5. Recommender Systems - MovieLens.ipynb

{
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "    <div style=\"width: 150px; float: left;\"> <img src=\"https://raw.githubusercontent.com/DataForScience/Networks/master/data/D4Sci_logo_ball.png\" alt=\"Data For Science, Inc\" align=\"left\" border=\"0\" width=160px> </div>\n",
    "    <div style=\"float: left; margin-left: 10px;\"> <h1>Graphs and Networks</h1>\n",
    "<h1>Recommender Systems</h1>\n",
    "        <p>Bruno Gonçalves<br/>\n",
    "        <a href=\"http://www.data4sci.com/\">www.data4sci.com</a><br/>\n",
    "            @bgoncalves, @data4sci</p></div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "from pprint import pprint\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt \n",
    "\n",
    "import watermark\n",
    "\n",
    "%load_ext watermark\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Watermark the notebook with current versions of all loaded libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.8.5\n",
      "IPython version      : 8.12.2\n",
      "\n",
      "Compiler    : Clang 10.0.0 \n",
      "OS          : Darwin\n",
      "Release     : 22.4.0\n",
      "Machine     : x86_64\n",
      "Processor   : i386\n",
      "CPU cores   : 16\n",
      "Architecture: 64bit\n",
      "\n",
      "Git hash: 9b30d4c9f20eabe04050cf37ac0737eccf407aee\n",
      "\n",
      "matplotlib: 3.7.1\n",
      "json      : 2.0.9\n",
      "pandas    : 1.5.3\n",
      "watermark : 2.1.0\n",
      "numpy     : 1.24.2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%watermark -n -v -m -g -iv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load default figure style"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('./d4sci.mplstyle')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use this simple example, where everything is easy to visualize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"data/bipartite.png\" width='400px'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by defining the adjacency matrix of our bipartite network. This is not the most efficient graph representation, but it is the most convenient in our case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ratings = pd.read_csv('data/ml-latest-small/ratings.csv')\n",
    "ratings = pd.pivot_table(ratings, index='userId', columns='movieId', values='rating')\n",
    "ratings.fillna(0, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
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      "text/plain": [
       "movieId  1       2       3       4       5       6       7       8       \\\n",
       "userId                                                                    \n",
       "1           4.0     0.0     4.0     0.0     0.0     4.0     0.0     0.0   \n",
       "2           0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
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       "...         ...     ...     ...     ...     ...     ...     ...     ...   \n",
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       "609         3.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "610         5.0     0.0     0.0     0.0     0.0     5.0     0.0     0.0   \n",
       "\n",
       "movieId  9       10      ...  193565  193567  193571  193573  193579  193581  \\\n",
       "userId                   ...                                                   \n",
       "1           0.0     0.0  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "2           0.0     0.0  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "3           0.0     0.0  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "4           0.0     0.0  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "5           0.0     0.0  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "...         ...     ...  ...     ...     ...     ...     ...     ...     ...   \n",
       "606         0.0     0.0  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "607         0.0     0.0  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "608         0.0     4.0  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "609         0.0     4.0  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "610         0.0     0.0  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "\n",
       "movieId  193583  193585  193587  193609  \n",
       "userId                                   \n",
       "1           0.0     0.0     0.0     0.0  \n",
       "2           0.0     0.0     0.0     0.0  \n",
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       "5           0.0     0.0     0.0     0.0  \n",
       "...         ...     ...     ...     ...  \n",
       "606         0.0     0.0     0.0     0.0  \n",
       "607         0.0     0.0     0.0     0.0  \n",
       "608         0.0     0.0     0.0     0.0  \n",
       "609         0.0     0.0     0.0     0.0  \n",
       "610         0.0     0.0     0.0     0.0  \n",
       "\n",
       "[610 rows x 9724 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ratings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Map to adjacency matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = ratings.copy()\n",
