matrix_factorization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 関係データ学習（後半）の実装\n",
    "## 行列分解\n",
    "moveleans 100K\n",
    "https://grouplens.org/datasets/movielens/100k/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>uid</th>\n",
       "      <th>mid</th>\n",
       "      <th>rating</th>\n",
       "      <th>timestamp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>196</td>\n",
       "      <td>242</td>\n",
       "      <td>3</td>\n",
       "      <td>881250949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>186</td>\n",
       "      <td>302</td>\n",
       "      <td>3</td>\n",
       "      <td>891717742</td>\n",
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       "      <td>878887116</td>\n",
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       "      <td>2</td>\n",
       "      <td>880606923</td>\n",
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       "      <td>4</td>\n",
       "      <td>884182806</td>\n",
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       "      <td>2</td>\n",
       "      <td>881171488</td>\n",
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       "      <td>3</td>\n",
       "      <td>891035994</td>\n",
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       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>224</td>\n",
       "      <td>29</td>\n",
       "      <td>3</td>\n",
       "      <td>888104457</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>303</td>\n",
       "      <td>785</td>\n",
       "      <td>3</td>\n",
       "      <td>879485318</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>122</td>\n",
       "      <td>387</td>\n",
       "      <td>5</td>\n",
       "      <td>879270459</td>\n",
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       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>194</td>\n",
       "      <td>274</td>\n",
       "      <td>2</td>\n",
       "      <td>879539794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>291</td>\n",
       "      <td>1042</td>\n",
       "      <td>4</td>\n",
       "      <td>874834944</td>\n",
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       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>234</td>\n",
       "      <td>1184</td>\n",
       "      <td>2</td>\n",
       "      <td>892079237</td>\n",
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       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>119</td>\n",
       "      <td>392</td>\n",
       "      <td>4</td>\n",
       "      <td>886176814</td>\n",
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       "      <th>21</th>\n",
       "      <td>167</td>\n",
       "      <td>486</td>\n",
       "      <td>4</td>\n",
       "      <td>892738452</td>\n",
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       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>299</td>\n",
       "      <td>144</td>\n",
       "      <td>4</td>\n",
       "      <td>877881320</td>\n",
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       "      <td>291</td>\n",
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       "      <td>95</td>\n",
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       "      <td>879196566</td>\n",
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       "      <th>26</th>\n",
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       "      <td>5</td>\n",
       "      <td>892430094</td>\n",
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       "      <td>102</td>\n",
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       "      <td>2</td>\n",
       "      <td>883748450</td>\n",
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       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>63</td>\n",
       "      <td>277</td>\n",
       "      <td>4</td>\n",
       "      <td>875747401</td>\n",
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       "      <td>5</td>\n",
       "      <td>876861185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
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       "      <th>99970</th>\n",
       "      <td>449</td>\n",
       "      <td>120</td>\n",
       "      <td>1</td>\n",
       "      <td>879959573</td>\n",
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       "    <tr>\n",
       "      <th>99971</th>\n",
       "      <td>661</td>\n",
       "      <td>762</td>\n",
       "      <td>2</td>\n",
       "      <td>876037121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99972</th>\n",
       "      <td>721</td>\n",
       "      <td>874</td>\n",
       "      <td>3</td>\n",
       "      <td>877137447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99973</th>\n",
       "      <td>821</td>\n",
       "      <td>151</td>\n",
       "      <td>4</td>\n",
       "      <td>874792889</td>\n",
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       "    <tr>\n",
       "      <th>99974</th>\n",
