Module7 - Lab3.ipynb

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    "colab": {
      "provenance": [],
      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/lakshmilikithabonthu/Fmml/blob/main/Module7%20-%20Lab3.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Iafzer7pAsvP"
      },
      "source": [
        "## Matrix Factorization (Based on Recommender System Example)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7HGtFwXPAyvW"
      },
      "source": [
        "Matrix factorization is a way to generate latent features when multiplying two different kinds of entities. Collaborative filtering is the application of matrix factorization useful to identify the relationship between items’ and users’ entities in a recommender system."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1Wau9bcSBSGA"
      },
      "source": [
        "Define a set of Users (U), items (D), R size of |U|, and |D|. The matrix |U|\\*|D| includes all the ratings given by users. The goal is to discover K latent features. Given with the input of two matrics matrices P (|U|\\*k) and Q (|D|\\*k), it would generate the product result R."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zy-HbwdABgiD"
      },
      "source": [
        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87U91jxhwdGRDcUnnzlbFjfJIKUgGCOaTbZDZ77mbIHcFneYZxfXPiW38XVy8LIBRMjhw0XX1NHpzb5BAzIMzsYyrnPAyDXRn9wvJgg7LUBJBqNERm+bwcyptduPFTnyP/ydzvfQJcECu0IqtjDzfbYp7xusbD/L7X5xkBkMYxFd2Ynjxj6PPPE3Z83BMwQ3K73kJS9ZWTQVyc3ZGJ4sheE5t22hsqXcSWsODDf1b3NzMyhHlVr7S1/60sFoNyUYjkGmZMyUbzjGQ2zkw1knkzPPbKd1zRzgnC1RnNKWtQ0O3D0fDG5TgvFbhmox/GMf+9jgmOmPdZG51hzGBCOLCLnAIg4CyeybKcE6EazrSHM+wQmCQZ6y+9McUAgGKbonh+yMOx5zTjl2rNMRID/kQo8EQXyf3YICK5kKefIvgupXvOIVs2TDp89o/2/PlWCy714aHyedaDfgBmAgKxXJXkSdDNTecCUGnUFgcjtq5jYIzjOlDo7fuQnXeW0DRTbmzWHpGgfGuDkWJRKGbV4x8qzNjOfKwF0vYnGNuZkKNpzIvo5of/W44wiuEakoE2Yxn/N3TRxans7ASc3ZjA9z52BscIKRcg698fc6oklUT5cEAYjJb30uQMhNbwhm3/UX1ysooi92+Mh2x02gwUnMoavma+50cFwqhIVrHe8w8plOTuZEt7OWaf3Gel8CBbgIbryHB4zmIt+T9IHNOJ95xx5OOnaOz8lBZ49sE+GfR4MrX0H/cq9Szks2/AC5wAEeeawT+chU6T7/Y3OHoJovZBNz6NOS13+uBEO5RUvuDeCgGHwAotzA1QkiW5AZC0ebp/banqljchGX38/tiJV+kIQbmjjLN7/5zUPZC5kRKqNj2M7vmszHzXO5+Y0SURDRhzTWzqGbrtz/4HhKnea3HJKyjxKbRVuZmS4rOzTlQYTuTJfVIRkGAQuODgayNjgg4Tkbg7QmhUgEHXCjF27spEd5LtP0nMlEGSmdIxPEz0Blo+bMwWyzXXh6jvH7ZFrjzSinHb/rd/Qd7rkpbzyOc3Pa7IjTQi5w8HnKLuyLE1PSpauO8T43bNJJek9f564OTK85ZSC6bw7jB0ROj53jPcz02Ox5EQyZ8Heaa5ahpIVYEqCSj0CKjguirO/yH/F9fBFbWCf/OTCac4xzJRgKjzjyAEYgJgKLM6BklJ4QfCba4NgBLTUUJbtRjVMTZc0ReU4BFekhCxGe56bpDI5QT3P6shDPD2KgjDcPwON4EGh65kyBOEjK9qUvfWmIJkUmnB8iW3oBz7ymyk1G6xonhFSUAjlrshPhmqdOJshFZjl31EvWojdRHNnAyfnhyyE5v7Ip2cAsUTsnixTJEYkLGF70ohddfRYU5zJnOW9MMGS9VGMTWcCf6j95yjSRsDkke2FLWZ9RQaB3eXQN24Jbgju/c47TymtzXZs5cbxKl2TFPyzZ6KZOVmztvBp5wByuiIQOp8HdZ8nOfZdMi24L2Ky5sLE8Vdn3x9DOlWAI1k4VEScnqscZETghcCCiVJ2TjzOx2JWIjLPXObhxiWAuwAmPwWXhetOSlVTWjjJOS8ZlI4I5c26cc8pk5iwK5RwZmGM4O07UmoBxlMiWViJ4czIyAdGr7GQdOZgfp4MQE/G6Pj1yzFN9l8goI1e4MTZOVYaJ0OkL4uBURXjmxJl6n7vpHWdeHpBqnrJfspibwEMwyiFLEsw2eh4yosvJ+AVs8KF7ggIRM1x9Llsc6/0259rlWHN6wQteMOg+RzstLe4y5mm/YXf0iB+SCZxXY9+ykNgJrNPoK51BsHQZ2QoCdHbJPtkgHc6tC+x0af8wBzbnSjAUl2At0CoDIZpxBCnaEoEpF3HqebQ8oBEM5yZl97vUn5cmGAYnkkvGdBroIRiOLv/rw/PSPvrRjw5RNKOmSBSFgvibk0dEr3rVqwZj91vjMIRpdHrauXf5zrnNU/SE0E5a9zFPcuGQ4SDijTOPHJOyLzlvskZodAh+yYYFI/BlcL53XZymyJhxyiZvvvLkYhhzaOZPF+fGNxnhIRGMa0y2w6HKAsfrMojQvBP0wNBv9PNwYObEppNtmdvSzbXR07kDjNPmHYJR7uK/ZCNpkQc/ZwMKO1QpCMHQc+SLlNibdlol5bR5nPd350owUXbgMHBAcljj5nNRKMYWzYhCMTunkQV0axscnnTR8XM3pMeBJuOiiJs4Iwbp2rzmXg3RiesUiSj/IRnf64mmRI/Kf7IXzm9JJz3GilNBDLkHguNeh6drSATlWhAuR+UaKT1CXJf5zC2XsbNEFAlQgq1MBa4yQ9kWkjE3/99EOSS168ho7vmRW6L/pUs9J83dHFwfnQ1BRHd9px9SO8Q5LYEPWZAJO6EjU7/nnEg2xMNXKAGHXFRylNIF3fyefmiyXIfbuRLMuglMPyMIJQyOQc0SoEpMHBwWF6n6z5mcY/btT8fY971og0MyD4vy2wrS8eZPibyKOiiMkgTn51p0jtr3XnXZEgXchMz2vUa/54hEj5TV2kkeMTIdO3X8kGIMxVwRznlGgpmbeTs3/MwPvvRE6czfDFP9Otky8iRL17ytPKd4nPSeTgpOyPGiIkxzIJcxwZw0335+WAjwF4JMekuX6ZHqAl9Bn5XO6DzdUlJcFwwe1hVd2Z5/aBPiXDl4XZTM8QISuchaMDmglUJ8tkRjoLnPQPmAcBEDx5XFU59zVAyaYlAGzsXf5msMPbtUlE1kL7kOWYFry6401yGCSfQdR2X8pRrCMF9zQKbZ+rjU+eYc17x1xmdDCL1IWZKMfM4YydF1kY/3S5I3wydT51TeGDeyTa09erMrHsahR9HFjOPaXCN50ruLIP5dr6m/Ww3yIrvoLRnKxBNcW5PmU2Q5PjuGtpz3muHqAR5HC1BOmpMHNOC9X6IlnRUZc1xKdOr4WXxj3Cl9cXLZn+4V8a2LLEJEnFDq3pRlTCCuxw47pZ6MGYJa4jqvhTFhrVwmO6QX1ulgmqzQa9aHlr5ec5FZKcUhOw4/awr0V4AhIqUz+wQOSsf03zXTw3GjL7I1JEe/2o4TAX6CLOlK1kDtMvO5gPdQNpGche5BEwwjTL1SZM9Yvcpk1NenxnXWxW76fRbdjI9c1D4tuuW/EmaxPlmLnSEch3khJ/OmCAzc+5SWTirNyIZ0xMVB5h8KySra1iMQzHxLR7KFPAvWAhOdLHx2HovHIk9ZtzU1MkQwIRm6REeQQjLH9Vd29qf0T/mYo6FzzpGgCKEiuGN5phhcXAMCPi85wStl3kPM8syP/6C/dJvfgBHd8R09gtUxtIMmmCmAnATmHivk9Jg53is9iBCVXtyf4r4PUYS1CuWW1LcZRVJVx1svsjDHuJGOYzk+inKaIhubs0BmMrS2sxEgo/FWZBmm8sLb3va2q5kC2cg64au2bePGPpnDWbMScNx0ZSuqDIPOcA7RVfMlXxsSzGF8w+1Z446/ZwMcjHGy+YUDym5HBJfS8kWtA21zPQIqGbtKgeBx6W3KsNcFbzaJzH1T8DbXvs2xCCVVnOy42+b3F3XsUREMkICcevZSLM4Z5G7b3AGeRzRwIMoPDFoUqSMVEavfMBKO5bWvfe3V9Zcsup4kZOczDqfBeZxHtH3SXI7lc5gpGdz2/1uRZZmve93rVq9//euHz2SckaGyIyes7Lg0wShpkJ8NKOROR+lrZMyh7koukQ0dMQ6dMa5roo/Kc2OCEe0eeiMjz9xiP0hm6d13WRt14yI5HAvB0KlxtncsPuKgCUbaLwoT/Y/LS8lkAK77zrFpIlaG5zhli21r0SEYjgmZuEFPxINcGLDaKBKRmVBSxu1zxmJxlwNg/O9+97uH9YGULJLNZL5KYqJwv+MUlf2cT6aUO9MP3UGc5/zIU4RLPqJe2QnsOFZ4ecqD7NFxuozGugx52H3o/ipyJA+ym7tx6MkmZEyeAGFXm668Yb7Oa452FoZ8fEdvUlv3OZ2n+67BtdG5BFbZsmoLP/1BanTGVndZGp0f28Pc1znneLAgN6W9bOOfc/zpWHDV2bJzH2qjR+QveBjLkl4LspMZpwTvOnzHNtgIXaQ7F90OnmBSKx0TDNAYYRidIKYEw1kDHNC7EoyMQqSjMwCGHKGbD6M3B/eCECzDzx3mIjI3WSIeTi13vIc4jON4DtKCsG2JiPE1r3nN4HwQ17bzvmhlWvr8ZM6hylxkLG5KI2OPf+FcEQ2yj2OGod+EYGBtK3bWzpaar+CDw3djJ/0NeXhSgsahain3mpf1PbqTBV1z1I1DD/zNsST4QVZI03tBjJKs8yEY5z+WZu6uzXWkOrHk3PkDnS2z6UNtiIXcp76Nvkdv+B7fp/ku9sEflmDOkC5D4SREGtY4xo1C+kx3LwSBYO7ssOG8kQAh7apIfi+jcKe9qHDapgQQEnKseaiRG0PZTCQtY0FalILjEbHqIjfz93uEhIRc+5LlnOm1HPL7RO7wQ8ayPU4ZtvRD6YuMgqtXTsvvBBqcNj3JVma/4czojePmbvQijwIhW4SIDOiBuSNHpVcOAQEqd2XBnmPg/Fxb5i/4MIbrgIHsTYZMhzho21bd7+OVUzkmvclmjLllcMzjIUC4CJjoBr1NC4n4jO7SYXrA39ANn+s+YxMX3Q46gwEgQxX9cyjjxliVsDgcRkkgjDBlKiAzVAZn2+Y2jYNCajIPZa1Nyw2IhcF7zQ2WSIYzyHqBaNp4HAhHQBGQCgeR53v5ve+OoYa+Da67HosMOGpY2nTh8S/k4w59pQ4Ew6nDdYwZ2eWfMskeGCBZ+D3C8dy4JQiG7AQmggQRJVlbE9IRnmyF3H2fKJXMZTbIj86aq57jldFS/vBoHJi47he/+MVDhm3Bmh4Zz/najhcBOsx/0G1+TCk0DcHwJbLdlP8FKY4LGcX3+Z8xF932JpjUkaVrMYDcSc1ARGFpWexMVMdhiMriaBmdnhaCARgiEeE7D+NiuKJChuw3SEF2AHhG6RyckFrlto2RMlbzJehNCcbv9JCaa8v9M0pmSiXjG/A4E/N3LnfSIxnXMc2Mtpk/eeiueyyP1Ld9l0ZZHUdO2cXmmslDN5dxCr7NPOY8Fo50RfSfDjNOFYHAa6w3ObcAQ3BCD1yjMegGmcAm96xE/+aas/HojU5XzcP8kITsRRBkPcjnujUhZJFH9giqEpgIomQ75hzd9+qaXP/LX/7y4Rl23jsf+TknJ4VoNtXdua79soyT7JM90SU6KugVQLIln41bfBYdSDY99XsJDMiMb1Du5C/ofG7L8J2/6ZEABcnoucmYnZuD8x1C25tgAOmClYDUhb0CO1s1x9sOGbl0n1C82tYr4lcSYlxZgA0wIlAgxxFydnHSHGOeoou57QYxDz3sz1B3Wchj9HnGFgLY1kgZN+XRXJ+/OURrK+NdMnEwvnM+17dv9Alj5EvhyIODIg9y4qh8l+ZzpOz6KCWZkAXMzFsEdQi7bBiNDOTWW28dMo5bbrnlDhshzpIP586Bw1Z5Seek6Sojdc2u96xxdjFYQZFzJyollzgBtkEfyEwQhUSQnu4YXfRqvqLWOBOBiPJHts1zRr5jJ37DiSFdduDztvkRQOQIhT3xQxw+38OmBBAC3XEjPzrsN47n7+idzu/p5KXRFTqg8XPOxSb5PuREZ/jO+F1rwcY3tnFl5nznIbS9CQagjEPpwq4pTkxLKsd40hgUJ8apxVgQCMfLaBgFgNIYJ/B0zoFzISSOAKAcKHaXyfidc+pKBozafSi7GBjHz7Eay7m2dTwhGHOOIiHVRD25PsfpOYdX7/dpWYPy9GnyUJbRIo8pwSBnikourpui2wElOuZ8D4lgRP1vfOMbB4JB/MkMzsIMcctkQuKul5EiX0RDTkh+WzlvIidOg7EjMIbPVpTIPLAVwZkHx8CROD+d1wUEOsIwX/ojUEEm9BsOdCtZCgzIWKBgXOdMhLvJPHvMdgiEYMjTNut3vetdV9dK+ET+ady8J0/BAp+kpM/v6TaokFcIhh7Qb7JOdcZ3