HW4 Q2 MatrixFactorization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "from scipy import spatial\n",
    "from collections import Counter\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ratings_train = pd.read_csv(\"hw4-data/ratings.csv\", names=[\"user_id\", \"movie_id\", \"rating\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#spread so that users are rownames, movies are colnames\n",
    "M_df = ratings_train.pivot(index=\"user_id\", columns=\"movie_id\", values=\"rating\")\n",
    "M = np.array(M_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def log_joint_likelihood(sigmasq, lam, M, U, V): #this is the MAP objective function\n",
    "    #M should be ndarray\n",
    "    #U is an dxN1 array. calling it T because each row corresponds to uiT in eqns\n",
    "    #V is dxN2 array\n",
    "    ##ui, vi should be np column vectors\n",
    "    term1 = -1/(2*sigmasq)*np.sum(np.nan_to_num(np.square(np.subtract(M, np.matmul(np.transpose(U),V))))) #should add an NA wherever there is missing an M, which takes care of staying in omega - need to make sure NA's are handled properly\n",
    "    term2 = -lam/2*np.sum(np.square(U))\n",
    "    term3 = -lam/2*np.sum(np.square(V))\n",
    "    return(term1 + term2 + term3)\n",
    "\n",
    "def update_ui(i, lam, sigmasq, d, omega_ui, V):\n",
    "    #V is dxN2 array\n",
    "    sum_outer_prods = sum( [np.dot(V[:,j].reshape(-1,1), np.transpose(V[:,j].reshape(-1,1))) for j in omega_ui] )\n",
    "    term1 = np.linalg.inv(np.add(lam*sigmasq*np.eye(d), sum_outer_prods))\n",
    "    term2 = sum( [np.dot(M[i,j], V[:,j].reshape(-1,1)) for j in omega_ui] )\n",
    "    updated_ui = np.matmul(term1, term2)\n",
    "    return(updated_ui) #returns a dx1 column vector\n",
    "\n",
    "def update_vj(j, lam, sigmasq, d, omega_vj, U):\n",
    "    #U is dxN1 array\n",
    "    sum_outer_prods = sum( [np.dot(U[:,i].reshape(-1,1), np.transpose(U[:,i].reshape(-1,1))) for i in omega_vj] )\n",
    "    term1 = np.linalg.inv(np.add(lam*sigmasq*np.eye(d), sum_outer_prods))\n",
    "    term2 = sum( [np.dot(M[i,j], U[:,i].reshape(-1,1)) for i in omega_vj] )\n",
    "    updated_vj = np.matmul(term1, term2)\n",
    "    return(updated_vj) #returns a dx1 column vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#parameters\n",
    "lam = 1\n",
    "sigmasq = 0.25\n",
    "d = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "#find omega_ui\n",
    "omega_ui = [np.where(x)[0] for x in np.logical_not(np.isnan(M))] #need index 0 bc it returns a tuple for some unknown reason\n",
    "\n",
    "#find omega_vj\n",
    "omega_vj = [np.where(x)[0] for x in np.transpose(np.logical_not(np.isnan(M)))] #need index 0 bc it returns a tuple for some unknown reason"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [],
   "source": [
    "##data structures to hold results from each round\n",
    "all_obj = {}\n",
    "all_RMSE = {}\n",
    "all_V = {}\n",
    "\n",
    "n_iter = 100; #how many iterations during model training\n",
    "\n",
    "for round in range(10):\n",
    "    ##MAP coordinate ascent algorithm\n",
    "    initial_V = np.transpose(np.random.multivariate_normal(np.zeros(10), np.eye(d), size=(M.shape[1])))\n",
    "    v = initial_V\n",
    "    obj = []\n",
    "    for iter in range(n_iter):\n",
    "        u = np.transpose(np.array([update_ui(i, lam, sigmasq, d, omega_ui[i], v) for i in range(M.shape[0])]).reshape(-1,d)) #need to transpose in order to get it back to a d x N1 matrix\n",
    "        v = np.transpose(np.array([update_vj(j, lam, sigmasq, d, omega_vj[j], u) for j in range(M.shape[1])]).reshape(-1,d)) #need to transpose in order to get it back to a d x N1 matrix\n",
    "        if iter >= 1:\n",
    "            obj.append(log_joint_likelihood(sigmasq, lam, M, u, v))\n",
    "    all_V[\"round\"+str(round)] = v\n",
    "    all_obj[\"round\"+str(round)] = obj\n",
    "    \n",
    "    ##plot\n",
    "    plt.plot(range(2,(n_iter+1), obj)\n",
    "\n",
    "    ##calculate RMSE test set`\n",
    "    predictions = np.dot(np.transpose(u), v)\n",
    "    ratings_test = pd.read_csv(\"hw4-data/ratings_test.csv\", names=[\"user_id\", \"movie_id\", \"rating\"])\n",
    "    ratings_test = ratings_test[ratings_test.movie_id.isin(M_df.columns.values)] #filter test to movies included in training (all users are found in training)   \n",
    "    test_user_inds = [M_df.index.get_loc(test_user) for test_user in ratings_test.user_id.values]\n",
    "    test_movie_inds = [M_df.columns.get_loc(test_movie) for test_movie in ratings_test.movie_id.values]\n",
    "    ratings_test['prediction'] = predictions[test_user_inds, test_movie_inds]\n",
    "    all_RMSE[\"round\"+str(round)] = np.sqrt(np.mean(np.square(np.subtract(ratings_test.rating.values, ratings_test.prediction.values))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
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2AlNtb8fhcFjssFME05s5BjMsdpWqdjWa4XAcFGRb/TjgsWPLC4HbnMJzOLJShhnSHIvZ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\n2czOAC4HZgKbu1tP0hOS6jp5zShg3XFEpym/lNN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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fecffd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"Iteration of Training\")\n",
