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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "View assignment [here](http://www.cs.ubc.ca/~nando/540-2013/lectures/homework2.pdf)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Exercise 1"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import numpy as np\n",
      "import pdb\n",
      "\n",
      "# MOVIES: Legally Blond; Matrix; Bourne Identity; You\u2019ve Got Mail;\n",
      "# The Devil Wears Prada; The Dark Knight; The Lord of the Rings.\n",
      "movie_titles = ['Legally Blond', 'Matrix', 'Bourne Identity',\n",
      "                'You\u2019ve Got Mail', 'The Devil Wears Prada',\n",
      "                'The Dark Knight', 'The Lord of the Rings']\n",
      "P = [[ 0, 0,-1, 0,-1, 1, 1],  # User 1\n",
      "     [-1, 1, 1,-1, 0, 1, 1],  # User 2\n",
      "     [ 0, 1, 1, 0, 0,-1, 1],  # User 3\n",
      "     [-1, 1, 1, 0, 0, 1, 1],  # User 4\n",
      "     [ 0, 1, 1, 0, 0, 1, 1],  # User 5\n",
      "     [ 1,-1, 1, 1, 1,-1, 0],  # User 6\n",
      "     [-1, 1,-1, 0,-1, 0, 1],  # User 7\n",
      "     [ 0,-1, 0, 1, 1,-1,-1],  # User 8\n",
      "     [ 0, 0,-1, 1, 1, 0,-1]]  # User 9\n",
      "P = np.array(P)\n",
      "C = np.abs(P) # Will be 0 only when P[i,j] == 0.\n",
      "print('Raw Preference Matrix:')\n",
      "print(P)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Raw Preference Matrix:\n",
        "[[ 0  0 -1  0 -1  1  1]\n",
        " [-1  1  1 -1  0  1  1]\n",
        " [ 0  1  1  0  0 -1  1]\n",
        " [-1  1  1  0  0  1  1]\n",
        " [ 0  1  1  0  0  1  1]\n",
        " [ 1 -1  1  1  1 -1  0]\n",
        " [-1  1 -1  0 -1  0  1]\n",
        " [ 0 -1  0  1  1 -1 -1]\n",
        " [ 0  0 -1  1  1  0 -1]]\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Parameters\n",
      "reg = 0.1 # regularization parameter\n",
      "f = 2     # number of factors\n",
      "m,n = P.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Random Initialization\n",
      "# X is (m x f)\n",
      "# Y is (f x n)\n",
      "X = 1 - 2*np.random.rand(m,f)\n",
      "Y = 1 - 2*np.random.rand(f,n)\n",
      "X *= 0.1\n",
      "Y *= 0.1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Alternating Ridge Regression\n",
      "for _ in xrange(100):\n",
      "    # Least-squares keeping Y fixed\n",
      "    X = np.linalg.solve(\n",
      "            np.dot(Y, Y.T) + reg * np.eye(f),\n",
      "            np.dot(Y, P.T)\n",
      "            ).T\n",
      "    # Least-squares keeping X fixed\n",
      "    Y = np.linalg.solve(\n",
      "            np.dot(X.T, X) + reg * np.eye(f),\n",
      "            np.dot(X.T, P)\n",
      "            )\n",
      "print('Alternating Ridge Regression:')\n",
      "print(np.dot(X,Y))\n",
      "print('Error for movies that users actually rated: %.2f'%np.sum((C*(P - np.dot(X,Y)))**2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Alternating Ridge Regression:\n",
        "[[-0.47047868  0.42881288 -0.92322674 -0.40431625 -0.82818449  0.71377038\n",
        "   0.35042258]\n",
        " [-0.57771631  1.11906024  0.94589649 -0.6138595  -0.41293394  0.72761475\n",
        "   1.24992152]\n",
        " [-0.08329304  0.47515025  1.23776778 -0.15067507  0.26037126  0.02607104\n",
        "   0.61430612]\n",
        " [-0.4797323   0.97615665  0.95005888 -0.51903623 -0.29509116  0.59242618\n",
        "   1.10279904]\n",
        " [-0.37593946  0.83720164  0.99806064 -0.42105221 -0.1576005   0.44610297\n",
        "   0.96413601]\n",
        " [ 0.67254752 -0.68837628  1.05514875  0.59290466  1.10703169 -1.00139291\n",
        "  -0.60521603]\n",
        " [-0.56690331  0.63195467 -0.7079191  -0.51001528 -0.88042456  0.83110331\n",
        "   0.58167835]\n",
        " [ 0.65941592 -0.96038474  0.03268862  0.63788069  0.79442036 -0.91013103\n",
        "  -0.98826639]\n",
        " [ 0.32613592 -0.67760237 -0.69495382  0.35562611  0.186357   -0.39923578\n",
        "  -0.76905741]]\n",
        "Error for movies that users actually rated: 5.73\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Re-initialize\n",
      "X = 1 - 2*np.random.rand(m,f)\n",
      "Y = 1 - 2*np.random.rand(f,n)\n",
      "X *= 0.1\n",
      "Y *= 0.1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Alternating Weighted Ridge Regression\n",
      "for _ in xrange(100):\n",
      "    # Each user u has a different set of weights Cu\n",
      "    for u,Cu in enumerate(C):\n",
      "        X[u] = np.linalg.solve(\n",
      "                    np.dot(Y, np.dot(np.diag(Cu), Y.T)) + reg * np.eye(f),\n",
      "                    np.dot(Y, np.dot(np.diag(Cu), P[u].T))\n",
