ex1_recommendations.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:97334233db391cb3ce28ca7909bd6b092712973b43e3c19aa6b917c8ae56eae3"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#%load ex1_recommendations.py"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import matplotlib\n",
      "matplotlib.rcParams['savefig.dpi'] = 2 * matplotlib.rcParams['savefig.dpi']\n",
      "from pandas.io.excel import read_excel\n",
      "from matrix_factorization import PMF\n",
      "import matplotlib.pyplot as plt\n",
      "from utils import download\n",
      "from scipy import sparse\n",
      "import numpy as np\n",
      "import zipfile\n",
      "import os"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A dataset of jokes and associated user ratings.\n",
      "Eigentaste: A Constant Time Collaborative Filtering Algorithm.\n",
      "Ken Goldberg, Theresa Roeder, Dhruv Gupta, and Chris Perkins.\n",
      "Information Retrieval, 4(2), 133-151. July 2001.\n",
      "http://eigentaste.berkeley.edu/dataset/\n",
      "\n",
      "We will use this dataset to test our simple recommendation algorithm."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dataset_url = \"http://eigentaste.berkeley.edu/dataset/jester_dataset_1_1.zip\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, download the jester dataset to jester_dataset_1_1.zip if it hasn't been\n",
      "downloaded yet"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dataset_fname = dataset_url.split(\"/\")[-1]\n",
      "if not os.path.exists(dataset_fname):\n",
      "    download(dataset_url, server_fname=dataset_fname)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The dataset is stored as an Excel spreadsheet (XLS).\n",
      "We can read it without unzipping using the zipfile library."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "archive = zipfile.ZipFile(dataset_fname, 'r')\n",
      "# Only one file in the zipfile we are reading from\n",
      "# archive.open returns a file-like object - perfect for sending to pandas\n",
      "file_handle = archive.open(archive.infolist()[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To read the actual XLS file, we can use pandas. For speed, we will only use the first 100 users"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dataframe = read_excel(file_handle)\n",
      "data = dataframe.values\n",
      "user_indices = data[:100, 0]\n",
      "ratings = data[:100, 1:]\n",
      "# Necessary because this is a view of the underlying data, want separate copy\n",
      "true_ratings = np.copy(data[:100, 1:])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this dataset, any rating of 99. means that a joke was unrated. Since these\n",
      "are floating point values, it is best to create the sparse array by hand.\n",
      "We can get these indices with np.where.\n",
      "\n",
      "We also want to use 80% of the rated data as training, and save the last 20% for validation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rated = np.where(ratings <= 10.)\n",
      "np.random.RandomState(1999)\n",
      "# Use 20% for validation\n",
      "n_validation = int(0.2 * len(rated[0]))\n",
      "idx = np.random.randint(0, len(rated[0]), n_validation)\n",
      "# Stack and transpose to get an (x, 2) array of indices\n",
      "validation_indices = np.vstack((rated[0], rated[1])).T[idx]\n",
      "# Set validation to NaN now\n",
      "ratings[validation_indices[:, 0], validation_indices[:, 1]] = 99.\n",
      "# Keep this mask for plotting to include validation\n",
      "mask = (ratings <= 10.)\n",
      "# Redo NaN check\n",
      "rated = np.where(ratings <= 10.)\n",
      "ratings = sparse.coo_matrix((ratings[rated[0], rated[1]], (rated[0], rated[1])))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Big Picture\n",
      "===============\n",
      "\n",
      "<img src=\"matrix_factorization.png\">"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "W = np.ones((10, 4))\n",
      "W.flat[::3] = 0.\n",
      "\n",
      "H = np.ones((4, 5))\n",
      "H[0, :] = 0.\n",
      "H[2, :] = 0.\n",
      "H.flat[::7] = 0.\n",
      "H.flat[::3] = 1."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f, axarr = plt.subplots(1, 2)\n",
      "axarr[0].matshow(np.dot(W, H), cmap=\"gray\")\n",
      "axarr[0].axis('off')\n",
      "axarr[1].axis('off')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "(0.0, 1.0, 0.0, 1.0)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAArIAAAIRCAYAAAC28V7AAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107cce7d0>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f, axarr = plt.subplots(1, 3)\n",
      "axarr[0].matshow(W, cmap=\"gray\")\n",
      "axarr[0].axis('off')\n",
      "axarr[1].matshow(H, cmap=\"gray\")\n",
      "axarr[1].axis('off')\n",
      "axarr[2].matshow(np.dot(W, H), cmap=\"gray\")\n",
      "axarr[2].axis('off')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "(-0.5, 4.5, 9.5, -0.5)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAsMAAAH2CAYAAACV04HBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e1ac350>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For now, treat this algorithm as a black box with input ratings,\n",
      "output recommendation basis matrices which can be used for predictions.\n",
      "\n",
      "If curious, see the docstrings of the function for the original paper.\n",
      "\n",
      "Probabilistic Matrix Factorization, R. Salakhutdinov and A. Mnih,            \n",
      "Advances in Neural Information Processing Systems 20, 2008  \n",
      "http://papers.nips.cc/paper/3208-probabilistic-matrix-factorization.pdf"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "W, H, m = PMF(ratings, minibatch_size=10, learning_rate=0.001, momentum=0.95,\n",
      "              regularization=0.75, max_epoch=100, rank=20, status_percentage=0.2, random_state=2000)\n",
      "predicted_ratings = np.dot(W, H.T) + m\n",
      "predicted_ratings = np.clip(predicted_ratings, -10, 10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Printing updates every 20 epochs\n",
        "Epoch 1 of 100"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean absolute error 4.235886\n",
        "Epoch 21 of 100"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean absolute error 3.208280\n",
        "Epoch 41 of 100"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean absolute error 3.234818\n",
        "Epoch 61 of 100"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean absolute error 3.232324\n",
        "Epoch 81 of 100"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean absolute error 3.188247\n",
        "Epoch 100 of 100"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Mean absolute error 3.218058\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Calculate mean absolute error on validation indices"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "val_truth = true_ratings[validation_indices[:, 0], validation_indices[:, 1]]\n",
      "val_predict = predicted_ratings[validation_indices[:, 0],\n",
      "                                validation_indices[:, 1]]\n",
      "# Mean absolute error\n",
      "mae = np.mean(np.abs(val_truth - val_predict))\n",
      "print(\"Validation mean absolute error %f\" % mae)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Validation mean absolute error 3.784543\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot the user prediction matrix"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f, axarr = plt.subplots(1, 2)\n",
      "axarr[0].matshow((true_ratings * mask), cmap=\"gray\")\n",
      "axarr[0].set_title(\"Ground truth ratings\")\n",
      "axarr[1].matshow((predicted_ratings * mask), cmap=\"gray\")\n",
      "axarr[1].set_title(\"Predicted ratings\\n Validation MAE %f\" % mae)\n",
      "axarr[0].axis(\"off\")\n",
      "axarr[1].axis(\"off\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "(-0.5, 99.5, 99.5, -0.5)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAtoAAAGVCAYAAADACFYXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYQSy0A4hhBBCCGEE/gGs0xAN3o65DAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e1e0150>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f, axarr = plt.subplots(1, 2)\n",
      "axarr[0].matshow(W, cmap=\"gray\")\n",
      "axarr[0].axis('off')\n",
      "axarr[1].matshow(H.T, cmap=\"gray\")\n",
      "axarr[1].axis('off')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "(-0.5, 99.5, 19.5, -0.5)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAm4AAAH2CAYAAADJdQCgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e1a3a50>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    }
   ],
   "metadata": {}
  }
 ]
}