    "A[A>0] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "A.fillna(0, inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The adjacency matrix is then:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>movieId</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>...</th>\n",
       "      <th>193565</th>\n",
       "      <th>193567</th>\n",
       "      <th>193571</th>\n",
       "      <th>193573</th>\n",
       "      <th>193579</th>\n",
       "      <th>193581</th>\n",
       "      <th>193583</th>\n",
       "      <th>193585</th>\n",
       "      <th>193587</th>\n",
       "      <th>193609</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>userId</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>606</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>607</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>608</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>609</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>610</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>610 rows × 9724 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "movieId  1       2       3       4       5       6       7       8       \\\n",
       "userId                                                                    \n",
       "1             1       0       1       0       0       1       0       0   \n",
       "2             0       0       0       0       0       0       0       0   \n",
       "3             0       0       0       0       0       0       0       0   \n",
       "4             0       0       0       0       0       0       0       0   \n",
       "5             1       0       0       0       0       0       0       0   \n",
       "...         ...     ...     ...     ...     ...     ...     ...     ...   \n",
       "606           1       0       0       0       0       0       1       0   \n",
       "607           1       0       0       0       0       0       0       0   \n",
       "608           1       1       1       0       0       0       0       0   \n",
       "609           1       0       0       0       0       0       0       0   \n",
       "610           1       0       0       0       0       1       0       0   \n",
       "\n",
       "movieId  9       10      ...  193565  193567  193571  193573  193579  193581  \\\n",
       "userId                   ...                                                   \n",
       "1             0       0  ...       0       0       0       0       0       0   \n",
       "2             0       0  ...       0       0       0       0       0       0   \n",
       "3             0       0  ...       0       0       0       0       0       0   \n",
       "4             0       0  ...       0       0       0       0       0       0   \n",
       "5             0       0  ...       0       0       0       0       0       0   \n",
       "...         ...     ...  ...     ...     ...     ...     ...     ...     ...   \n",
       "606           0       0  ...       0       0       0       0       0       0   \n",
       "607           0       0  ...       0       0       0       0       0       0   \n",
       "608           0       1  ...       0       0       0       0       0       0   \n",
       "609           0       1  ...       0       0       0       0       0       0   \n",
       "610           0       0  ...       0       0       0       0       0       0   \n",
       "\n",
       "movieId  193583  193585  193587  193609  \n",
       "userId                                   \n",
       "1             0       0       0       0  \n",
       "2             0       0       0       0  \n",
       "3             0       0       0       0  \n",
       "4             0       0       0       0  \n",
       "5             0       0       0       0  \n",
       "...         ...     ...     ...     ...  \n",
       "606           0       0       0       0  \n",
       "607           0       0       0       0  \n",
       "608           0       0       0       0  \n",
       "609           0       0       0       0  \n",
       "610           0       0       0       0  \n",
       "\n",
       "[610 rows x 9724 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.astype('int')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In total, we have 610 users and 9724 movies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(610, 9724)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can easily calculate the degree of each kind of nodes as well, by simply summing over the rows or columns. This corresponds to the number of movies each user rated and the number of users that rated each movie, respectively:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "k_user = A.sum(axis=1)\n",
    "k_movie = A.sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "userId\n",
       "1       232.0\n",
       "2        29.0\n",
       "3        39.0\n",
       "4       216.0\n",
       "5        44.0\n",
       "        ...  \n",
       "606    1115.0\n",
       "607     187.0\n",
       "608     831.0\n",
       "609      37.0\n",
       "610    1302.0\n",
       "Length: 610, dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k_user"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "movieId\n",
       "1         215.0\n",
       "2         110.0\n",
       "3          52.0\n",
       "4           7.0\n",
       "5          49.0\n",
       "          ...  \n",
