-114.56</td>\n",
              "      <td>33.69</td>\n",
              "      <td>17.0</td>\n",
              "      <td>720.0</td>\n",
              "      <td>174.0</td>\n",
              "      <td>333.0</td>\n",
              "      <td>117.0</td>\n",
              "      <td>1.6509</td>\n",
              "      <td>85700.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-114.57</td>\n",
              "      <td>33.64</td>\n",
              "      <td>14.0</td>\n",
              "      <td>1501.0</td>\n",
              "      <td>337.0</td>\n",
              "      <td>515.0</td>\n",
              "      <td>226.0</td>\n",
              "      <td>3.1917</td>\n",
              "      <td>73400.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-114.57</td>\n",
              "      <td>33.57</td>\n",
              "      <td>20.0</td>\n",
              "      <td>1454.0</td>\n",
              "      <td>326.0</td>\n",
              "      <td>624.0</td>\n",
              "      <td>262.0</td>\n",
              "      <td>1.9250</td>\n",
              "      <td>65500.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-8513b64e-14ff-4ec1-81d6-c714795afa99 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-8513b64e-14ff-4ec1-81d6-c714795afa99');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df.columns\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XCeIl4kMJc59",
        "outputId": "901067be-45ac-4c64-a890-f5ed5c85326a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Index(['longitude', 'latitude', 'housing_median_age', 'total_rooms',\n",
              "       'total_bedrooms', 'population', 'households', 'median_income',\n",
              "       'median_house_value'],\n",
              "      dtype='object')"
            ]
          },
          "metadata": {},
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df = df.rename(columns={'oldName1': 'newName1', 'oldName2': 'newName2'})\n"
      ],
      "metadata": {
        "id": "foQSY_tvJOua"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "import seaborn as sns\n",
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "\n",
        "\n",
        "sns.set(style = \"darkgrid\")\n",
        "\n",
        "fig = plt.figure()\n",
        "ax = fig.add_subplot(111, projection = '3d')\n",
        "\n",
        "x = df['total_bedrooms'][:50]\n",
        "y = df['housing_median_age'][:50]\n",
        "z = df['median_house_value'][:50]\n",
        "\n",
        "ax.set_xlabel(\"total_bedrooms\")\n",
        "ax.set_ylabel(\"housing_median_age\")\n",
        "ax.set_zlabel(\"median_house_value\")\n",
        "\n",
        "ax.scatter(x, y, z)\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "LaSdj2-HItaG",
        "outputId": "b2eb481c-76f5-4b0a-b099-bc1f90c475df"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Task :\n",
        "## Download a CSV file from the internet, upload it to your google drive.\n",
        "## Read the CSV file and plot graphs using different combination of features and write your analysis\n",
        "## Ex : IRIS flower datasaet"
      ],
      "metadata": {
        "id": "vGGbRUz3J8Ju"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5dypbmSwAXXA",
        "outputId": "a6997a5a-f54a-4b33-c0cf-a10a5629b443"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "\n",
        "data = pd.read_csv('/content/drive/MyDrive/Weather Data.csv')"
      ],
      "metadata": {
        "id": "eTQU8VdoAgus"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "data"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "45ht513IBohs",
        "outputId": "5f5821d9-6038-4353-dadc-bd4c9666208d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "             Date/Time  Temp_C  Dew Point Temp_C  Rel Hum_%  Wind Speed_km/h  \\\n",
              "0        1/1/2012 0:00    -1.8              -3.9         86                4   \n",
              "1        1/1/2012 1:00    -1.8              -3.7         87                4   \n",
              "2        1/1/2012 2:00    -1.8              -3.4         89                7   \n",
              "3        1/1/2012 3:00    -1.5              -3.2         88                6   \n",
              "4        1/1/2012 4:00    -1.5              -3.3         88                7   \n",
              "...                ...     ...               ...        ...              ...   \n",
              "8779  12/31/2012 19:00     0.1              -2.7         81               30   \n",
              "8780  12/31/2012 20:00     0.2              -2.4         83               24   \n",
              "8781  12/31/2012 21:00    -0.5              -1.5         93               28   \n",
              "8782  12/31/2012 22:00    -0.2              -1.8         89               28   \n",
              "8783  12/31/2012 23:00     0.0              -2.1         86               30   \n",
              "\n",
              "      Visibility_km  Press_kPa               Weather  \n",
              "0               8.0     101.24                   Fog  \n",
              "1               8.0     101.24                   Fog  \n",
              "2               4.0     101.26  Freezing Drizzle,Fog  \n",
              "3               4.0     101.27  Freezing Drizzle,Fog  \n",
              "4               4.8     101.23                   Fog  \n",
              "...             ...        ...                   ...  \n",