       "      <td>764</td>\n",
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       "      <td>3</td>\n",
       "      <td>876243046</td>\n",
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       "      <td>537</td>\n",
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       "      <td>886031752</td>\n",
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       "      <th>99976</th>\n",
       "      <td>618</td>\n",
       "      <td>628</td>\n",
       "      <td>2</td>\n",
       "      <td>891308019</td>\n",
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       "    <tr>\n",
       "      <th>99977</th>\n",
       "      <td>487</td>\n",
       "      <td>291</td>\n",
       "      <td>3</td>\n",
       "      <td>883445079</td>\n",
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       "    <tr>\n",
       "      <th>99978</th>\n",
       "      <td>113</td>\n",
       "      <td>975</td>\n",
       "      <td>5</td>\n",
       "      <td>875936424</td>\n",
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       "    <tr>\n",
       "      <th>99979</th>\n",
       "      <td>943</td>\n",
       "      <td>391</td>\n",
       "      <td>2</td>\n",
       "      <td>888640291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99980</th>\n",
       "      <td>864</td>\n",
       "      <td>685</td>\n",
       "      <td>4</td>\n",
       "      <td>888891900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99981</th>\n",
       "      <td>750</td>\n",
       "      <td>323</td>\n",
       "      <td>3</td>\n",
       "      <td>879445877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99982</th>\n",
       "      <td>279</td>\n",
       "      <td>64</td>\n",
       "      <td>1</td>\n",
       "      <td>875308510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99983</th>\n",
       "      <td>646</td>\n",
       "      <td>750</td>\n",
       "      <td>3</td>\n",
       "      <td>888528902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99984</th>\n",
       "      <td>654</td>\n",
       "      <td>370</td>\n",
       "      <td>2</td>\n",
       "      <td>887863914</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99985</th>\n",
       "      <td>617</td>\n",
       "      <td>582</td>\n",
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       "      <td>883789294</td>\n",
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       "    <tr>\n",
       "      <th>99986</th>\n",
       "      <td>913</td>\n",
       "      <td>690</td>\n",
       "      <td>3</td>\n",
       "      <td>880824288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99987</th>\n",
       "      <td>660</td>\n",
       "      <td>229</td>\n",
       "      <td>2</td>\n",
       "      <td>891406212</td>\n",
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       "    <tr>\n",
       "      <th>99988</th>\n",
       "      <td>421</td>\n",
       "      <td>498</td>\n",
       "      <td>4</td>\n",
       "      <td>892241344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99989</th>\n",
       "      <td>495</td>\n",
       "      <td>1091</td>\n",
       "      <td>4</td>\n",
       "      <td>888637503</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99990</th>\n",
       "      <td>806</td>\n",
       "      <td>421</td>\n",
       "      <td>4</td>\n",
       "      <td>882388897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99991</th>\n",
       "      <td>676</td>\n",
       "      <td>538</td>\n",
       "      <td>4</td>\n",
       "      <td>892685437</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99992</th>\n",
       "      <td>721</td>\n",
       "      <td>262</td>\n",
       "      <td>3</td>\n",
       "      <td>877137285</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99993</th>\n",
       "      <td>913</td>\n",
       "      <td>209</td>\n",
       "      <td>2</td>\n",
       "      <td>881367150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99994</th>\n",
       "      <td>378</td>\n",
       "      <td>78</td>\n",
       "      <td>3</td>\n",
       "      <td>880056976</td>\n",
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       "    <tr>\n",
       "      <th>99995</th>\n",
       "      <td>880</td>\n",
       "      <td>476</td>\n",
       "      <td>3</td>\n",
       "      <td>880175444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99996</th>\n",
       "      <td>716</td>\n",
       "      <td>204</td>\n",
       "      <td>5</td>\n",
       "      <td>879795543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99997</th>\n",
       "      <td>276</td>\n",
       "      <td>1090</td>\n",
       "      <td>1</td>\n",
       "      <td>874795795</td>\n",
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       "    <tr>\n",
       "      <th>99998</th>\n",
       "      <td>13</td>\n",
       "      <td>225</td>\n",
       "      <td>2</td>\n",