    "plt.ylabel(\"Value of Objective Function\")\n",
    "plt.legend([\"run \" + i for i in [str(j) for j in range(1,11)]])\n",
    "plt.title(\"Objective Function for 10 Runs of Algorithm (100 Iterations each)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 353,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Final Value Objective Func</th>\n",
       "      <th>RMSE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>run 5</th>\n",
       "      <td>-90920.944242</td>\n",
       "      <td>1.099170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>run 9</th>\n",
       "      <td>-90973.581990</td>\n",
       "      <td>1.099235</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>run 2</th>\n",
       "      <td>-91043.595610</td>\n",
       "      <td>1.120456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>run 10</th>\n",
       "      <td>-91150.280993</td>\n",
       "      <td>1.110056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>run 7</th>\n",
       "      <td>-91150.649560</td>\n",
       "      <td>1.120586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>run 4</th>\n",
       "      <td>-91233.660803</td>\n",
       "      <td>1.134907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>run 8</th>\n",
       "      <td>-91248.360135</td>\n",
       "      <td>1.087196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>run 3</th>\n",
       "      <td>-91270.889453</td>\n",
       "      <td>1.123257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>run 6</th>\n",
       "      <td>-91298.358491</td>\n",
       "      <td>1.143245</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>run 1</th>\n",
       "      <td>-91349.274275</td>\n",
       "      <td>1.113955</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Final Value Objective Func      RMSE\n",
       "run 5                -90920.944242  1.099170\n",
       "run 9                -90973.581990  1.099235\n",
       "run 2                -91043.595610  1.120456\n",
       "run 10               -91150.280993  1.110056\n",
       "run 7                -91150.649560  1.120586\n",
       "run 4                -91233.660803  1.134907\n",
       "run 8                -91248.360135  1.087196\n",
       "run 3                -91270.889453  1.123257\n",
       "run 6                -91298.358491  1.143245\n",
       "run 1                -91349.274275  1.113955"
      ]
     },
     "execution_count": 353,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_values = pd.DataFrame({\"Final Value Objective Func\" : [all_obj[x][n_iter-2] for x in all_obj], \n",
    "                             \"RMSE\" : [all_RMSE[x] for x in all_RMSE]}, index = [\"run \" + i for i in [str(j) for j in range(1,11)]])\n",
    "final_values.sort_values('Final Value Objective Func', ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-90920.944241767196"
      ]
     },
     "execution_count": 232,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max([all_obj[x][n_iter-2] for x in all_obj]) #round4 (labeled \"run5\" on plot, table) had the highest objective function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>movie</th>\n",
       "      <th>movie_id</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>Toy Story (1995)</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>GoldenEye (1995)</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>Four Rooms (1995)</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>Get Shorty (1995)</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>Copycat (1995)</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>Shanghai Triad (Yao a yao yao dao waipo qiao) ...</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>Twelve Monkeys (1995)</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>Babe (1995)</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>Dead Man Walking (1995)</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>Richard III (1995)</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10</td>\n",
       "      <td>Seven (Se7en) (1995)</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>11</td>\n",
       "      <td>Usual Suspects, The (1995)</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>12</td>\n",
       "      <td>Mighty Aphrodite (1995)</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>13</td>\n",
       "      <td>Postino, Il (1994)</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>14</td>\n",
       "      <td>Mr. Holland's Opus (1995)</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>15</td>\n",
       "      <td>French Twist (Gazon maudit) (1995)</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>16</td>\n",
       "      <td>From Dusk Till Dawn (1996)</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>17</td>\n",
       "      <td>White Balloon, The (1995)</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>18</td>\n",
       "      <td>Antonia's Line (1995)</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>19</td>\n",
       "      <td>Angels and Insects (1995)</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>20</td>\n",
