Low_Rank_Approximation.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "18110091_Q5_A2.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rUyS5Dwrigd5"
      },
      "source": [
        "**Importing Modules**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NkTytNPexflZ"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import random\n",
        "import csv\n",
        "import requests\n",
        "from IPython.display import display\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.optimize import curve_fit"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zfhu0Tiwij7n"
      },
      "source": [
        "**Lowrank Function**<br>\n",
        "Function to calculate the low rank approximation of the input matrix."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5mVLigYcx3x_"
      },
      "source": [
        "def lowrank(U,S,V,k):\n",
        "  UR = U[:, :k]\n",
        "  SR = np.diag(S[:k])\n",
        "  VR = V[:k, :]\n",
        "  result = np.dot(np.dot(UR,SR), VR)\n",
        "\n",
        "  return result"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JnzQeb7Bu3Bo"
      },
      "source": [
        "**Importing Ratings Data**<br>\n",
        "The ratings data is imported and the aggregate ratings for each movie and user are stored as an array in separate dictionaries."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QgsEOr_3c8aD"
      },
      "source": [
        "uniq_movId = {}\n",
        "count = 0\n",
        "rating = []\n",
        "movie_avg = {}\n",
        "user_avg = {}\n",
        "\n",
        "url = 'https://raw.githubusercontent.com/kushagra-18110091/http_test/main/ratings_small.csv'\n",
        "ratings = requests.get(url, allow_redirects=True)\n",
        "open('ratings.csv', 'wb').write(ratings.content)\n",
        "\n",
        "file = open('ratings.csv', 'r')\n",
        "CSVFile = csv.reader(file)\n",
        "next(CSVFile, None)\n",
        "userId = 1\n",
        "\n",
        "for row in CSVFile:\n",
        "    if(row[0] not in user_avg):\n",
        "        user_avg[row[0]] = [float(row[2]),1]\n",
        "    else :\n",
        "        user_avg[row[0]][0] += float(row[2])\n",
        "        user_avg[row[0]][1] += 1\n",
        "\n",
        "    userId = max(userId,int(row[0]))\n",
        "    if(row[1] not in uniq_movId):\n",
        "        uniq_movId[row[1]] = count \n",
        "        count += 1\n",
        "        movie_avg[row[1]] = [float(row[2]),1]\n",
        "    else:\n",
        "        movie_avg[row[1]][0] += float(row[2])\n",
        "        movie_avg[row[1]][1] += 1\n",
        "\n",
        "    rating.append(row[:-1]) \n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c98xpNkgg3T9"
      },
      "source": [
        "**Creating Test and Train Data**<br>\n",
        "The test and training data are create from the rating array and all non present entries are replaced by 2.5 assuming that ratings are between 1-5."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gucjqkKL4xBF"
      },
      "source": [
        "rows, cols = (userId+1, len(uniq_movId))\n",
        "rating_array =  [[2.5]*(cols) for i in range(rows)]\n",
        "\n",
        "random.shuffle(rating)\n",
        "train = rating[len(rating)//5 :]\n",
        "test = rating[: len(rating)//5]\n",
        "\n",
        "for i in range(len(train)):\n",
        "  rating_array[int(train[i][0])][int(uniq_movId[train[i][1]])] = float(train[i][2])\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VV9HB3SRhKVd"
      },
      "source": [
        "**Calculating SVD**<br>\n",
        "The SVD for the rating array is calculated and stored in U, S and V matrices."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jRmlY1baOs6r"
      },
      "source": [
        "U, S, V = np.linalg.svd(rating_array, full_matrices=False)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OaNic340hZUh"
      },
      "source": [
        "**Calculating Low Rank Approximation**<br>\n",
        "The low rank approximation of the matrix is calculated using U, S and V matrices calculated above. The squared error for each entry is then calculated using the test data. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MTMjtBzMlmMo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "74b0efe3-4556-446b-9c2f-cb56d777aef6"
      },
      "source": [
        "lowrank_error = []\n",
        "\n",
        "for k in range(1,100):\n",
        "  rating_lowrank = lowrank(U,S,V,k)\n",
        "  error = 0\n",
        "  for i in range(len(test)):\n",
        "    error += (float(test[i][2]) - rating_lowrank[int(test[i][0])][int(uniq_movId[test[i][1]])]) ** 2\n",