fB+fRx/oLr9nPN+RffScnu267rwdCme9Dvg0AAAE8UlEQVQfvTfBuChAiKgAaB0hjbPTU5aJ4wVa0kNMzaklYxhP2fEMiDA4CMBzBCI3hmRs3zt/hOP3Im+RAUEmkzgbiv8ekfNu85t1x44JZN33S3zGqVAuJKF8gmjTNpGH8h6MyWSX7G+JayJbRohQGE8idrI9i1wyH3qi0wtjIFr6wbBd8xLk4tzRpfHaiMDHe05HJ5eUNBJ4pRwmGhZEKZk5RgRL9xPZuiYtWWoqCQjNdR3CTqIldOKix4Q7fWQj9ImDFwxoyIdMx2Uyx9PX+D1+09owOxPEGWvcEnTGt9ILxwv8YscCbt/nt/yqkvEhZa7XXQFmr3/AAEzK7qLj9AMUYvF9ThGH6zXROqA5RR1QXqfNGIno8srYfG4sY4yJxDjAZ8Q553TMa/U9XHSZ4zbyiEwSMZEDYp8q/kXgRuYpJSEEBMpgd5EtPUUudIcO0pvo36ZktQsGbEAnG3MgHySij23EdZlXjlc2sylBhQDRiFw9reCtb33rUD6m534jC1IaE03rvrNtmcNpmx+ByJI8p+sevovvy5mjq/F7XukdH5Wggh+btqylxu8JJOiL8cmdvSbIMCZ90P2dz6djnuf7vTMYFxGAsOkSzTm6nXEzZBMlUd6l5LHZTOY7yrWIyOdo0dU5xtpmjDgYTkTfpoSBOBCsciZnppzpHivvQ7Y5xpoNsuH49owdt7m8S3cseXLuOp2SGS/Roi+Hsqay7TXuTTDbnrDHF4EisDkCnFeeVIBoRbI2OyitKc+MCQaxZJOAz9dFxJufuUcWgf0RKMHsj2FHKAKLIRCCsaCvXCkzydMifJcNMCmHvvKVrxzW32SvJZjFxNKBN0SgBLMhUD2sCFwEAkjEpgsLvBZvkYYa/HitTblGrd6rY2xyQUh+21YELhKBEsxFot9zF4EzEMhCMIKxI8yicHaQZaeZIay3WA8IweSJEmcM36+LwKIIlGAWhbeDF4H9EMjmADuDPErGw1Dd+6BMlnvMZCoIBQk5RsbjeITTVgQuEoESzEWi33MXgQ0RQBhuytM++MEPDov8SmWazAaxeNyQ+yQs9FuvsVW1rQhcJAIlmItEv+cuAhsiYPu5hXs3JCMUazG5z8HfPrPu4lVZbZcbjDecSg8rAhsjsPeNlhufqQcWgSKwMwK58dINdhb4rb/kPhdlNISCcPTczLfzyfrDIjATAiWYmYDsMEWgCBSBInBHBFqkrUYUgSJQBIrAIgiUYBaBtYMWgSJQBIpACaY6UASKQBEoAosgUIJZBNYOWgSKQBEoAiWY6kARKAJFoAgsgkAJZhFYO2gRKAJFoAiUYKoDRaAIFIEisAgCJZhFYO2gRaAIFIEiUIKpDhSBIlAEisAiCJRgFoG1gxaBIlAEikAJpjpQBIpAESgCiyBQglkE1g5aBIpAESgCJZjqQBEoAkWgCCyCQAlmEVg7aBEoAkWgCJRgqgNFoAgUgSKwCAIlmEVg7aBFoAgUgSJQgqkOFIEiUASKwCIIlGAWgbWDFoEiUASKQAmmOlAEikARKAKLIFCCWQTWDloEikARKAIlmOpAESgCRaAILIJACWYRWDtoESgCRaAIlGCqA0WgCBSBIrAIAiWYRWDtoEWgCBSBIlCCqQ4UgSJQBIrAIgiUYBaBtYMWgSJQBIpACaY6UASKQBEoAosgUIJZBNYOWgSKQBEoAv8He79kD0uZikcAAAAASUVORK5CYII=)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wvsHAiq8BnYk"
      },
      "source": [
        "Matrix P represents the association between a user and the features while matrix Q represents the association between an item and the features. We can get the prediction of a rating of an item by the calculation of the dot product of the two vectors corresponding to u_i and d_j."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yGLuUqPABsj2"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YcI45w46BuXB"
      },
      "source": [
        "To get two entities of both P and Q, we need to initialize the two matrices and calculate the difference of the product named as matrix M. Next, we minimize the difference through the iterations. The method is called gradient descent, aiming at finding a local minimum of the difference."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NEOKwxXGB202"
      },
      "source": [
        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)\n",
        "\n",
        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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AEh6o6AV-HID"
      },
      "source": [
        "import numpy\n",
        "\n",
        "def matrix_factorization(R, P, Q, K, steps=5000, alpha=0.0002, beta=0.02):\n",
        "    '''\n",
        "    R: rating matrix\n",
        "    P: |U| * K (User features matrix)\n",
        "    Q: |D| * K (Item features matrix)\n",
        "    K: latent features\n",
        "    steps: iterations\n",
        "    alpha: learning rate\n",
        "    beta: regularization parameter'''\n",
        "    Q = Q.T\n",
        "\n",
        "    for step in range(steps):\n",
        "        for i in range(len(R)):\n",
        "            for j in range(len(R[i])):\n",
        "                if R[i][j] > 0:\n",
        "                    # calculate error\n",
