movielens.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Collaborative Filterting on MovieLens Dataset\n",
    "\n",
    "In this notebook, I'm making an attempt to \"unwrap\" abstaction layers of this [fast.ai lecture](http://course.fast.ai/lessons/lesson5.html) where the author is explaining how to use embeddings to build a simple recommendation system.\n",
    "\n",
    "In other words, I'm going to directly use PyTorch framework to train a small deep learning model to predict user ratings for specific movies. The original lesson's notebook is presented [here](https://github.com/fastai/fastai/blob/master/courses/dl1/lesson5-movielens.ipynb).\n",
    "\n",
    "> **Note:** The notebook requires Python 3.6 or above. Otherwise, replace `pathlib` objects with plain paths, and interpolated strings with `format()` calls to make it compatible with the older versions of the interpreter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import io\n",
    "import os\n",
    "import math\n",
    "import copy\n",
    "import pickle\n",
    "import zipfile\n",
    "from textwrap import wrap\n",
    "from pathlib import Path\n",
    "from itertools import zip_longest\n",
    "from collections import defaultdict\n",
    "from urllib.error import URLError\n",
    "from urllib.request import urlopen\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "import torch\n",
    "from torch import nn\n",
    "from torch import optim\n",
    "from torch.nn import functional as F \n",
    "from torch.optim.lr_scheduler import _LRScheduler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function below ensures that we seed all random generators with the same value to get reproducible results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def set_random_seed(state=1):\n",
    "    gens = (np.random.seed, torch.manual_seed, torch.cuda.manual_seed)\n",
    "    for set_state in gens:\n",
    "        set_state(state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "RANDOM_STATE = 1\n",
    "set_random_seed(RANDOM_STATE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Dataset Downloading\n",
    "\n",
    "In the original post, the `ml-latest-small` archive with movies and users is used but there are a few other bigger datasets. You can download any of them. However, some of the datasets use different format to store the records. The function `read_data` tries to read content of the dataset if it is stored with `.csv` or `.dat` extensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def try_download(url, download_path):\n",
    "    archive_name = url.split('/')[-1]\n",
    "    folder_name, _ = os.path.splitext(archive_name)\n",
    "    \n",
    "    try:\n",
    "        r = urlopen(url)\n",
    "    except URLError as e:\n",
    "        print('Cannot download the data. Error: %s' % s)\n",
    "        return \n",
    "\n",
    "    assert r.status == 200\n",
    "    data = r.read()\n",
    "\n",
    "    with zipfile.ZipFile(io.BytesIO(data)) as arch:\n",
    "        arch.extractall(download_path)\n",
    "        \n",
    "    print('The archive is extracted into folder: %s' % download_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def read_data(path):\n",
    "    files = {}\n",
    "    for filename in path.glob('*'):\n",
    "        if filename.suffix == '.csv':\n",
    "            files[filename.stem] = pd.read_csv(filename)\n",
    "        elif filename.suffix == '.dat':\n",
    "            if filename.stem == 'ratings':\n",
    "                columns = ['userId', 'movieId', 'rating', 'timestamp']\n",
    "            else:\n",
    "                columns = ['movieId', 'title', 'genres']\n",
    "            data = pd.read_csv(filename, sep='::', names=columns, engine='python')\n",
    "            files[filename.stem] = data\n",
    "    return files['ratings'], files['movies']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following archives from the [Grouplens repository](http://files.grouplens.org/datasets/movielens) can be downloaded and read with the functions defined above:\n",
    "\n",
    "* `ml-latest-small`\n",
    "* `ml-1m`\n",
    "* `ml-10m`\n",
    "* `ml-20m`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pick any other dataset instead\n",
    "archive_url = f'http://files.grouplens.org/datasets/movielens/ml-latest-small.zip'\n",
    "download_path = Path.home() / 'data' / 'movielens'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The archive is extracted into folder: /home/ck/data/movielens\n"