        "\n",
        "  lowrank_error.append(error)\n",
        "\n",
        "print(lowrank_error)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[36280.54908803819, 33443.92557016882, 32312.86795361154, 31601.034609112237, 31423.618939958553, 31412.29257847922, 31330.45919243365, 31056.94095263504, 31002.564698731425, 30912.140209561072, 30975.77180374384, 31012.16233363711, 31098.733327982976, 31161.0255754459, 31183.528029484325, 31304.11804753768, 31436.704276727633, 31479.426927708624, 31557.016924568867, 31620.59774063933, 31689.825449631808, 31774.645903377383, 31828.150231115655, 31922.75307301092, 31983.079331865592, 32035.21853387761, 32099.074889659125, 32143.87204579086, 32208.846305528295, 32276.95805362152, 32356.638838121457, 32433.801595751556, 32516.802821418776, 32626.3652763992, 32680.161118102616, 32825.48223034625, 32902.695223682655, 32989.51980274846, 33044.76271683718, 33105.26491259393, 33217.31528045608, 33329.472802816934, 33423.66996847748, 33513.17057172596, 33562.54614153261, 33643.470200334654, 33740.24840741875, 33809.47756175662, 33864.06740071913, 33936.886694751316, 34003.94350514147, 34093.54949777099, 34138.980384543094, 34203.17431025335, 34302.575819019396, 34355.12135675331, 34405.76070431638, 34503.01632718972, 34591.12338362551, 34663.73172473292, 34710.64157211393, 34811.36066452821, 34891.477478825036, 34987.06155483519, 35065.39121253817, 35146.20641203945, 35211.48361386635, 35298.70378891817, 35368.04395758442, 35434.141797634205, 35469.37618353895, 35557.474605886324, 35632.768027657476, 35688.09160189855, 35739.27909940026, 35795.7392592952, 35881.819433829485, 35941.631198083596, 36014.41856809084, 36080.569507876164, 36143.89932606994, 36206.19346860089, 36263.38580326078, 36305.92160303014, 36368.71374210749, 36422.439406357546, 36473.748247614094, 36504.27633876278, 36555.699734719725, 36605.09758747204, 36666.18784795033, 36699.36919391299, 36752.884151148966, 36805.18067052408, 36864.0766230844, 36916.91764205423, 36941.433118006426, 36993.99231956942, 37037.628940337294]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iH774QUhh30k"
      },
      "source": [
        "**Calculating Average User and Movie Rating**<br>\n",
        "The average user and movie ratings are calculated using the dictionaries created in the first step."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FRn8Ko1Z9RIX"
      },
      "source": [
        "ui = []\n",
        "nj = []\n",
        "matrix = []\n",
        "\n",
        "for i in range(len(test)):\n",
        "  ui.append(user_avg[test[i][0]][0]/user_avg[test[i][0]][1])\n",
        "  nj.append(movie_avg[test[i][1]][0]/movie_avg[test[i][1]][1])\n",
        "  matrix.append((float(test[i][2])))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DFXnFYgfiMCh"
      },
      "source": [
        "**Calculating Base Line Error**<br>\n",
        "The base line error is calculated using the baseline algorithm."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rBuWgAbI88FK",
        "outputId": "82db4dfc-387d-43e5-c32c-f0d7c341669f"
      },
      "source": [
        "base_error = 0\n",
        "\n",
        "def func_obj(X, a, b):\n",
        "    ui,nj = X\n",
        "    return a*ui+b*nj\n",
        "\n",
        "fit = curve_fit(func_obj, (ui,nj), matrix)\n",
        "alpha = fit[0][0]\n",
        "beta = fit[0][1]\n",
        "\n",
        "for i in range(len(test)):\n",
        "  base_error += ((alpha*ui[i] + beta*nj[i]) - float(test[i][2]))**2\n",
        "\n",
        "print(base_error)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "14131.499102815249\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nAu1dm8eikBS"
      },
      "source": [
        "**Plotting the results**<br>\n",
        "The errors calculated using the test data and the base line error are plotted."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 562
        },
        "id": "wFhLQOayB_ak",
        "outputId": "f1f717cc-1dd0-4314-fbbc-6fba167b6734"
      },
      "source": [
        "x = []\n",
        "y = []\n",
        "for k in range(1,100):\n",
        "  x.append(k)\n",
        "  y.append(base_error)\n",
        "  \n",
        "plt.figure(dpi=150)  \n",
        "plt.plot(x, lowrank_error, label = \"Error\")\n",
        "plt.plot(x, y, label = \"Base Algo Error\")\n",
        "  \n",
        "plt.xlabel('K')\n",
        "plt.ylabel('Error')\n",
        "  \n",
        "plt.legend()\n",
        "  \n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 900x600 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}