       "193581      1.0\n",
       "193583      1.0\n",
       "193585      1.0\n",
       "193587      1.0\n",
       "193609      1.0\n",
       "Length: 9724, dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k_movie"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The User-User and Movie-Movie one-mode projections are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "UU = A.dot(A.T)\n",
    "MM = A.T.dot(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(610, 610)\n"
     ]
    }
   ],
   "source": [
    "pprint(UU.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(9724, 9724)\n"
     ]
    }
   ],
   "source": [
    "pprint(MM.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Similarity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us define the similarity between two users (UU) or movies (MM) to simply be the fraction of edges user u shares with user u. For convenience, we supply the one-mode UU projection directly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def similarity(X, kx):\n",
    "    S = X.copy().astype('float')\n",
    "    \n",
    "    for i in X.index:\n",
    "        for j in X.columns:\n",
    "            S.loc[i, j]/= np.min([kx[i], kx[j]])\n",
    "\n",
    "    return S"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our similarity is then:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "userId       1         2         3         4         5         6         7    \\\n",
      "userId                                                                         \n",
      "1       1.000000  0.068966  0.179487  0.208333  0.295455  0.142241  0.171053   \n",
      "2       0.068966  1.000000  0.000000  0.034483  0.034483  0.068966  0.103448   \n",
      "3       0.179487  0.000000  1.000000  0.025641  0.025641  0.076923  0.000000   \n",
      "4       0.208333  0.034483  0.025641  1.000000  0.272727  0.125000  0.144737   \n",
      "5       0.295455  0.034483  0.025641  0.272727  1.000000  0.818182  0.204545   \n",
      "...          ...       ...       ...       ...       ...       ...       ...   \n",
      "606     0.362069  0.172414  0.205128  0.444444  0.522727  0.203822  0.532895   \n",
      "607     0.320856  0.034483  0.102564  0.155080  0.340909  0.192513  0.184211   \n",
      "608     0.586207  0.206897  0.230769  0.342593  0.681818  0.353503  0.690789   \n",
      "609     0.243243  0.034483  0.000000  0.081081  0.270270  0.594595  0.162162   \n",
      "610     0.297414  0.620690  0.179487  0.245370  0.318182  0.098726  0.539474   \n",
      "\n",
      "userId       8         9         10   ...       601       602       603  \\\n",
      "userId                                ...                                 \n",
      "1       0.319149  0.108696  0.042857  ...  0.108911  0.200000  0.474138   \n",
      "2       0.034483  0.000000  0.172414  ...  0.379310  0.034483  0.068966   \n",
      "3       0.025641  0.000000  0.000000  ...  0.051282  0.051282  0.230769   \n",
      "4       0.191489  0.021739  0.064286  ...  0.148515  0.170370  0.643519   \n",
      "5       0.431818  0.000000  0.068182  ...  0.090909  0.704545  0.568182   \n",
      "...          ...       ...       ...  ...       ...       ...       ...   \n",
      "606     0.489362  0.326087  0.285714  ...  0.534653  0.340741  0.327678   \n",
      "607     0.340426  0.021739  0.035714  ...  0.108911  0.214815  0.508021   \n",
      "608     0.851064  0.391304  0.192857  ...  0.376238  0.525926  0.264741   \n",
      "609     0.459459  0.000000  0.054054  ...  0.054054  0.621622  0.351351   \n",
      "610     0.361702  0.304348  0.378571  ...  0.683168  0.214815  0.170732   \n",
      "\n",
      "userId       604       605       606       607       608       609       610  \n",
      "userId                                                                        \n",
      "1       0.120000  0.158371  0.362069  0.320856  0.586207  0.243243  0.297414  \n",
      "2       0.000000  0.000000  0.172414  0.034483  0.206897  0.034483  0.620690  \n",
      "3       0.000000  0.025641  0.205128  0.102564  0.230769  0.000000  0.179487  \n",
      "4       0.090000  0.074074  0.444444  0.155080  0.342593  0.081081  0.245370  \n",
      "5       0.431818  0.318182  0.522727  0.340909  0.681818  0.270270  0.318182  \n",
      "...          ...       ...       ...       ...       ...       ...       ...  \n",
      "606     0.230000  0.330317  1.000000  0.401070  0.305656  0.405405  0.200000  \n",
      "607     0.190000  0.122995  0.401070  1.000000  0.620321  0.324324  0.326203  \n",
      "608     0.530000  0.348416  0.305656  0.620321  1.000000  0.621622  0.356197  \n",
      "609     0.378378  0.243243  0.405405  0.324324  0.621622  1.000000  0.270270  \n",
      "610     0.170000  0.285068  0.200000  0.326203  0.356197  0.270270  1.000000  \n",
      "\n",
      "[610 rows x 610 columns]\n"
     ]
    }
   ],
   "source": [
    "S = similarity(UU, k_user)\n",
    "print(S)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Naturally, this symmilarity metric is symmetric"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(S-S.T).mean().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can predict scores for all user/item pairs. The score for each user-item pair will be the average similarity of all users that have rated that item"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_score(A, S):\n",