        "                    eij = R[i][j] - numpy.dot(P[i,:],Q[:,j])\n",
        "\n",
        "                    for k in range(K):\n",
        "                        # calculate gradient with a and beta parameter\n",
        "                        P[i][k] = P[i][k] + alpha * (2 * eij * Q[k][j] - beta * P[i][k])\n",
        "                        Q[k][j] = Q[k][j] + alpha * (2 * eij * P[i][k] - beta * Q[k][j])\n",
        "\n",
        "        eR = numpy.dot(P,Q)\n",
        "        e = 0\n",
        "        for i in range(len(R)):\n",
        "            for j in range(len(R[i])):\n",
        "                if R[i][j] > 0:\n",
        "                    e = e + pow(R[i][j] - numpy.dot(P[i,:],Q[:,j]), 2)\n",
        "                    for k in range(K):\n",
        "                        e = e + (beta/2) * (pow(P[i][k],2) + pow(Q[k][j],2))\n",
        "        # 0.001: local minimum\n",
        "        if e < 0.001:\n",
        "            break\n",
        "\n",
        "    return P, Q.T"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5Wze_fjKCRz5"
      },
      "source": [
        "R = [\n",
        "     [5,3,0,1],\n",
        "     [4,0,0,1],\n",
        "     [1,1,0,5],\n",
        "     [1,0,0,4],\n",
        "     [0,1,5,4],    \n",
        "     [2,1,3,0],\n",
        "    ]\n",
        "\n",
        "R = numpy.array(R)\n",
        "# N: num of User\n",
        "N = len(R)\n",
        "# M: num of Movie\n",
        "M = len(R[0])\n",
        "# Num of Features\n",
        "K = 3\n",
        "\n",
        " \n",
        "P = numpy.random.rand(N,K)\n",
        "Q = numpy.random.rand(M,K)\n",
        "\n",
        " \n",
        "\n",
        "nP, nQ = matrix_factorization(R, P, Q, K)\n",
        "\n",
        "nR = numpy.dot(nP, nQ.T)"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P51JmjVPCg_y"
      },
      "source": [
        "The predicted matrix is generated below. As you can see, the predicted matrix has similar output with the true values, and the 0 ratings are replaced with the prediction based on the similar users’ preferences on movies."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VhPzLvuhCZzo",
        "outputId": "0572306c-f8f2-4d69-8df3-46ed113c8132"
      },
      "source": [
        "print(nR)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[5.01393033 2.90915879 4.25603052 1.00332115]\n",
            " [3.97000038 2.34000291 3.3171867  0.99920929]\n",
            " [1.06687066 0.85945651 5.01872077 4.9719651 ]\n",
            " [0.98162847 0.80596038 3.70600861 3.97912312]\n",
            " [1.66563535 1.10986301 4.95268366 4.0019696 ]\n",
            " [1.89640013 1.15198649 2.99677998 1.7868748 ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JYPp7vZuDF3H"
      },
      "source": [
        "## SVD (Continuing the Recommender System Example)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BxPbbpPODQXY"
      },
      "source": [
        "When it comes to dimensionality reduction, the Singular Value Decomposition (SVD) is a popular method in linear algebra for matrix factorization in machine learning. Such a method shrinks the space dimension from N-dimension to K-dimension (where K < N) and reduces the number of features. SVD constructs a matrix with the row of users and columns of items and the elements are given by the users’ ratings. Singular value decomposition decomposes a matrix into three other matrices and extracts the factors from the factorization of a high-level (user-item-rating) matrix."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wdX2UCYCDw4u"
      },
      "source": [