       "      <td>882399156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99999</th>\n",
       "      <td>12</td>\n",
       "      <td>203</td>\n",
       "      <td>3</td>\n",
       "      <td>879959583</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100000 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       uid   mid  rating  timestamp\n",
       "0      196   242       3  881250949\n",
       "1      186   302       3  891717742\n",
       "2       22   377       1  878887116\n",
       "3      244    51       2  880606923\n",
       "4      166   346       1  886397596\n",
       "5      298   474       4  884182806\n",
       "6      115   265       2  881171488\n",
       "7      253   465       5  891628467\n",
       "8      305   451       3  886324817\n",
       "9        6    86       3  883603013\n",
       "10      62   257       2  879372434\n",
       "11     286  1014       5  879781125\n",
       "12     200   222       5  876042340\n",
       "13     210    40       3  891035994\n",
       "14     224    29       3  888104457\n",
       "15     303   785       3  879485318\n",
       "16     122   387       5  879270459\n",
       "17     194   274       2  879539794\n",
       "18     291  1042       4  874834944\n",
       "19     234  1184       2  892079237\n",
       "20     119   392       4  886176814\n",
       "21     167   486       4  892738452\n",
       "22     299   144       4  877881320\n",
       "23     291   118       2  874833878\n",
       "24     308     1       4  887736532\n",
       "25      95   546       2  879196566\n",
       "26      38    95       5  892430094\n",
       "27     102   768       2  883748450\n",
       "28      63   277       4  875747401\n",
       "29     160   234       5  876861185\n",
       "...    ...   ...     ...        ...\n",
       "99970  449   120       1  879959573\n",
       "99971  661   762       2  876037121\n",
       "99972  721   874       3  877137447\n",
       "99973  821   151       4  874792889\n",
       "99974  764   596       3  876243046\n",
       "99975  537   443       3  886031752\n",
       "99976  618   628       2  891308019\n",
       "99977  487   291       3  883445079\n",
       "99978  113   975       5  875936424\n",
       "99979  943   391       2  888640291\n",
       "99980  864   685       4  888891900\n",
       "99981  750   323       3  879445877\n",
       "99982  279    64       1  875308510\n",
       "99983  646   750       3  888528902\n",
       "99984  654   370       2  887863914\n",
       "99985  617   582       4  883789294\n",
       "99986  913   690       3  880824288\n",
       "99987  660   229       2  891406212\n",
       "99988  421   498       4  892241344\n",
       "99989  495  1091       4  888637503\n",
       "99990  806   421       4  882388897\n",
       "99991  676   538       4  892685437\n",
       "99992  721   262       3  877137285\n",
       "99993  913   209       2  881367150\n",
       "99994  378    78       3  880056976\n",
       "99995  880   476       3  880175444\n",
       "99996  716   204       5  879795543\n",
       "99997  276  1090       1  874795795\n",
       "99998   13   225       2  882399156\n",
       "99999   12   203       3  879959583\n",
       "\n",
       "[100000 rows x 4 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"./ml-100k/u.data\", names=[\"uid\", \"mid\", \"rating\", \"timestamp\"], sep=\"\\t\")\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pylab as plt\n",
    "import seaborn\n",
    "import numpy as np\n",
    "\n",
    "def plot_matrix(matrix, clusters=None):\n",
    "    f, ax = plt.subplots(figsize=(10, 10))\n",
    "    plt.pcolormesh(matrix, cmap=plt.cm.Blues )\n",
    "    plt.xlabel(\"movie id\")\n",
    "    plt.ylabel(\"user id\")\n",
    "    if not clusters is None:\n",
    "        clusters_diff = np.r_[[0], np.diff(clusters)]\n",
    "        print(clusters_diff)\n",
    "        for i,c in enumerate(clusters_diff):\n",
    "            if c==1:\n",
    "                ax.axhline(i, c=\"grey\") #, linewidth=1)\n",
    "                ax.axvline(i, c=\"grey\")#, linewidth=1)\n",
    "    plt.savefig(\"../../temp.svg\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = np.zeros((data[\"uid\"].max(), data[\"mid\"].max()))\n",
    "for i,item in data.iterrows():\n",
    "    X[item[\"uid\"]-1, item[\"mid\"]-1] = item[\"rating\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "943 1682\n"
     ]
    }
   ],
   "source": [
    "print(data[\"uid\"].max(), data[\"mid\"].max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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eM4zsqmzYVE7h7Zunt1S1DiI6Stj4G6ZdOSOaf28k5iD1osfP4kP7Icx6nikkLHcRzHcRzHcZwB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\nmuy16TYMDW3tKd2njQTq4bqx67mk0HEcx3Ecx3EcZ0Cseg/XJ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8GUiv1XujfK+8Hb3lfH/KUMu6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\ni0pYfJP1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f352a3bfdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_matrix(X[:500, :500])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1次交互勾配降下法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import copy \n",