     ]
    }
   ],
   "source": [
    "try_download(archive_url, download_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total 8\r\n",
      "drwxrwxr-x 2 ck ck 4096 Aug 10 20:20 ml-1m\r\n",
      "drwxrwxr-x 2 ck ck 4096 Aug 10 20:15 ml-latest-small\r\n"
     ]
    }
   ],
   "source": [
    "!ls -l $download_path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pick one of the available folders\n",
    "ratings, movies = read_data(download_path / 'ml-1m')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Dataset Preview\n",
    "\n",
    "First of all, let's repeat the steps of the lecture where the dataset is loaded and prepared for further analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>userId</th>\n",
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      "text/plain": [
       "   userId  movieId  rating  timestamp\n",
       "0       1     1193       5  978300760\n",
       "1       1      661       3  978302109\n",
       "2       1      914       3  978301968\n",
       "3       1     3408       4  978300275\n",
       "4       1     2355       5  978824291"
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     },
     "execution_count": 14,
     "metadata": {},
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    }
   ],
   "source": [
    "ratings.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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       "      <th>1</th>\n",
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       "      <td>Jumanji (1995)</td>\n",
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       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>Grumpier Old Men (1995)</td>\n",
       "      <td>Comedy|Romance</td>\n",
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       "      <th>3</th>\n",
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      "text/plain": [
       "   movieId                               title                        genres\n",
       "0        1                    Toy Story (1995)   Animation|Children's|Comedy\n",
       "1        2                      Jumanji (1995)  Adventure|Children's|Fantasy\n",
       "2        3             Grumpier Old Men (1995)                Comedy|Romance\n",
       "3        4            Waiting to Exhale (1995)                  Comedy|Drama\n",
       "4        5  Father of the Bride Part II (1995)                        Comedy"
      ]
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     "execution_count": 15,
     "metadata": {},
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   ],
   "source": [
    "movies.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tabular_preview(ratings, n=15):\n",
    "    \"\"\"Creates a cross-tabular view of users vs movies.\"\"\"\n",
    "    \n",
    "    user_groups = ratings.groupby('userId')['rating'].count()\n",
    "    top_users = user_groups.sort_values(ascending=False)[:15]\n",
    "\n",
    "    movie_groups = ratings.groupby('movieId')['rating'].count()\n",
    "    top_movies = movie_groups.sort_values(ascending=False)[:15]\n",
    "\n",
    "    top = (\n",
    "        ratings.\n",
    "        join(top_users, rsuffix='_r', how='inner', on='userId').\n",
    "        join(top_movies, rsuffix='_r', how='inner', on='movieId'))\n",
    "\n",
    "    return pd.crosstab(top.userId, top.movieId, top.rating, aggfunc=np.sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
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       "      <td>2.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2909</th>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3618</th>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4169</th>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4277</th>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4344</th>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5795</th>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "movieId  110   260   480   589   593   608   1196  1198  1210  1270  1580  \\\n",
       "userId                                                                      \n",
       "889       4.0   4.0   3.0   5.0   5.0   4.0   4.0   NaN   3.0   4.0   3.0   \n",
       "1015      4.0   5.0   4.0   5.0   5.0   5.0   4.0   5.0   4.0   4.0   4.0   \n",
       "1150      2.0   5.0   NaN   2.0   3.0   5.0   4.0   2.0   3.0   2.0   2.0   \n",
       "1181      3.0   4.0   2.0   5.0   3.0   3.0   4.0   3.0   3.0   3.0   4.0   \n",