        "The factorisation of this matrix is done by the singular value decomposition. It finds factors of matrices from the factorisation of a high-level (user-item-rating) matrix. The singular value decomposition is a method of decomposing a matrix into three other matrices as given below:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5BHA_lArDy5g"
      },
      "source": [
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N_HxawLkEFzL"
      },
      "source": [
        "Where A is a m x n utility matrix, U is a m x r orthogonal left singular matrix, which represents the relationship between users and latent factors, S is a r x r diagonal matrix, which describes the strength of each latent factor and V is a r x n diagonal right singular matrix, which indicates the similarity between items and latent factors. The latent factors here are the characteristics of the items, for example, the genre of the music. The SVD decreases the dimension of the utility matrix A by extracting its latent factors. It maps each user and each item into a r-dimensional latent space. This mapping facilitates a clear representation of relationships between users and items. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sJlAQUIWSlU5"
      },
      "source": [
        "## Working with Text 1 : Bag of Words Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2PRkDXxsSyTv"
      },
      "source": [
        "A problem with modeling text is that it is messy, and techniques like machine learning algorithms prefer well defined fixed-length inputs and outputs. Machine learning algorithms cannot work with raw text directly; the text must be converted into numbers. Specifically, vectors of numbers."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oXXl_VVxS8Ip"
      },
      "source": [
        "A bag-of-words model, or BoW for short, is a way of extracting features from text for use in modeling, such as with machine learning algorithms.\n",
        "\n",
        "The approach is very simple and flexible, and can be used in a myriad of ways for extracting features from documents.\n",
        "\n",
        "A bag-of-words is a representation of text that describes the occurrence of words within a document. It involves two things:\n",
        "\n",
        "    A vocabulary of known words.\n",
        "    A measure of the presence of known words.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cJNr4iHKTmOv"
      },
      "source": [
        "Let's try BoW model on an example\n",
        "\n",
        "The sentences are - \n",
        "\n",
        "1.   grey is a dull color\n",
        "2.   orange is a fruit\n",
        "3.   orange is a colour\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ep8b9b7wCtu2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "85500cb8-d7c6-45f9-9732-86eeb35d8cbb"
      },
      "source": [
        "sentences = [[\"grey\", \"is\", \"a\", \"dull\", \"colour\"], [\"orange\", \"is\", \"a\", \"fruit\"], [\"orange\", \"is\", \"a\", \"colour\"]]\n",
        "# Add your sentences here and see the embeddings\n",
        "\n",
        "# The vocabulary is - \n",
        "# vocabulary = [\"grey\", \"is\", \"a\", \"dull\", \"colour\", \"orange\", \"fruit\"]\n",
        "\n",
        "vocabulary = []\n",
        "for sentence in sentences:\n",
        "  for word in sentence:\n",
        "    if word not in vocabulary:\n",
        "      vocabulary.append(word)\n",
        "\n",
        "print(vocabulary)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "['grey', 'is', 'a', 'dull', 'colour', 'orange', 'fruit']\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Mi5MGLXUUpo"
      },
      "source": [