              "8779            9.7     100.13                  Snow  \n",
              "8780            9.7     100.03                  Snow  \n",
              "8781            4.8      99.95                  Snow  \n",
              "8782            9.7      99.91                  Snow  \n",
              "8783           11.3      99.89                  Snow  \n",
              "\n",
              "[8784 rows x 8 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-6cb366aa-c81f-4ac6-9472-38d540def4dd\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Date/Time</th>\n",
              "      <th>Temp_C</th>\n",
              "      <th>Dew Point Temp_C</th>\n",
              "      <th>Rel Hum_%</th>\n",
              "      <th>Wind Speed_km/h</th>\n",
              "      <th>Visibility_km</th>\n",
              "      <th>Press_kPa</th>\n",
              "      <th>Weather</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1/1/2012 0:00</td>\n",
              "      <td>-1.8</td>\n",
              "      <td>-3.9</td>\n",
              "      <td>86</td>\n",
              "      <td>4</td>\n",
              "      <td>8.0</td>\n",
              "      <td>101.24</td>\n",
              "      <td>Fog</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1/1/2012 1:00</td>\n",
              "      <td>-1.8</td>\n",
              "      <td>-3.7</td>\n",
              "      <td>87</td>\n",
              "      <td>4</td>\n",
              "      <td>8.0</td>\n",
              "      <td>101.24</td>\n",
              "      <td>Fog</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1/1/2012 2:00</td>\n",
              "      <td>-1.8</td>\n",
              "      <td>-3.4</td>\n",
              "      <td>89</td>\n",
              "      <td>7</td>\n",
              "      <td>4.0</td>\n",
              "      <td>101.26</td>\n",
              "      <td>Freezing Drizzle,Fog</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1/1/2012 3:00</td>\n",
              "      <td>-1.5</td>\n",
              "      <td>-3.2</td>\n",
              "      <td>88</td>\n",
              "      <td>6</td>\n",
              "      <td>4.0</td>\n",
              "      <td>101.27</td>\n",
              "      <td>Freezing Drizzle,Fog</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1/1/2012 4:00</td>\n",
              "      <td>-1.5</td>\n",
              "      <td>-3.3</td>\n",
              "      <td>88</td>\n",
              "      <td>7</td>\n",
              "      <td>4.8</td>\n",
              "      <td>101.23</td>\n",
              "      <td>Fog</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8779</th>\n",
              "      <td>12/31/2012 19:00</td>\n",
              "      <td>0.1</td>\n",
              "      <td>-2.7</td>\n",
              "      <td>81</td>\n",
              "      <td>30</td>\n",
              "      <td>9.7</td>\n",
              "      <td>100.13</td>\n",
              "      <td>Snow</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8780</th>\n",
              "      <td>12/31/2012 20:00</td>\n",
              "      <td>0.2</td>\n",
              "      <td>-2.4</td>\n",
              "      <td>83</td>\n",
              "      <td>24</td>\n",
              "      <td>9.7</td>\n",
              "      <td>100.03</td>\n",
              "      <td>Snow</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8781</th>\n",
              "      <td>12/31/2012 21:00</td>\n",
              "      <td>-0.5</td>\n",
              "      <td>-1.5</td>\n",
              "      <td>93</td>\n",
              "      <td>28</td>\n",
              "      <td>4.8</td>\n",
              "      <td>99.95</td>\n",
              "      <td>Snow</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8782</th>\n",
              "      <td>12/31/2012 22:00</td>\n",
              "      <td>-0.2</td>\n",
              "      <td>-1.8</td>\n",
              "      <td>89</td>\n",
              "      <td>28</td>\n",
              "      <td>9.7</td>\n",
              "      <td>99.91</td>\n",
              "      <td>Snow</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8783</th>\n",
              "      <td>12/31/2012 23:00</td>\n",
              "      <td>0.0</td>\n",
              "      <td>-2.1</td>\n",
              "      <td>86</td>\n",
              "      <td>30</td>\n",
              "      <td>11.3</td>\n",
              "      <td>99.89</td>\n",
              "      <td>Snow</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>8784 rows × 8 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-6cb366aa-c81f-4ac6-9472-38d540def4dd')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
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              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
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              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
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        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "9jFXKm0PBsgZ",
        "outputId": "1884b5aa-e4b4-47e7-eb01-c54eb0ac6ae6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       Date/Time  Temp_C  Dew Point Temp_C  Rel Hum_%  Wind Speed_km/h  \\\n",
              "0  1/1/2012 0:00    -1.8              -3.9         86                4   \n",
              "1  1/1/2012 1:00    -1.8              -3.7         87                4   \n",