       "      <td>Muppet Treasure Island (1996)</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>21</td>\n",
       "      <td>Braveheart (1995)</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>22</td>\n",
       "      <td>Taxi Driver (1976)</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>23</td>\n",
       "      <td>Rumble in the Bronx (1995)</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>24</td>\n",
       "      <td>Birdcage, The (1996)</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>25</td>\n",
       "      <td>Brothers McMullen, The (1995)</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>26</td>\n",
       "      <td>Bad Boys (1995)</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>27</td>\n",
       "      <td>Apollo 13 (1995)</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>28</td>\n",
       "      <td>Batman Forever (1995)</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>29</td>\n",
       "      <td>Belle de jour (1967)</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1651</th>\n",
       "      <td>1651</td>\n",
       "      <td>Temptress Moon (Feng Yue) (1996)</td>\n",
       "      <td>1652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1652</th>\n",
       "      <td>1652</td>\n",
       "      <td>Entertaining Angels: The Dorothy Day Story (1996)</td>\n",
       "      <td>1653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1653</th>\n",
       "      <td>1653</td>\n",
       "      <td>Chairman of the Board (1998)</td>\n",
       "      <td>1654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1654</th>\n",
       "      <td>1654</td>\n",
       "      <td>Favor, The (1994)</td>\n",
       "      <td>1655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1655</th>\n",
       "      <td>1655</td>\n",
       "      <td>Little City (1998)</td>\n",
       "      <td>1656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1656</th>\n",
       "      <td>1656</td>\n",
       "      <td>Target (1995)</td>\n",
       "      <td>1657</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1657</th>\n",
       "      <td>1657</td>\n",
       "      <td>Substance of Fire, The (1996)</td>\n",
       "      <td>1658</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1658</th>\n",
       "      <td>1658</td>\n",
       "      <td>Getting Away With Murder (1996)</td>\n",
       "      <td>1659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1659</th>\n",
       "      <td>1659</td>\n",
       "      <td>Small Faces (1995)</td>\n",
       "      <td>1660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1660</th>\n",
       "      <td>1660</td>\n",
       "      <td>New Age, The (1994)</td>\n",
       "      <td>1661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1661</th>\n",
       "      <td>1661</td>\n",
       "      <td>Rough Magic (1995)</td>\n",
       "      <td>1662</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1662</th>\n",
       "      <td>1662</td>\n",
       "      <td>Nothing Personal (1995)</td>\n",
       "      <td>1663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1663</th>\n",
       "      <td>1663</td>\n",
       "      <td>8 Heads in a Duffel Bag (1997)</td>\n",
       "      <td>1664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1664</th>\n",
       "      <td>1664</td>\n",
       "      <td>Brother's Kiss, A (1997)</td>\n",
       "      <td>1665</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1665</th>\n",
       "      <td>1665</td>\n",
       "      <td>Ripe (1996)</td>\n",
       "      <td>1666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1666</th>\n",
       "      <td>1666</td>\n",
       "      <td>Next Step, The (1995)</td>\n",
       "      <td>1667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1667</th>\n",
       "      <td>1667</td>\n",
       "      <td>Wedding Bell Blues (1996)</td>\n",
       "      <td>1668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1668</th>\n",
       "      <td>1668</td>\n",
       "      <td>MURDER and murder (1996)</td>\n",
       "      <td>1669</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1669</th>\n",
       "      <td>1669</td>\n",
       "      <td>Tainted (1998)</td>\n",
       "      <td>1670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1670</th>\n",
       "      <td>1670</td>\n",
       "      <td>Further Gesture, A (1996)</td>\n",
       "      <td>1671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1671</th>\n",
       "      <td>1671</td>\n",
       "      <td>Kika (1993)</td>\n",
       "      <td>1672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1672</th>\n",
       "      <td>1672</td>\n",
       "      <td>Mirage (1995)</td>\n",
       "      <td>1673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1673</th>\n",
       "      <td>1673</td>\n",
       "      <td>Mamma Roma (1962)</td>\n",
       "      <td>1674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1674</th>\n",
       "      <td>1674</td>\n",
       "      <td>Sunchaser, The (1996)</td>\n",