    "    # sum the scores of each rater for each movie, weighted by similarity\n",
    "    v = S.dot(A)\n",
    "    \n",
    "    # Get the norm across all similarities\n",
    "    norms = S.sum(axis=0)-np.diag(S)\n",
    "    \n",
    "    # Divide by the norm to normalize the scores\n",
    "    v = v.div(norms).fillna(0)\n",
    "\n",
    "    return v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predicted scores are then:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
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       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>...</th>\n",
       "      <th>193565</th>\n",
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       "      <th>193585</th>\n",
       "      <th>193587</th>\n",
       "      <th>193609</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>userId</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.41</td>\n",
       "      <td>0.48</td>\n",
       "      <td>0.61</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.13</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.56</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.23</td>\n",
       "      <td>0.31</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.23</td>\n",
       "      <td>...</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.12</td>\n",
       "      <td>0.17</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.16</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.29</td>\n",
       "      <td>0.32</td>\n",
       "      <td>0.38</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.36</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.47</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.67</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.74</td>\n",
       "      <td>...</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>606</th>\n",
       "      <td>0.57</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.56</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.67</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>607</th>\n",
       "      <td>0.41</td>\n",
       "      <td>0.49</td>\n",
       "      <td>0.55</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.58</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>608</th>\n",
       "      <td>0.76</td>\n",
       "      <td>0.86</td>\n",
       "      <td>0.94</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.34</td>\n",
       "      <td>0.23</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.21</td>\n",
       "      <td>1.05</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>609</th>\n",
       "      <td>0.41</td>\n",
       "      <td>0.55</td>\n",
       "      <td>0.59</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.13</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.69</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>610</th>\n",
       "      <td>0.58</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.46</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.64</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>610 rows × 9811 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        1       2       3       4       5       6       7       8       \\\n",
       "userId                                                                   \n",
       "1         0.41    0.48    0.61    0.02    0.11    0.21    0.13    0.02   \n",
       "2         0.23    0.31    0.22    0.00    0.05    0.10    0.04    0.01   \n",
       "3         0.12    0.17    0.21    0.01    0.04    0.07    0.04    0.01   \n",
       "4         0.29    0.32    0.38    0.01    0.08    0.14    0.10    0.01   \n",
       "5         0.47    0.64    0.67    0.04    0.14    0.24    0.16    0.03   \n",
       "...        ...     ...     ...     ...     ...     ...     ...     ...   \n",
       "606       0.57    0.58    0.56    0.03    0.12    0.24    0.16    0.02   \n",
       "607       0.41    0.49    0.55    0.02    0.11    0.20    0.12    0.02   \n",
       "608       0.76    0.86    0.94    0.03    0.20    0.34    0.23    0.03   \n",
       "609       0.41    0.55    0.59    0.03    0.12    0.21    0.13    0.02   \n",
       "610       0.58    0.58    0.46    0.01    0.10    0.24    0.11    0.01   \n",
       "\n",
       "        9       10      ...  193565  193567  193571  193573  193579  193581  \\\n",
       "userId                  ...                                                   \n",
       "1         0.10    0.56  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "2         0.03    0.23  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "3         0.03    0.16  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "4         0.06    0.36  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "5         0.08    0.74  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "...        ...     ...  ...     ...     ...     ...     ...     ...     ...   \n",
       "606       0.10    0.67  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "607       0.10    0.58  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "608       0.21    1.05  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "609       0.09    0.69  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "610       0.10    0.64  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "\n",