              "2  1/1/2012 2:00    -1.8              -3.4         89                7   \n",
              "3  1/1/2012 3:00    -1.5              -3.2         88                6   \n",
              "4  1/1/2012 4:00    -1.5              -3.3         88                7   \n",
              "\n",
              "   Visibility_km  Press_kPa               Weather  \n",
              "0            8.0     101.24                   Fog  \n",
              "1            8.0     101.24                   Fog  \n",
              "2            4.0     101.26  Freezing Drizzle,Fog  \n",
              "3            4.0     101.27  Freezing Drizzle,Fog  \n",
              "4            4.8     101.23                   Fog  "
            ],
            "text/html": [
              "\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Date/Time</th>\n",
              "      <th>Temp_C</th>\n",
              "      <th>Dew Point Temp_C</th>\n",
              "      <th>Rel Hum_%</th>\n",
              "      <th>Wind Speed_km/h</th>\n",
              "      <th>Visibility_km</th>\n",
              "      <th>Press_kPa</th>\n",
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              "      <td>Fog</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1/1/2012 2:00</td>\n",
              "      <td>-1.8</td>\n",
              "      <td>-3.4</td>\n",
              "      <td>89</td>\n",
              "      <td>7</td>\n",
              "      <td>4.0</td>\n",
              "      <td>101.26</td>\n",
              "      <td>Freezing Drizzle,Fog</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1/1/2012 3:00</td>\n",
              "      <td>-1.5</td>\n",
              "      <td>-3.2</td>\n",
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              "      <td>Freezing Drizzle,Fog</td>\n",
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              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1/1/2012 4:00</td>\n",
              "      <td>-1.5</td>\n",
              "      <td>-3.3</td>\n",
              "      <td>88</td>\n",
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              "      <td>Fog</td>\n",
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              "  </tbody>\n",
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              "\n",
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              "\n",
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              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-982758ee-0e6a-47ec-859a-c2ae0312cba5');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
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              "  "
            ]
          },
          "metadata": {},
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data.columns"
      ],
      "metadata": {
        "id": "qoYta7ExgIKN",
        "outputId": "7e0b4155-7c7e-4f76-8555-7bbd84ac30df",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Index(['Date/Time', 'Temp_C', 'Dew Point Temp_C', 'Rel Hum_%',\n",
              "       'Wind Speed_km/h', 'Visibility_km', 'Press_kPa', 'Weather'],\n",
              "      dtype='object')"
            ]
          },
          "metadata": {},
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data = data.rename(columns={'oldName1': 'newName1', 'oldName2': 'newName2'})"
      ],
      "metadata": {
        "id": "-vmO2-SVg1xX"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "import seaborn as sns\n",
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "\n",
        "\n",
        "sns.set(style = \"darkgrid\")\n",
        "\n",
        "fig = plt.figure()\n",
        "ax = fig.add_subplot(111, projection = '3d')\n",
        "\n",
        "x = data['Temp_C'][:50]\n",
        "y = data['Dew Point Temp_C'][:50]\n",
        "z = data['Visibility_km'][:50]\n",
        "\n",
        "ax.set_xlabel(\"Temp_C\")\n",
        "ax.set_ylabel(\"Dew Point Temp_C\")\n",
        "ax.set_zlabel(\"Visibility_km\")\n",
        "\n",
        "ax.scatter(x, y, z)\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "neqtTApGB7RK",
        "outputId": "00434bc3-346a-419d-9e7b-1c990b034005"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "EXPLANATION\n",
        "\n",
        "ANALYSIS FOR ABOVE DATASET\n",
        "\n",
        "From the above data it shows the weather details\n",
        "\n",
        "we have considered the\n",
        "1. X-axis as Temp_C\n",
        "2. Y-axis as Dew Point Temp_C\n",
        "3. Z-axis as Visibility_km\n",
        "\n",
        "we have taken this data from the Internet and uploaded the dataset in the google drive\n",
        "Then we have mounted the data set from google drive to colab\n",
        "We have plotted the data accordingly.\n",
        "We can observe that Increase in Temp_C leads to increase in Visibility_km.\n",
        "We can observe that when Temp_C and and Visibility_km are constant there is a decrease in Dew Point Temp_c"
      ],
      "metadata": {
        "id": "EgTq6c75DkKt"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Augmentation\n",
        "It is a technique to increase the diversity of our training set by applying random (but realistic) transformations, such as image rotation, change of color etc. When we have limited training data, we can augment our data with help of these techniques."