        "Now we need to find which words occur in a given sentence and hence assign each sentence a corresponding vector based upon multiple metrics.\n",
        "\n",
        "This can be done in a few ways :\n",
        "1. Boolean count of whether the word occurs in a sentence\n",
        "2. Counts of each word that occurs in a sentence\n",
        "3. Frequency of words out of all oher words in a sentence\n",
        "4. TF-IDF (will be covered in next lab)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Rvokt1ZmUJsa"
      },
      "source": [
        "# We shall implement point 2 now\n",
        "\n",
        "bow_sentences = []\n",
        "\n",
        "for sentence in sentences:\n",
        "  bow_representation = [0 for i in range(len(vocabulary))]\n",
        "  for indx, word in enumerate(vocabulary):\n",
        "    if word in sentence:\n",
        "      bow_representation[indx]+=1\n",
        "  bow_sentences.append(bow_representation)"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iUZEFrN8W_Rb",
        "outputId": "c6efe876-b4ac-41b8-aa0a-9ee111988c90"
      },
      "source": [
        "print(bow_sentences)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1, 1, 1, 1, 1, 0, 0], [0, 1, 1, 0, 0, 1, 1], [0, 1, 1, 0, 1, 1, 0]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bt7b5JhbXHjj"
      },
      "source": [
        "**You can now try to add your sentences and see how it works!**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qLEr5EK0XPH1"
      },
      "source": [
        "## Working with Text 2 : LSI (Latent Semantic Indexing)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L9b76qrJYHFH"
      },
      "source": [
        "Now, we will introduce an indexing and retrieval method: the Latent Semantic Indexing (LSI). It uses a mathematical technique called singular value decomposition (SVD) to identify patterns in the relationships between the terms and concepts contained in a corpus (unstructured collection of documents).\n",
        "\n",
        "Latent Semantic Indexing is a common technique in the NLP field. It is used to analyze relationships between a set of documents and the terms they contain in order to produce a set of concepts related to the documents and terms."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DKGOSpS1YPrz"
      },
      "source": [
        "LSI is based on the distributional hypothesis which states that words that are close in meaning will occur in similar pieces of text. The starting point is the representation matrix $A$ of the distribution of the words within the set of documents. It is a $m * n$ matrix where $m$ is the number of unique words and $n$ is the corpus cardinality. The element $a_{ij}$ represents the frequency of the word $i$ in the document $j$.\n",
        "\n",
        "Singular Value Decomposition (SVD) is consequently applied to the matrix A in order to reduce the dimensionality of the data."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H7_wuOReY0ah"
      },
      "source": [
        "The SVD computes the term and document vector spaces by approximating the single term-frequency matrix $A$ as follows:\n",
        "\n",
        "$$\n",
        "A \\approx TSD^T\n",
        "$$\n",
        "\n",
        "where $T$ is the $m * r$ term-concept vector matrix, $S$ is the $r * r$ singular values matrix, $D$ is the $n * r$ concept-document vector matrix, such that\n",
        "\n",
        "$$\n",
        "T^{T}T = I_r \\\\\n",
        "D^{T}D = I_r \\\\\n",
        "S_{11}\\ge S_{22}\\ge ... \\ge S_{rr} \\ge 0 \\\\ S_{ij}=0 \\hspace{1cm} \\forall i \\ne j\n",
        "$$\n",
        "\n",