       "1449      3.0   3.0   2.0   2.0   5.0   5.0   3.0   4.0   2.0   2.0   4.0   \n",
       "1680      1.0   2.0   5.0   5.0   5.0   5.0   5.0   5.0   3.0   3.0   4.0   \n",
       "1941      5.0   5.0   5.0   3.0   5.0   4.0   5.0   5.0   5.0   5.0   5.0   \n",
       "1980      4.0   4.0   4.0   4.0   5.0   5.0   4.0   5.0   4.0   5.0   4.0   \n",
       "2063      5.0   4.0   4.0   2.0   5.0   2.0   4.0   4.0   4.0   4.0   3.0   \n",
       "2909      5.0   5.0   5.0   4.0   5.0   5.0   5.0   5.0   5.0   5.0   5.0   \n",
       "3618      3.0   4.0   4.0   3.0   5.0   4.0   3.0   4.0   3.0   4.0   3.0   \n",
       "4169      4.0   5.0   5.0   4.0   5.0   5.0   5.0   5.0   5.0   4.0   4.0   \n",
       "4277      5.0   5.0   5.0   5.0   5.0   5.0   5.0   5.0   4.0   5.0   4.0   \n",
       "4344      5.0   5.0   4.0   4.0   2.0   5.0   5.0   5.0   5.0   4.0   3.0   \n",
       "5795      5.0   5.0   5.0   4.0   5.0   4.0   5.0   5.0   4.0   5.0   1.0   \n",
       "\n",
       "movieId  2028  2571  2762  2858  \n",
       "userId                           \n",
       "889       3.0   5.0   NaN   2.0  \n",
       "1015      5.0   5.0   5.0   4.0  \n",
       "1150      2.0   1.0   2.0   4.0  \n",
       "1181      4.0   5.0   4.0   3.0  \n",
       "1449      3.0   4.0   4.0   4.0  \n",
       "1680      5.0   3.0   5.0   5.0  \n",
       "1941      5.0   3.0   5.0   1.0  \n",
       "1980      5.0   5.0   5.0   5.0  \n",
       "2063      2.0   5.0   4.0   5.0  \n",
       "2909      5.0   4.0   5.0   5.0  \n",
       "3618      3.0   3.0   4.0   4.0  \n",
       "4169      5.0   4.0   5.0   5.0  \n",
       "4277      5.0   5.0   5.0   5.0  \n",
       "4344      2.0   5.0   5.0   5.0  \n",
       "5795      5.0   1.0   2.0   5.0  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tabular_preview(ratings, movies)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Dataset Preparation\n",
    "\n",
    "Next we need a couple of helpers to prepare the data and make it ready for the training loop. The first one was already implemented in the original post:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_dataset(ratings, top=None):\n",
    "    if top is not None:\n",
    "        ratings.groupby('userId')['rating'].count()\n",
    "    \n",
    "    unique_users = ratings.userId.unique()\n",
    "    user_to_index = {old: new for new, old in enumerate(unique_users)}\n",
    "    new_users = ratings.userId.map(user_to_index)\n",
    "    \n",
    "    unique_movies = ratings.movieId.unique()\n",
    "    movie_to_index = {old: new for new, old in enumerate(unique_movies)}\n",
    "    new_movies = ratings.movieId.map(movie_to_index)\n",
    "    \n",
    "    n_users = unique_users.shape[0]\n",
    "    n_movies = unique_movies.shape[0]\n",
    "    \n",
    "    X = pd.DataFrame({'user_id': new_users, 'movie_id': new_movies})\n",
    "    y = ratings['rating'].astype(np.float32)\n",
    "    return (n_users, n_movies), (X, y), (user_to_index, movie_to_index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Embeddings: 6040 users, 3706 movies\n",
      "Dataset shape: (1000209, 2)\n",
      "Target shape: (1000209,)\n"
     ]
    }
   ],
   "source": [
    "(n, m), (X, y), _ = create_dataset(ratings)\n",
    "print(f'Embeddings: {n} users, {m} movies')\n",
    "print(f'Dataset shape: {X.shape}')\n",
    "print(f'Target shape: {y.shape}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second one is a small class that allows to iterate through the dataset one batch after another:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "class ReviewsIterator:\n",
    "    \n",
    "    def __init__(self, X, y, batch_size=32, shuffle=True):\n",
    "        X, y = np.asarray(X), np.asarray(y)\n",
    "        \n",
    "        if shuffle:\n",
    "            index = np.random.permutation(X.shape[0])\n",
    "            X, y = X[index], y[index]\n",
    "            \n",
    "        self.X = X\n",
    "        self.y = y\n",
    "        self.batch_size = batch_size\n",
    "        self.shuffle = shuffle\n",
    "        self.n_batches = int(math.ceil(X.shape[0] // batch_size))\n",
    "        self._current = 0\n",
    "        \n",
    "    def __iter__(self):\n",
    "        return self\n",
    "    \n",
    "    def __next__(self):\n",
    "        return self.next()\n",
    "    \n",
    "    def next(self):\n",
    "        if self._current >= self.n_batches:\n",
    "            raise StopIteration()\n",
    "        k = self._current\n",