       "        193583  193585  193587  193609  \n",
       "userId                                  \n",
       "1          0.0     0.0     0.0     0.0  \n",
       "2          0.0     0.0     0.0     0.0  \n",
       "3          0.0     0.0     0.0     0.0  \n",
       "4          0.0     0.0     0.0     0.0  \n",
       "5          0.0     0.0     0.0     0.0  \n",
       "...        ...     ...     ...     ...  \n",
       "606        0.0     0.0     0.0     0.0  \n",
       "607        0.0     0.0     0.0     0.0  \n",
       "608        0.0     0.0     0.0     0.0  \n",
       "609        0.0     0.0     0.0     0.0  \n",
       "610        0.0     0.0     0.0     0.0  \n",
       "\n",
       "[610 rows x 9811 columns]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = predict_score(A, S)\n",
    "v.round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Similarity based on Ratings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us define the similarity between two users (UU) or movies (MM) to simply be the fraction of edges user u shares with user u. For convenience, we supply the one-mode UU projection directly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "UUr = ratings.dot(ratings.T)\n",
    "MMr = ratings.T.dot(ratings)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our similarity is then:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "userId        1          2          3          4          5          6    \\\n",
      "userId                                                                     \n",
      "1       19.702586   1.379310   2.064103   3.388889   4.954545   2.379310   \n",
      "2        1.379310  16.215517   0.000000   0.155172   0.310345   1.206897   \n",
      "3        2.064103   0.000000  10.192308   0.064103   0.064103   0.128205   \n",
      "4        3.388889   0.155172   0.064103  14.361111   4.068182   1.453704   \n",
      "5        4.954545   0.310345   0.064103   4.068182  14.181818  10.863636   \n",
      "...           ...        ...        ...        ...        ...        ...   \n",
      "606      5.956897   2.646552   0.826923   6.432870   7.522727   2.579618   \n",
      "607      5.203209   0.517241   0.525641   2.096257   4.636364   2.951872   \n",
      "608      8.105603   3.301724   1.032051   3.692130   7.352273   3.466561   \n",
      "609      3.432432   0.413793   0.000000   0.972973   3.540541   7.405405   \n",
      "610      5.786638  10.465517   2.243590   3.793981   4.715909   1.460191   \n",
      "\n",
      "userId       7         8         9         10   ...        601       602  \\\n",
      "userId                                          ...                        \n",
      "1       3.039474  5.000000  2.239130  0.335714  ...   2.410891  3.377778   \n",
      "2       0.887931  0.517241  0.000000  2.077586  ...   6.775862  0.517241   \n",
      "3       0.000000  0.064103  0.000000  0.000000  ...   0.115385  0.102564   \n",
      "4       1.815789  1.893617  0.326087  0.510714  ...   2.118812  2.170370   \n",
      "5       2.647727  6.181818  0.000000  0.715909  ...   1.727273  9.750000   \n",
      "...          ...       ...       ...       ...  ...        ...       ...   \n",
      "606     7.052632  6.680851  4.869565  3.258929  ...   9.814356  4.407407   \n",
      "607     2.815789  5.340426  0.326087  0.164286  ...   2.188119  3.244444   \n",
      "608     8.754934  9.659574  4.945652  2.176786  ...   6.698020  5.733333   \n",
      "609     2.121622  5.837838  0.000000  0.486486  ...   0.864865  7.459459   \n",
      "610     7.476974  5.765957  5.239130  4.867857  ...  13.457921  3.633333   \n",
      "\n",
      "userId       603       604       605        606        607        608  \\\n",
      "userId                                                                  \n",
      "1       7.318966  1.700000  2.314480   5.956897   5.203209   8.105603   \n",
      "2       1.017241  0.000000  0.000000   2.646552   0.517241   3.301724   \n",
      "3       1.448718  0.000000  0.269231   0.826923   0.525641   1.032051   \n",
      "4       9.004630  1.050000  1.074074   6.432870   2.096257   3.692130   \n",
      "5       7.090909  5.227273  4.159091   7.522727   4.636364   7.352273   \n",
      "...          ...       ...       ...        ...        ...        ...   \n",
      "606     4.501060  2.925000  4.109729  13.900448   5.443850   3.758424   \n",
      "607     6.593583  2.620000  1.671123   5.443850  15.262032   7.727273   \n",
      "608     3.034898  5.280000  3.792986   3.758424   7.727273  10.986462   \n",
      "609     3.810811  4.567568  2.608108   4.702703   4.324324   6.324324   \n",
      "610     2.679745  2.555000  3.632353   3.068161   5.430481   5.059868   \n",
      "\n",
      "userId        609        610  \n",
      "userId                        \n",
      "1        3.432432   5.786638  \n",
      "2        0.413793  10.465517  \n",
      "3        0.000000   2.243590  \n",
      "4        0.972973   3.793981  \n",
      "5        3.540541   4.715909  \n",
      "...           ...        ...  \n",
      "606      4.702703   3.068161  \n",