      ],
      "metadata": {
        "id": "UEjCCSQh1d7A"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from keras.datasets import mnist\n",
        "# set randomseed\n",
        "rng = np.random.default_rng(seed=42)\n",
        "from sklearn.utils.extmath import cartesian\n",
        "from skimage.transform import rotate, AffineTransform, warp\n",
        "import math"
      ],
      "metadata": {
        "id": "XePcTeKI1dGJ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "For this lab we will use a subset of MNIST that is very small, to better understand the effect of augmentation."
      ],
      "metadata": {
        "id": "ZP0Z3oOT2Vqo"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#loading the dataset\n",
        "(train_X, train_y), (test_X, test_y) = mnist.load_data()\n",
        "train_X = train_X/255\n",
        "test_X = test_X/255\n",
        "\n",
        "print(\"original data size:\",train_X.shape)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7miTQ_032Rxv",
        "outputId": "daacaff5-e8f7-4cd2-e44a-6f04c297da9a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "original data size: (60000, 28, 28)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(train_X[0].shape,train_y[0])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "79iYoK4a2Y8w",
        "outputId": "2c82980b-2648-487d-a0c9-e1c7d035213e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(28, 28) 5\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.imshow(train_X[0])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "F-ne2Jrl6R3-",
        "outputId": "53e72f59-c2e2-47fa-df83-1bde3482d954"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fb45d24a810>"
            ]
          },
          "metadata": {},
          "execution_count": 63
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "train_X = train_X[::1200,:,:].copy() # subsample. Otherwise it will take too long!\n",
        "train_y = train_y[::1200].copy() # do the same to the labels\n",
        "\n",
        "print(\"Now it is:\", train_X.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "g3YMYR2L6VqQ",
        "outputId": "e7d87d18-de36-4933-de45-647602bad177"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Now it is: (50, 28, 28)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Augmentation 1: rotation\n",
        "Let us try rotating the image a little. We will use skimage library for this."
      ],
      "metadata": {
        "id": "JgN85vRl6847"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.imshow(train_X[2], cmap='gray')\n",
        "plt.show()\n",
        "print(train_X[2].shape)\n",
        "plt.imshow(rotate(train_X[2],45), cmap='gray')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 554
        },
        "id": "jStJv7xG6cNI",