       "      <td>1675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1675</th>\n",
       "      <td>1675</td>\n",
       "      <td>War at Home, The (1996)</td>\n",
       "      <td>1676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1676</th>\n",
       "      <td>1676</td>\n",
       "      <td>Sweet Nothing (1995)</td>\n",
       "      <td>1677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1677</th>\n",
       "      <td>1677</td>\n",
       "      <td>Mat' i syn (1997)</td>\n",
       "      <td>1678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1678</th>\n",
       "      <td>1678</td>\n",
       "      <td>B. Monkey (1998)</td>\n",
       "      <td>1679</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1679</th>\n",
       "      <td>1679</td>\n",
       "      <td>Sliding Doors (1998)</td>\n",
       "      <td>1680</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1681</th>\n",
       "      <td>1681</td>\n",
       "      <td>Scream of Stone (Schrei aus Stein) (1991)</td>\n",
       "      <td>1682</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1676 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      index                                              movie  movie_id\n",
       "0         0                                   Toy Story (1995)         1\n",
       "1         1                                   GoldenEye (1995)         2\n",
       "2         2                                  Four Rooms (1995)         3\n",
       "3         3                                  Get Shorty (1995)         4\n",
       "4         4                                     Copycat (1995)         5\n",
       "5         5  Shanghai Triad (Yao a yao yao dao waipo qiao) ...         6\n",
       "6         6                              Twelve Monkeys (1995)         7\n",
       "7         7                                        Babe (1995)         8\n",
       "8         8                            Dead Man Walking (1995)         9\n",
       "9         9                                 Richard III (1995)        10\n",
       "10       10                               Seven (Se7en) (1995)        11\n",
       "11       11                         Usual Suspects, The (1995)        12\n",
       "12       12                            Mighty Aphrodite (1995)        13\n",
       "13       13                                 Postino, Il (1994)        14\n",
       "14       14                          Mr. Holland's Opus (1995)        15\n",
       "15       15                 French Twist (Gazon maudit) (1995)        16\n",
       "16       16                         From Dusk Till Dawn (1996)        17\n",
       "17       17                          White Balloon, The (1995)        18\n",
       "18       18                              Antonia's Line (1995)        19\n",
       "19       19                          Angels and Insects (1995)        20\n",
       "20       20                      Muppet Treasure Island (1996)        21\n",
       "21       21                                  Braveheart (1995)        22\n",
       "22       22                                 Taxi Driver (1976)        23\n",
       "23       23                         Rumble in the Bronx (1995)        24\n",
       "24       24                               Birdcage, The (1996)        25\n",
       "25       25                      Brothers McMullen, The (1995)        26\n",
       "26       26                                    Bad Boys (1995)        27\n",
       "27       27                                   Apollo 13 (1995)        28\n",
       "28       28                              Batman Forever (1995)        29\n",
       "29       29                               Belle de jour (1967)        30\n",
       "...     ...                                                ...       ...\n",
       "1651   1651                   Temptress Moon (Feng Yue) (1996)      1652\n",
       "1652   1652  Entertaining Angels: The Dorothy Day Story (1996)      1653\n",
       "1653   1653                       Chairman of the Board (1998)      1654\n",
       "1654   1654                                  Favor, The (1994)      1655\n",
       "1655   1655                                 Little City (1998)      1656\n",
       "1656   1656                                      Target (1995)      1657\n",
       "1657   1657                      Substance of Fire, The (1996)      1658\n",
       "1658   1658                    Getting Away With Murder (1996)      1659\n",
       "1659   1659                                 Small Faces (1995)      1660\n",
       "1660   1660                                New Age, The (1994)      1661\n",
       "1661   1661                                 Rough Magic (1995)      1662\n",
       "1662   1662                            Nothing Personal (1995)      1663\n",
       "1663   1663                     8 Heads in a Duffel Bag (1997)      1664\n",
       "1664   1664                           Brother's Kiss, A (1997)      1665\n",
       "1665   1665                                        Ripe (1996)      1666\n",
       "1666   1666                              Next Step, The (1995)      1667\n",