      "607      4.324324   5.430481  \n",
      "608      6.324324   5.059868  \n",
      "609     10.891892   3.945946  \n",
      "610      3.945946  14.340054  \n",
      "\n",
      "[610 rows x 610 columns]\n"
     ]
    }
   ],
   "source": [
    "Sr = similarity(UUr, k_user)\n",
    "print(Sr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "userId        1          2          3          4          5          6    \\\n",
      "userId                                                                     \n",
      "1       19.702586   1.379310   2.064103   3.388889   4.954545   2.379310   \n",
      "2        1.379310  16.215517   0.000000   0.155172   0.310345   1.206897   \n",
      "3        2.064103   0.000000  10.192308   0.064103   0.064103   0.128205   \n",
      "4        3.388889   0.155172   0.064103  14.361111   4.068182   1.453704   \n",
      "5        4.954545   0.310345   0.064103   4.068182  14.181818  10.863636   \n",
      "...           ...        ...        ...        ...        ...        ...   \n",
      "606      5.956897   2.646552   0.826923   6.432870   7.522727   2.579618   \n",
      "607      5.203209   0.517241   0.525641   2.096257   4.636364   2.951872   \n",
      "608      8.105603   3.301724   1.032051   3.692130   7.352273   3.466561   \n",
      "609      3.432432   0.413793   0.000000   0.972973   3.540541   7.405405   \n",
      "610      5.786638  10.465517   2.243590   3.793981   4.715909   1.460191   \n",
      "\n",
      "userId       7         8         9         10   ...        601       602  \\\n",
      "userId                                          ...                        \n",
      "1       3.039474  5.000000  2.239130  0.335714  ...   2.410891  3.377778   \n",
      "2       0.887931  0.517241  0.000000  2.077586  ...   6.775862  0.517241   \n",
      "3       0.000000  0.064103  0.000000  0.000000  ...   0.115385  0.102564   \n",
      "4       1.815789  1.893617  0.326087  0.510714  ...   2.118812  2.170370   \n",
      "5       2.647727  6.181818  0.000000  0.715909  ...   1.727273  9.750000   \n",
      "...          ...       ...       ...       ...  ...        ...       ...   \n",
      "606     7.052632  6.680851  4.869565  3.258929  ...   9.814356  4.407407   \n",
      "607     2.815789  5.340426  0.326087  0.164286  ...   2.188119  3.244444   \n",
      "608     8.754934  9.659574  4.945652  2.176786  ...   6.698020  5.733333   \n",
      "609     2.121622  5.837838  0.000000  0.486486  ...   0.864865  7.459459   \n",
      "610     7.476974  5.765957  5.239130  4.867857  ...  13.457921  3.633333   \n",
      "\n",
      "userId       603       604       605        606        607        608  \\\n",
      "userId                                                                  \n",
      "1       7.318966  1.700000  2.314480   5.956897   5.203209   8.105603   \n",
      "2       1.017241  0.000000  0.000000   2.646552   0.517241   3.301724   \n",
      "3       1.448718  0.000000  0.269231   0.826923   0.525641   1.032051   \n",
      "4       9.004630  1.050000  1.074074   6.432870   2.096257   3.692130   \n",
      "5       7.090909  5.227273  4.159091   7.522727   4.636364   7.352273   \n",
      "...          ...       ...       ...        ...        ...        ...   \n",
      "606     4.501060  2.925000  4.109729  13.900448   5.443850   3.758424   \n",
      "607     6.593583  2.620000  1.671123   5.443850  15.262032   7.727273   \n",
      "608     3.034898  5.280000  3.792986   3.758424   7.727273  10.986462   \n",
      "609     3.810811  4.567568  2.608108   4.702703   4.324324   6.324324   \n",
      "610     2.679745  2.555000  3.632353   3.068161   5.430481   5.059868   \n",
      "\n",
      "userId        609        610  \n",
      "userId                        \n",
      "1        3.432432   5.786638  \n",
      "2        0.413793  10.465517  \n",
      "3        0.000000   2.243590  \n",
      "4        0.972973   3.793981  \n",
      "5        3.540541   4.715909  \n",
      "...           ...        ...  \n",
      "606      4.702703   3.068161  \n",
      "607      4.324324   5.430481  \n",
      "608      6.324324   5.059868  \n",
      "609     10.891892   3.945946  \n",
      "610      3.945946  14.340054  \n",
      "\n",
      "[610 rows x 610 columns]\n"
     ]
    }
   ],
   "source": [
    "print(Sr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Naturally, this symmilarity metric is symmetric"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(Sr-Sr.T).mean().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predicted scores are then:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
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       "      <th>193571</th>\n",
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       "      <th>193585</th>\n",
       "      <th>193587</th>\n",
       "      <th>193609</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>userId</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.41</td>\n",
       "      <td>0.49</td>\n",
       "      <td>1.96</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.13</td>\n",
       "      <td>0.26</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.77</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.21</td>\n",