        "outputId": "63212ffe-42b1-48cd-d974-d5effaeb8371"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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SUhJMJpPrHu/y8nIkJSX51QDn+QPD3iZHhN68zfND8qKvr0+6cOGCa33Xrl3S9u3bJUmSJJPJJA0ODnobQpbBYJAASA9aebCspH9K7Yu9sTe5fwaDQTZ7Xg/7tVotli5d6lpPTk5GR0eHt4cRkcL59TFeTqcTBw8eRGpqqutn2dnZcDgcWL58OfLy8qDRaILeJBEFn1/X9n/88cfo7OzEF198AZVKBbvdDr1ej8HBQWzduhUmkwkffvhhKPslomDx9dx8165dUk5OjjQyMjJu/eeff5aysrJ8Hc6F5/zsjb2FpreAz/kBYM+ePWhoaIDNZnMd1t+5cwfDw8MAgNHRUdTX18NsNvsyHBEpgNdz/mvXrmH//v0wGo3IyMgAAMTHxyM3NxdFRUWIiorC6OgoFi9ejPfffz/kDRNRcPB+fh8otS+AvU2WCL3xfn4iGhfDTyQohp9IUAw/kaAYfiJBMfxEgmL4iQTF8BMJiuEnEhTDTyQohp9IUAw/kaAYfiJB+fUxXqEQHx/vtm4wGCLUiTyl9gWwt8l63HvzzJaniN/SS0SRwcN+IkEx/ESCYviJBMXwEwmK4ScSFMNPJCiGn0hQDD+RoBh+IkFF/PJeAGhpaUFBQQFu374NrVYLq9UKo9EY6bYAAKmpqdBoNIiOjgYA5OfnY9myZWHvw2q1or6+Hrdu3UJNTQ1MJhMAZWy7iXpTwrbr6+vDtm3b0NbWBo1GA4PBgJKSEuh0Oly5cgVFRUUYGRnB/PnzsXv3bsTGxiqit6SkJJhMJqhU9/fP5eXlSEpKCm4Dfn+zZghkZ2dL1dXVkiRJUnV1tZSdnR3hjh5asWKF1NTUFOk2pIsXL0odHR2P9KOEbTdRb0rYdn19fdKFCxdc67t27ZK2b98uORwO6cUXX5QuXrwoSZIk2Ww2qaCgQBG9SZIkmUwmaXBwMKTPH/HD/p6eHjQ2NiItLQ0AkJaWhsbGRvT29ka4M2WxWCzQ6/VuP1PKthuvN6XQarVYunSpaz05ORkdHR1oaGhAdHQ0LBYLACAjIwN1dXWK6C1cIn7Yb7fbMWfOHKjVagCAWq1GXFwc7HY7dDpdhLu7Lz8/H5IkISUlBZs3b0ZMTEykWwLAbecvp9OJgwcPIjU1FXa7HfPmzXPVdDodnE6n6/Qpkr09kJ2dDYfDgeXLlyMvL8/1DdnBEvE9v9JVVVXhxIkTOHbsGCRJQklJSaRbmjKUtu1KS0sxc+ZMZGVlRbSP8Xj2dv78efz444+oqqrC9evXYbPZgv6cEQ+/Xq9HZ2cnHA4HAMDhcKCrq0sxh5EP+tBoNMjMzMTly5cj3NFD3Ha+s1qtaG1txWeffQaVSgW9Xu92iN3b2wuVShWRvb5nb8DDbffEE0/g9ddfD8m2i3j4Y2NjYTabUVtbCwCora2F2WxWxGHr0NAQBgYGANz/2uRTp07BbDZHuKuHuO18s2fPHjQ0NMBms7kOnRctWoTh4WFcunQJAHDo0CGsXr1aEb3duXMHw8PDAIDR0VHU19eHZNsp4sM8mpubUVBQgP7+fsTExMBqtWLBggWRbgvt7e3Iy8uDw+GA0+lEYmIiCgsLERcXF/ZeysrKcPr0aXR3d2P27NnQarU4efKkIrbdeL1VVlYqYttdu3YNaWlpMBqNmDFjBoD7n3Bjs9lw+fJlFBcXu031PfXUUxHvLTc3F0VFRYiKisLo6CgWL16MHTt2YNasWUF9fkWEn4jCL+KH/UQUGQw/kaAYfiJBMfxEgmL4iQTF8BMJiuEnEhTDTySo/wO/rmmqHog84gAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(28, 28)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fb45d1aa390>"
            ]
          },
          "metadata": {},
          "execution_count": 65
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "After rotating, the the class of the image is still the same. Let us make a function to rotate multiple images by random angles. We want a slightly different image every time we run this function. So, we generate a random number between 0 and 1 and change it so that it lies between -constraint/2 and +constraint/2"
      ],
      "metadata": {
        "id": "phr4sXEb94Q8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def augRotate(sample, angleconstraint):\n",
        "  if angleconstraint==0:\n",
        "    return sample\n",
        "\n",
        "  print(\"shape of sample before is:\", sample.shape)\n",
        "  print(\"len(sample.shape)\", len(sample.shape))\n",
        "  if len(sample.shape)==2:\n",
        "    sample = np.expand_dims(sample, 0)  # make sure the sample is 3 dimensional\n",
        "    print(\"shape of sample is:\", sample.shape)\n",
        "  angle = rng.random(len(sample)) # generate random numbers for angles\n",
        "  print(\"angle is:\", angle)\n",
        "  angle = (angle-0.5)*angleconstraint # make the random angle constrained\n",
        "  print(\"angle with constraint is:\", angle)\n",
        "  nsample = sample.copy() # preallocate the augmented array to make it faster\n",
        "  for ii in range(len(sample)):\n",
        "    nsample[ii] = rotate(sample[ii], angle[ii])\n",
        "  return np.squeeze(nsample) # take care if the input had only one sample."