    "original_X = copy.deepcopy(X) \n",
    "X = X[:100, :100]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "reg = 0.001\n",
    "learning_rate = 0.002\n",
    "convergence_boader = 0.0001\n",
    "R = 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "I = X.shape[0]\n",
    "J = X.shape[1]\n",
    "U = np.mat(np.random.random((I, R)))\n",
    "V = np.mat(np.random.random((J, R)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dU = lambda U,V: -X*V + U * (V.T*V + reg*np.mat(np.identity(R)))\n",
    "dV = lambda U,V: -X.T*U + V * (U.T*U + reg*np.mat(np.identity(R)))\n",
    "error = lambda U,V: 0.5*np.sum(np.array(X-U*V.T)**2) + 0.5*reg*np.sum( np.sum(np.array(U)**2,axis=0) + np.sum(np.array(V)**2,axis=0))\n",
    "err_hist = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "for i in range(2000):\n",
    "    e = error(U,V)\n",
    "    U -= learning_rate * dU(U,V)\n",
    "    V -= learning_rate * dV(U,V)\n",
    "    err_hist.append(e)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kqaKiQsePH1dVVZX27Nkj27a1atWq4H0vXbpUWVlZqq2tVWVlpfbu3avKyspIHRoAAABi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\nyRKMFwYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f350b1fd160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(err_hist)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f35099f79b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(figsize=(20, 10))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.pcolormesh(X, cmap=plt.cm.Blues )\n",
    "plt.xlabel(\"movie id\")\n",
    "plt.ylabel(\"user id\")\n",
    "plt.subplot(122)\n",
    "plt.pcolormesh(np.array(U*V.T), cmap=plt.cm.Blues )\n",
    "plt.xlabel(\"movie id\")\n",
    "plt.ylabel(\"user id\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 擬似2次交互勾配法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "reg = 0.001\n",
    "learning_rate = 0.1\n",
    "convergence_boader = 0.0001\n",
    "R = 20\n",
    "\n",
    "I = X.shape[0]\n",
    "J = X.shape[1]\n",
    "U = np.mat(np.random.random((I, R)))\n",
    "V = np.mat(np.random.random((J, R)))\n",
    "err_hist = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0aJGmTJmiuXPnqra2Nuaxu3fv1pw5czR16lQtWbJEgUAgMtbR0aENGzaosLBQBQUFWrly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\nAAAc/xcAv+yziBQdYQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f35098b3b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(2000):\n",
    "    e = error(U,V)\n",
    "    U = (1-learning_rate)*U + learning_rate * X*V*((V.T*V+reg*np.mat(np.identity(R))).I)\n",
    "    V = (1-learning_rate)*V + learning_rate * X.T*U*((U.T*U+reg*np.mat(np.identity(R))).I)\n",
    "    err_hist.append(e)\n",
    "plt.plot(err_hist)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3509a1e860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(figsize=(20, 10))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.pcolormesh(X, cmap=plt.cm.Blues )\n",
    "plt.xlabel(\"movie id\")\n",
    "plt.ylabel(\"user id\")\n",
    "plt.subplot(122)\n",
    "plt.pcolormesh(np.array(U*V.T), cmap=plt.cm.Blues )\n",
    "plt.xlabel(\"movie id\")\n",
    "plt.ylabel(\"user id\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = original_X\n",
    "reg = 0.001\n",
    "learning_rate = 0.01\n",
    "convergence_boader = 0.0001\n",
    "R = 100\n",
    "\n",
    "I = X.shape[0]\n",
    "J = X.shape[1]\n",
    "U = np.mat(np.random.random((I, R)))\n",
    "V = np.mat(np.random.random((J, R)))\n",
    "err_hist=[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pFdD6cCP1YSEUAKAqSg+gSTI01ChrGAAAFKwpAugOO+EBACqj9IPoE+tAAQCqpCkqoA6j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\nJYACAFCo/w/GLmB+IhujxAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f350b1f3c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(2000):\n",
    "    e = error(U,V)\n",
    "    U = (1-learning_rate)*U + learning_rate * X*V*((V.T*V+reg*np.mat(np.identity(R))).I)\n",
    "    V = (1-learning_rate)*V + learning_rate * X.T*U*((U.T*U+reg*np.mat(np.identity(R))).I)\n",
    "    err_hist.append(e)\n",
    "plt.plot(err_hist)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(943, 1682)\n"
     ]
    }
   ],
   "source": [
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f351fb13fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(figsize=(20, 10))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.pcolormesh(X[:100, :100], cmap=plt.cm.Blues )\n",
    "plt.xlabel(\"movie id\")\n",
    "plt.ylabel(\"user id\")\n",
    "plt.subplot(122)\n",
    "plt.pcolormesh(np.array(U*V.T)[:100, :100], cmap=plt.cm.Blues )\n",
    "plt.xlabel(\"movie id\")\n",
    "plt.ylabel(\"user id\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}