       "      <td>0.31</td>\n",
       "      <td>0.68</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.31</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.04</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.07</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.23</td>\n",
       "      <td>0.26</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.40</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.38</td>\n",
       "      <td>0.54</td>\n",
       "      <td>1.78</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.83</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>606</th>\n",
       "      <td>0.49</td>\n",
       "      <td>0.50</td>\n",
       "      <td>1.53</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.79</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>607</th>\n",
       "      <td>0.35</td>\n",
       "      <td>0.43</td>\n",
       "      <td>1.56</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.71</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>608</th>\n",
       "      <td>0.55</td>\n",
       "      <td>0.63</td>\n",
       "      <td>2.11</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.30</td>\n",
       "      <td>0.18</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.15</td>\n",
       "      <td>1.05</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>609</th>\n",
       "      <td>0.30</td>\n",
       "      <td>0.43</td>\n",
       "      <td>1.45</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.19</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.73</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>610</th>\n",
       "      <td>0.55</td>\n",
       "      <td>0.56</td>\n",
       "      <td>1.47</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.29</td>\n",
       "      <td>0.13</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.87</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>610 rows × 9811 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        1       2       3       4       5       6       7       8       \\\n",
       "userId                                                                   \n",
       "1         0.41    0.49    1.96    0.02    0.13    0.26    0.14    0.02   \n",
       "2         0.21    0.31    0.68    0.00    0.06    0.12    0.04    0.01   \n",
       "3         0.04    0.05    0.24    0.00    0.01    0.03    0.01    0.00   \n",
       "4         0.23    0.26    0.99    0.01    0.08    0.14    0.09    0.01   \n",
       "5         0.38    0.54    1.78    0.03    0.14    0.24    0.15    0.03   \n",
       "...        ...     ...     ...     ...     ...     ...     ...     ...   \n",
       "606       0.49    0.50    1.53    0.03    0.12    0.25    0.15    0.01   \n",
       "607       0.35    0.43    1.56    0.02    0.11    0.21    0.12    0.02   \n",
       "608       0.55    0.63    2.11    0.02    0.16    0.30    0.18    0.02   \n",
       "609       0.30    0.43    1.45    0.02    0.11    0.19    0.11    0.02   \n",
       "610       0.55    0.56    1.47    0.02    0.12    0.29    0.13    0.01   \n",
       "\n",
       "        9       10      ...  193565  193567  193571  193573  193579  193581  \\\n",
       "userId                  ...                                                   \n",
       "1         0.10    0.77  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "2         0.02    0.31  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "3         0.01    0.07  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "4         0.05    0.40  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "5         0.07    0.83  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "...        ...     ...  ...     ...     ...     ...     ...     ...     ...   \n",
       "606       0.09    0.79  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "607       0.09    0.71  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "608       0.15    1.05  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "609       0.07    0.73  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "610       0.10    0.87  ...     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "\n",
       "        193583  193585  193587  193609  \n",
       "userId                                  \n",
       "1          0.0     0.0     0.0     0.0  \n",
       "2          0.0     0.0     0.0     0.0  \n",
       "3          0.0     0.0     0.0     0.0  \n",
       "4          0.0     0.0     0.0     0.0  \n",
       "5          0.0     0.0     0.0     0.0  \n",
       "...        ...     ...     ...     ...  \n",
       "606        0.0     0.0     0.0     0.0  \n",
       "607        0.0     0.0     0.0     0.0  \n",
       "608        0.0     0.0     0.0     0.0  \n",
       "609        0.0     0.0     0.0     0.0  \n",
       "610        0.0     0.0     0.0     0.0  \n",
       "\n",
       "[610 rows x 9811 columns]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = predict_score(A, Sr)\n",
    "v.round(2)"
   ]
  },
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    "     <img src=\"data/D4Sci_logo_full.png\" alt=\"Data For Science, Inc\" align=\"center\" border=\"0\" width=300px> \n",
    "</div>"
   ]
  }
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