       "1667   1667                          Wedding Bell Blues (1996)      1668\n",
       "1668   1668                           MURDER and murder (1996)      1669\n",
       "1669   1669                                     Tainted (1998)      1670\n",
       "1670   1670                          Further Gesture, A (1996)      1671\n",
       "1671   1671                                        Kika (1993)      1672\n",
       "1672   1672                                      Mirage (1995)      1673\n",
       "1673   1673                                  Mamma Roma (1962)      1674\n",
       "1674   1674                              Sunchaser, The (1996)      1675\n",
       "1675   1675                            War at Home, The (1996)      1676\n",
       "1676   1676                               Sweet Nothing (1995)      1677\n",
       "1677   1677                                  Mat' i syn (1997)      1678\n",
       "1678   1678                                   B. Monkey (1998)      1679\n",
       "1679   1679                               Sliding Doors (1998)      1680\n",
       "1681   1681          Scream of Stone (Schrei aus Stein) (1991)      1682\n",
       "\n",
       "[1676 rows x 3 columns]"
      ]
     },
     "execution_count": 305,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "movies = pd.read_table(\"hw4-data/movies.txt\", header = None, names=['movie'])\n",
    "movies.reset_index(inplace=True) #row number is movie id, dif number of movies in this and in our training data so need to add the key as a feature (cant simply index)\n",
    "movies['movie_id'] = movies.index+1 #bc index starts at 0\n",
    "movies = movies[movies.movie_id.isin(M_df.columns.values)] #filter test to movies included in training (all users are found in training)   \n",
    "movies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10, 1676)\n",
      "(1676, 1676)\n"
     ]
    }
   ],
   "source": [
    "v = all_V['round4']\n",
    "print(v.shape)\n",
    "dists = spatial.distance.squareform(spatial.distance.pdist(np.transpose(v))) #finds distance bw rows,so must tranpose first \n",
    "print(dists.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 346,
   "metadata": {},
   "outputs": [],
   "source": [
    "closest_movies_dfs = {}\n",
    "for movie in ['Star Wars', 'My Fair Lady', 'GoodFellas']:\n",
    "    movie_id = int(movies[movies.movie.str.contains(movie)]['movie_id']) #np.nonzero(movie_mappings.movie.str.contains(movie))[0][0]\n",
    "    movie_ind = M_df.columns.get_loc(movie_id)\n",
    "    inds_of_closest_neighbs = np.argsort(dists[movie_ind,])[1:11]\n",
    "    closest_neighbs_ids = M_df.columns[inds_of_closest_neighbs]\n",
    "    closest_movies_dfs[movie] = pd.DataFrame({\"Closest Movies\" : movies[movies.movie_id.isin(closest_neighbs_ids)]['movie'], \"Distance\" : np.sort(dists[movie_ind,])[1:11]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 351,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Closest Movies</th>\n",
       "      <th>Distance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>Terminator 2: Judgment Day (1991)</td>\n",
       "      <td>0.304748</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>171</th>\n",
       "      <td>Empire Strikes Back, The (1980)</td>\n",
       "      <td>0.502703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>173</th>\n",
       "      <td>Raiders of the Lost Ark (1981)</td>\n",
       "      <td>0.647912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>180</th>\n",
       "      <td>Return of the Jedi (1983)</td>\n",
       "      <td>0.870934</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>194</th>\n",
       "      <td>Terminator, The (1984)</td>\n",
       "      <td>0.892668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>203</th>\n",
       "      <td>Back to the Future (1985)</td>\n",
       "      <td>0.929025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>209</th>\n",
       "      <td>Indiana Jones and the Last Crusade (1989)</td>\n",
       "      <td>0.957644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>428</th>\n",
       "      <td>Day the Earth Stood Still, The (1951)</td>\n",
       "      <td>0.966905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1006</th>\n",
       "      <td>Waiting for Guffman (1996)</td>\n",
       "      <td>0.974156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1268</th>\n",
       "      <td>Love in the Afternoon (1957)</td>\n",
       "      <td>0.985527</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 Closest Movies  Distance\n",
       "95            Terminator 2: Judgment Day (1991)  0.304748\n",
       "171             Empire Strikes Back, The (1980)  0.502703\n",
       "173              Raiders of the Lost Ark (1981)  0.647912\n",
       "180                   Return of the Jedi (1983)  0.870934\n",
       "194                      Terminator, The (1984)  0.892668\n",
       "203                   Back to the Future (1985)  0.929025\n",
       "209   Indiana Jones and the Last Crusade (1989)  0.957644\n",
       "428       Day the Earth Stood Still, The (1951)  0.966905\n",