      ],
      "metadata": {
        "id": "B3ai_7aN7Csn"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "This function returns a slightly different image each time we call it. So we can increase the number of images in the sample by any multiple."
      ],
      "metadata": {
        "id": "udOWwYj2-Bsy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "sample = train_X[20]\n",
        "angleconstraint = 70\n",
        "# show the original image\n",
        "plt.imshow(sample, cmap='gray')\n",
        "plt.show()\n",
        "plt.subplot(1,3,1)\n",
        "plt.imshow(augRotate(sample, angleconstraint), cmap='gray') # show an augmented image\n",
        "plt.subplot(1,3,2)\n",
        "plt.imshow(augRotate(sample, angleconstraint), cmap='gray') # show another augmented image from the same sample\n",
        "plt.subplot(1,3,3)\n",
        "plt.imshow(augRotate(sample, angleconstraint), cmap='gray') # one more image from the same sample"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 680
        },
        "id": "vyO8Ap9-98LZ",
        "outputId": "46291115-430d-4a2f-fd74-8c5f8ffc0af0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "shape of sample before is: (28, 28)\n",
            "len(sample.shape) 2\n",
            "shape of sample is: (1, 28, 28)\n",
            "angle is: [0.77395605]\n",
            "angle with constraint is: [19.1769234]\n",
            "shape of sample before is: (28, 28)\n",
            "len(sample.shape) 2\n",
            "shape of sample is: (1, 28, 28)\n",
            "angle is: [0.43887844]\n",
            "angle with constraint is: [-4.27850922]\n",
            "shape of sample before is: (28, 28)\n",
            "len(sample.shape) 2\n",
            "shape of sample is: (1, 28, 28)\n",
            "angle is: [0.85859792]\n",
            "angle with constraint is: [25.10185439]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fb45d13c390>"
            ]
          },
          "metadata": {},
          "execution_count": 67
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let us try one more augmentation, Shear: A transformation in which all points along a given line remain fixed while other points are shifted parallel to by a\n",
        " distance proportional to their perpendicular distance from. Shearing a plane figure does not change its area."
      ],
      "metadata": {
        "id": "siEhyuX0AyZP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def shear(sample, amount):\n",
        "  tform = AffineTransform(shear = amount) # create the shear transform\n",
        "  img = warp(sample, tform) # apply the shear\n",
        "  # this makes the digit off-center. Since all the images in the test set are centralized, we will do the same here\n",
        "  col = img.sum(0).nonzero()[0]\n",
        "  row = img.sum(1).nonzero()[0]\n",
        "  if len(col)>0 and len(row)>0:\n",
        "    xshift = int(sample.shape[0]/2 - (row[0]+row[-1])/2)\n",
        "    yshift = int(sample.shape[1]/2 - (col[0]+col[-1])/2)\n",
        "    img = np.roll(img, (xshift, yshift),(0,1))\n",
        "  return img"
      ],
      "metadata": {
        "id": "46nKQ_Qj-Elg"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "sample = train_X[2]\n",
        "plt.imshow(sample, cmap='gray')\n",
        "plt.show()\n",
        "\n",
        "# apply shear\n",
        "plt.imshow(shear(sample, 0.4), cmap='gray')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 536
        },
        "id": "Zae7PZcUBDt8",
        "outputId": "e404ea24-9a91-4b55-ae2e-33641ca12739"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fb45f307a10>"
            ]
          },
          "metadata": {},
          "execution_count": 69
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Let us also see skeletonization of image"
      ],
      "metadata": {
        "id": "4NglWyeSDtxr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from skimage.morphology import skeletonize\n"
      ],
      "metadata": {
        "id": "XQMsvuD5BITy"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "skeleton = skeletonize(train_X[2],method='lee')\n",
        "plt.imshow(skeleton, cmap='gray')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "ze1kf_0BD0YP",