        "The next step is to truncate the SVD and keep only the largest $k$ << $r$ diagonal entries in the singular value matrix $S$, where $k$ is typically on the order 100 to 300 dimensions. This effectively reduces the term matrix $T$ size to $m * k$ and the document matrix $D$ size to $n * k$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cNNb2E9IqAU8"
      },
      "source": [
        "Let us now get started with the code! Note that we will use a library **gensim**, which does most of the hard work for us."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IaUepUbPXDXK",
        "outputId": "33086f37-ab95-454c-b5ce-6fd873001008"
      },
      "source": [
        "# Install requires lirbaries\n",
        "\n",
        "!pip install --upgrade gensim\n",
        "import pandas as pd\n",
        "import gensim\n",
        "from gensim.parsing.preprocessing import preprocess_documents"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Requirement already satisfied: gensim in /usr/local/lib/python3.9/dist-packages (4.3.1)\n",
            "Requirement already satisfied: scipy>=1.7.0 in /usr/local/lib/python3.9/dist-packages (from gensim) (1.10.1)\n",
            "Requirement already satisfied: smart-open>=1.8.1 in /usr/local/lib/python3.9/dist-packages (from gensim) (6.3.0)\n",
            "Requirement already satisfied: numpy>=1.18.5 in /usr/local/lib/python3.9/dist-packages (from gensim) (1.22.4)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KChn5d4Uk2Gd",
        "outputId": "4a99661a-bfbe-4ce6-ea68-353b3ca9d203"
      },
      "source": [
        "!curl -L -o 'movies.csv' 'https://drive.google.com/uc?export=download&id=1F9l2PUvLtmd75_VFrqNnH-x_AR7zIhQW'"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current\n",
            "                                 Dload  Upload   Total   Spent    Left  Speed\n",
            "  0     0    0     0    0     0      0      0 --:--:--  0:00:07 --:--:--     0"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NozEZe9Dbcqz"
      },
      "source": [
        "df = pd.read_csv('movies.csv', sep=',', usecols = ['Release Year', 'Title', 'Plot'])\n",
        "df = df[df['Release Year'] >= 2000] # Use a subset of the data\n",
        "text_corpus = df['Plot'].values # Get the movie plots"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0pQSHl6SbxHZ"
      },
      "source": [
        "print(text_corpus)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yCbeuHM7bw4x"
      },
      "source": [
        "processed_corpus = preprocess_documents(text_corpus) # Preprocess the text\n",
        "dictionary = gensim.corpora.Dictionary(processed_corpus) \n",
        "bow_corpus = [dictionary.doc2bow(text) for text in processed_corpus] # Find the BoW representations"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a2Lt8O52j0iM"
      },
      "source": [
        "tfidf = gensim.models.TfidfModel(bow_corpus, smartirs='npu') # Perform TF-IDF to get the matrix\n",
        "corpus_tfidf = tfidf[bow_corpus]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gWsfVTL6j3Nj"
      },
      "source": [
        "lsi = gensim.models.LsiModel(corpus_tfidf, num_topics=1000) # Perform LSI\n",
        "index = gensim.similarities.MatrixSimilarity(lsi[corpus_tfidf])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "btVKvUuBj_GX"
      },
      "source": [
        "new_doc = \"In the arcade at night the video game characters leave their games. The protagonist is a girl from a candy racing game who glitches\"\n",
        "# new_doc = \"Boy studies ballet in secret. His father wants him to go to the gym and boxe. They raise money for audition in London\"\n",