      "                    ).T\n",
      "    for i,Ci in enumerate(C.T):\n",
      "        Y[:,i] = np.linalg.solve(\n",
      "                    np.dot(X.T, np.dot(np.diag(Ci), X)) + reg * np.eye(f),\n",
      "                    np.dot(X.T, np.dot(np.diag(Ci), P[:, i]))\n",
      "                    )\n",
      "print('Alternating Weighted Ridge Regression:')\n",
      "print(np.dot(X,Y))\n",
      "print('Error for movies that users actually rated: %.2f'%np.sum((C*(P - np.dot(X,Y)))**2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Alternating Weighted Ridge Regression:\n",
        "[[-0.8785934   0.75591055 -0.84723564 -0.90527554 -0.91301451  1.22456781\n",
        "   0.7703408 ]\n",
        " [-0.96653212  1.12037936  0.83860294 -1.00626954 -1.00818432  0.72382856\n",
        "   1.10750498]\n",
        " [-0.32540594  0.55731684  1.38658549 -0.34526083 -0.34179019 -0.14502803\n",
        "   0.53505323]\n",
        " [-0.96804918  1.12194066  0.83870998 -1.00784188 -1.00976418  0.72539036\n",
        "   1.10906571]\n",
        " [-0.95829148  1.11193016  0.83821615 -0.99772977 -0.99960303  0.71527644\n",
        "   1.09905574]\n",
        " [ 0.92243741 -0.80265369  0.83420677  0.95077543  0.95869447 -1.26620706\n",
        "  -0.81690604]\n",
        " [-1.02704309  0.8941689  -0.92578349 -1.05861242 -1.06741822  1.40873236\n",
        "   0.90998839]\n",
        " [ 0.95137278 -0.98077431 -0.07728943  0.98609905  0.99077203 -0.97584608\n",
        "  -0.98024936]\n",
        " [ 0.89692922 -1.06910816 -0.9585243   0.93486255  0.93596746 -0.60822952\n",
        "  -1.05423328]]\n",
        "Error for movies that users actually rated: 2.01\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Exercise 2"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "not_C = abs(1 - C) # movies not rated\n",
      "P_hat = np.dot(X, Y)\n",
      "top_movie_id = np.argmax(P_hat - (4*C), axis=1)\n",
      "for u, tm_id in zip(range(m), top_movie_id):\n",
      "    print('User %d liked %s'%(u+1, ', '.join([movie_titles[i] for i,p in enumerate(P[u]) if p == 1])))\n",
      "    print('User %d disliked %s'%(u+1, ', '.join([movie_titles[i] for i,p in enumerate(P[u]) if p == -1])))\n",
      "    print('For user %d the top movie is movie n.%d (%s) - predicted vote %.2f\\n'% \\\n",
      "          (u+1, tm_id+1, movie_titles[tm_id], P_hat[u,tm_id]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "User 1 liked The Dark Knight, The Lord of the Rings\n",
        "User 1 disliked Bourne Identity, The Devil Wears Prada\n",
        "For user 1 the top movie is movie n.2 (Matrix) - predicted vote 0.76\n",
        "\n",
        "User 2 liked Matrix, Bourne Identity, The Dark Knight, The Lord of the Rings\n",
        "User 2 disliked Legally Blond, You\u2019ve Got Mail\n",
        "For user 2 the top movie is movie n.5 (The Devil Wears Prada) - predicted vote -1.01\n",
        "\n",
        "User 3 liked Matrix, Bourne Identity, The Lord of the Rings\n",
        "User 3 disliked The Dark Knight\n",
        "For user 3 the top movie is movie n.1 (Legally Blond) - predicted vote -0.33\n",
        "\n",
        "User 4 liked Matrix, Bourne Identity, The Dark Knight, The Lord of the Rings\n",
        "User 4 disliked Legally Blond\n",
        "For user 4 the top movie is movie n.4 (You\u2019ve Got Mail) - predicted vote -1.01\n",
        "\n",
        "User 5 liked Matrix, Bourne Identity, The Dark Knight, The Lord of the Rings\n",
        "User 5 disliked \n",
        "For user 5 the top movie is movie n.1 (Legally Blond) - predicted vote -0.96\n",
        "\n",
        "User 6 liked Legally Blond, Bourne Identity, You\u2019ve Got Mail, The Devil Wears Prada\n",
        "User 6 disliked Matrix, The Dark Knight\n",
        "For user 6 the top movie is movie n.7 (The Lord of the Rings) - predicted vote -0.82\n",
        "\n",
        "User 7 liked Matrix, The Lord of the Rings\n",
        "User 7 disliked Legally Blond, Bourne Identity, The Devil Wears Prada\n",
        "For user 7 the top movie is movie n.6 (The Dark Knight) - predicted vote 1.41\n",
        "\n",
        "User 8 liked You\u2019ve Got Mail, The Devil Wears Prada\n",
        "User 8 disliked Matrix, The Dark Knight, The Lord of the Rings\n",
        "For user 8 the top movie is movie n.1 (Legally Blond) - predicted vote 0.95\n",
        "\n",
        "User 9 liked You\u2019ve Got Mail, The Devil Wears Prada\n",
        "User 9 disliked Bourne Identity, The Lord of the Rings\n",
        "For user 9 the top movie is movie n.1 (Legally Blond) - predicted vote 0.90\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 7
    }
   ],
   "metadata": {}
  }
 ]
}