       "1006                 Waiting for Guffman (1996)  0.974156\n",
       "1268               Love in the Afternoon (1957)  0.985527"
      ]
     },
     "execution_count": 351,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "closest_movies_dfs['Star Wars']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 348,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Closest Movies</th>\n",
       "      <th>Distance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Babe (1995)</td>\n",
       "      <td>0.768321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>132</th>\n",
       "      <td>Gone with the Wind (1939)</td>\n",
       "      <td>0.801736</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>142</th>\n",
       "      <td>Sound of Music, The (1965)</td>\n",
       "      <td>0.858096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>416</th>\n",
       "      <td>Parent Trap, The (1961)</td>\n",
       "      <td>0.858263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>418</th>\n",
       "      <td>Mary Poppins (1964)</td>\n",
       "      <td>0.934540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>601</th>\n",
       "      <td>American in Paris, An (1951)</td>\n",
       "      <td>0.941190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>605</th>\n",
       "      <td>All About Eve (1950)</td>\n",
       "      <td>0.944712</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>628</th>\n",
       "      <td>Victor/Victoria (1982)</td>\n",
       "      <td>0.981944</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>706</th>\n",
       "      <td>Enchanted April (1991)</td>\n",
       "      <td>0.997569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1146</th>\n",
       "      <td>My Family (1995)</td>\n",
       "      <td>1.011438</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    Closest Movies  Distance\n",
       "7                      Babe (1995)  0.768321\n",
       "132      Gone with the Wind (1939)  0.801736\n",
       "142     Sound of Music, The (1965)  0.858096\n",
       "416        Parent Trap, The (1961)  0.858263\n",
       "418            Mary Poppins (1964)  0.934540\n",
       "601   American in Paris, An (1951)  0.941190\n",
       "605           All About Eve (1950)  0.944712\n",
       "628         Victor/Victoria (1982)  0.981944\n",
       "706         Enchanted April (1991)  0.997569\n",
       "1146              My Family (1995)  1.011438"
      ]
     },
     "execution_count": 348,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "closest_movies_dfs['My Fair Lady']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 349,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Closest Movies</th>\n",
       "      <th>Distance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>126</th>\n",
       "      <td>Godfather, The (1972)</td>\n",
       "      <td>0.532443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>176</th>\n",
       "      <td>Good, The Bad and The Ugly, The (1966)</td>\n",
       "      <td>0.670239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>179</th>\n",
       "      <td>Apocalypse Now (1979)</td>\n",
       "      <td>0.674657</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>184</th>\n",
       "      <td>Psycho (1960)</td>\n",
       "      <td>0.685926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>186</th>\n",
       "      <td>Godfather: Part II, The (1974)</td>\n",
       "      <td>0.719666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>187</th>\n",
       "      <td>Full Metal Jacket (1987)</td>\n",
       "      <td>0.750065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>503</th>\n",
       "      <td>Bonnie and Clyde (1967)</td>\n",
       "      <td>0.757353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>507</th>\n",
       "      <td>People vs. Larry Flynt, The (1996)</td>\n",
       "      <td>0.893697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>645</th>\n",
       "      <td>Once Upon a Time in the West (1969)</td>\n",
       "      <td>0.914318</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>692</th>\n",
       "      <td>Casino (1995)</td>\n",
       "      <td>0.919381</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             Closest Movies  Distance\n",
       "126                   Godfather, The (1972)  0.532443\n",
       "176  Good, The Bad and The Ugly, The (1966)  0.670239\n",
       "179                   Apocalypse Now (1979)  0.674657\n",
       "184                           Psycho (1960)  0.685926\n",
       "186          Godfather: Part II, The (1974)  0.719666\n",
       "187                Full Metal Jacket (1987)  0.750065\n",
       "503                 Bonnie and Clyde (1967)  0.757353\n",
       "507      People vs. Larry Flynt, The (1996)  0.893697\n",
       "645     Once Upon a Time in the West (1969)  0.914318\n",
       "692                           Casino (1995)  0.919381"
      ]
     },
     "execution_count": 349,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "closest_movies_dfs['GoodFellas']"
   ]
  }
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