        "\n",
        "new_doc = gensim.parsing.preprocessing.preprocess_string(new_doc)\n",
        "new_vec = dictionary.doc2bow(new_doc)\n",
        "vec_bow_tfidf = tfidf[new_vec]\n",
        "vec_lsi = lsi[vec_bow_tfidf]\n",
        "sims = index[vec_lsi]\n",
        "for s in sorted(enumerate(sims), key=lambda item: -item[1])[:10]:\n",
        "    print(f\"{df['Title'].iloc[s[0]]} : {str(s[1])}\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f0X0MppJrKrR"
      },
      "source": [
        "As you can see we give the description of the movie \"Wreck-it Ralph\" and it appears as the third recommended. We are doing a great job with LSI!\n",
        "\n",
        "Feel free to change the description and see what movies you get :)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KxXwYyCkrls-"
      },
      "source": [
        "## Points to think about \n",
        "\n",
        "1. How exactly does matrix factorization help us in the recommendation procedure? Why can we not simply model the user-movie matrix?\n",
        "\n",
        "2. What do the rows of the matrix $T$ represent? (Definition of $T$ is above in the introduction to LSI)."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "1.solution"
      ],
      "metadata": {
        "id": "NBUuPWJqkrTf"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Matrix factorization is a powerful technique used in recommendation systems to predict the preferences of a user for items (movies, books, products, etc.) that they have not yet interacted with. The basic idea of matrix factorization is to decompose a large user-item interaction matrix into two smaller matrices: a user matrix and an item matrix, where each row of the user matrix represents a user's preference for latent factors and each column of the item matrix represents the strength of the item's association with these factors.\n",
        "\n",
        "The reason we cannot simply model the user-movie matrix directly is that it suffers from the \"cold-start\" problem, which arises when a new user or a new item is introduced to the system. In this case, the user-movie matrix will be incomplete or entirely empty, making it impossible to make accurate recommendations. Matrix factorization overcomes this problem by creating a lower-dimensional representation of the user-item matrix, which allows for the identification of latent factors that can be used to make predictions about new users and items."
      ],
      "metadata": {
        "id": "l3zptOIBk3by"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "2.Solution"
      ],
      "metadata": {
        "id": "a5g46tlBlmT8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In LSI , where T represents m∗r   term-concept vector,. Here rows = m =  number of unique words"
      ],
      "metadata": {
        "id": "2s4cTnF7lpWQ"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KkrJ4_--tYe3"
      },
      "source": [
        "## Resources and References\n",
        "\n",
        "1. https://medium.com/betacom/latent-semantic-indexing-in-python-85880414b4de\n",
        "2. https://www.analyticssteps.com/blogs/introduction-latent-semantic-analysis-lsa-and-latent-dirichlet-allocation-lda\n",
        "3. https://towardsdatascience.com/recommendation-system-matrix-factorization-d61978660b4b\n",
        "4. https://analyticsindiamag.com/singular-value-decomposition-svd-application-recommender-system/\n",
        "5. https://machinelearningmastery.com/gentle-introduction-bag-words-model/"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "1DXBI8c0laGz"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}