        "outputId": "704a9241-742c-40eb-8cdf-6ac3916d9ab7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fb45f73bd10>"
            ]
          },
          "metadata": {},
          "execution_count": 71
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Structuring elements that are repeatedly used for thinning\n",
        "\n",
        "S1 = np.array([[0,0,0],[-1,1,-1],[1,1,1]]) # -1 for dont care\n",
        "S2 = np.array([[-1,0,0],[1,1,0],[-1,1,-1]])\n",
        "\n",
        "\n",
        "def CheckMatch(window,kernel):\n",
        "  for i in range(window.shape[0]):\n",
        "        for j in range(window.shape[1]):\n",
        "            if kernel[i,j]!=-1 and window[i,j]!=kernel[i,j]:\n",
        "                return False\n",
        "  return True\n",
        "\n",
        "def ApplyKernel(image,kernel): #used\n",
        "  height, width =  image.shape\n",
        "  res = np.copy(image)\n",
        "  for i in range(1,height-1):\n",
        "    for j in range (1,width-1):\n",
        "      window = image[i-1:i+2,j-1:j+2]\n",
        "      #print('window shape',window.shape)\n",
        "      Match_result = CheckMatch(window,kernel)\n",
        "      if (Match_result):\n",
        "        res[i,j]=0\n",
        "  return res\n",
        "\n",
        "\n",
        "\n",
        "def Skeletonization(image):\n",
        "  '''pass binary image'''\n",
        "  #new = np.copy(image)\n",
        "  #old = np.zeros(image.shape,dtype=np.uint8)\n",
        "  count = 1\n",
        "  change = 1000\n",
        "  while (change >0.01):\n",
        "    print('count',count)\n",
        "    new = image\n",
        "    new = ApplyKernel(new,S1)\n",
        "    new = ApplyKernel(new,S2)\n",
        "    new = ApplyKernel(new,np.rot90(S1,1)) #90 degree rotate\n",
        "    new = ApplyKernel(new,np.rot90(S2,1))\n",
        "    new = ApplyKernel(new,np.rot90(S1,2)) # 180 degree rotate\n",
        "    new = ApplyKernel(new,np.rot90(S2,2))\n",
        "    new = ApplyKernel(new,np.rot90(S1,3)) # 270 degree rotate\n",
        "    new = ApplyKernel(new,np.rot90(S2,3))\n",
        "    count+= 1\n",
        "    change = np.mean(np.abs(new-image))\n",
        "    image = new\n",
        "    plt.imshow(new,cmap='gray')\n",
        "    plt.show()\n",
        "  return new"
      ],
      "metadata": {
        "id": "ewpZG5b-D9F3"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "binarized  =( train_X[0] > 0 ).astype(np.uint8)"
      ],
      "metadata": {
        "id": "LwgK5XObNcjD"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "skeleton_five = Skeletonization(binarized)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "oyQrnHghLADQ",
        "outputId": "340e0f93-3795-4ca6-ec37-13551a2fa9c7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "count 1\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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ej6uvr0+S1NfXp3g87ovN1idPnujRo0eSnn5s8qVLlxSPx8uc6l+M3eKcOHFCg4OD6u3tnd90Xr9+vaanp3X9+nVJ0tmzZ7Vjxw5fZHvw4IGmp6clSbOzs+rv7y/K2PnizTxu3bqlzs5OPXz4UNXV1Uomk1q3bl25Y+nPP/9Ue3u70um0MpmM6uvr9dlnn6m2trbkWQ4fPqwrV65ofHxcK1asUCgU0sWLF30xdv+V7dSpU74Yu5s3b6q5uVnRaFTLli2T9PQdbnp7ezUwMKDu7u7npvpWrlxZ9mx79+5VV1eXAoGAZmdntXHjRn366ad66623Cvr6vig/gNIr+2Y/gPKg/IBRlB8wivIDRlF+wCjKDxhF+QGjKD9g1P8A5dQoV/VEO9QAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "count 2\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "count 3\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "count 4\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "count 5\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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kyRM9evRI0tPLJl+8eFGxWKzMqf7B2C3N8ePHNTw8rEQisTB13rBhg2ZmZnTt2jVJ0pkzZ7Rr1y5fZHvw4IFmZmYkSXNzcxocHCzK2Pniwzxu3bql7u5uPXz4UDU1NYrH41q/fn25Y+mPP/5QZ2en0um0MpmMGhoa9Omnn6qurq7kWY4cOaLLly9rYmJCq1atUjAY1IULF3wxdv+V7eTJk74Yu5s3b6q1tVWRSEQrVqyQ9PQTbhKJhIaGhtTb2/vMUt/q1avLnm3//v3q6elRRUWF5ubmtGnTJn3yySd64403Cvr7fVF+AKVX9mk/gPKg/IBRlB8wivIDRlF+wCjKDxhF+QGjKD9g1P8AH1C/YcV04IMAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "1uZdnNdTMpfn"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}