    "        self._current += 1\n",
    "        bs = self.batch_size\n",
    "        return self.X[k*bs:(k + 1)*bs], self.y[k*bs:(k + 1)*bs]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A convenice function `batches` allows us to split the dataset into smaller chunks during training/validation process:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def batches(X, y, bs=32, shuffle=True):\n",
    "    for xb, yb in ReviewsIterator(X, y, bs, shuffle):\n",
    "        xb = torch.LongTensor(xb)\n",
    "        yb = torch.FloatTensor(yb)\n",
    "        yield xb, yb.view(-1, 1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[2234, 3808],\n",
      "        [ 143, 1388],\n",
      "        [ 849, 4509],\n",
      "        [2393, 1016]])\n",
      "tensor([[4.],\n",
      "        [4.],\n",
      "        [2.],\n",
      "        [3.]])\n"
     ]
    }
   ],
   "source": [
    "for x_batch, y_batch in batches(X, y, bs=4):\n",
    "    print(x_batch)\n",
    "    print(y_batch)\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Embeddings\n",
    "\n",
    "In this secion we're going to create an `nn.Module` for our embedding network. The main difference from the class provided in the original post is that this class is a bit more generic: it allows to create a network of arbirary depth, with or without dropouts. Also, the `forward` method accepts an additional `minmax` argument which is expected to be a tuple with minimum and maximum values of ratings from the dataset to normalize the predicted value into specific range.\n",
    "\n",
    "Note that to create a group of hidden layers we use a [generator](https://wiki.python.org/moin/Generators) function `gen_layers` that yields linear and dropout layers depending on values from `hidden` and `dropouts` arrays. Also note that we use the `nn.Sequence` class to group hidden layers into a single module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "class EmbeddingNet(nn.Module):\n",
    "    \"\"\"\n",
    "    Creates a dense network with embedding layers.\n",
    "    \n",
    "    Args:\n",
    "    \n",
    "        n_users:            \n",
    "            Number of unique users in the dataset.\n",
    "\n",
    "        n_movies: \n",
    "            Number of unique movies in the dataset.\n",
    "\n",
    "        n_factors: \n",
    "            Number of columns in the embeddings matrix.\n",
    "\n",
    "        embedding_dropout: \n",
    "            Dropout rate to apply right after embeddings layer.\n",
    "\n",
    "        hidden:\n",
    "            A single integer or a list of integers defining the number of \n",
    "            units in hidden layer(s).\n",
    "\n",
    "        dropouts: \n",
    "            A single integer or a list of integers defining the dropout \n",
    "            layers rates applyied right after each of hidden layers.\n",
    "            \n",
    "    \"\"\"\n",
    "    def __init__(self, n_users, n_movies,\n",
    "                 n_factors=50, embedding_dropout=0.02, \n",
    "                 hidden=10, dropouts=0.2):\n",
    "        \n",
    "        super().__init__()\n",
    "        hidden = get_list(hidden)\n",
    "        dropouts = get_list(dropouts)\n",
    "        n_last = hidden[-1]\n",
    "        \n",
    "        def gen_layers(n_in):\n",
    "            \"\"\"\n",
    "            A generator that yields a sequence of hidden layers and \n",
    "            their activations/dropouts.\n",
    "            \n",
    "            Note that the function captures `hidden` and `dropouts` \n",
    "            values from the outer scope.\n",
    "            \"\"\"\n",
    "            nonlocal hidden, dropouts\n",
    "            assert len(dropouts) <= len(hidden)\n",
    "            \n",
    "            for n_out, rate in zip_longest(hidden, dropouts):\n",
    "                yield nn.Linear(n_in, n_out)\n",
    "                yield nn.ReLU()\n",
    "                if rate is not None and rate > 0.:\n",
    "                    yield nn.Dropout(rate)\n",
    "                n_in = n_out\n",
    "            \n",
    "        self.u = nn.Embedding(n_users, n_factors)\n",
    "        self.m = nn.Embedding(n_movies, n_factors)\n",
    "        self.drop = nn.Dropout(embedding_dropout)\n",
    "        self.hidden = nn.Sequential(*list(gen_layers(n_factors * 2)))\n",
    "        self.fc = nn.Linear(n_last, 1)\n",
    "        self._init()\n",
    "        \n",
    "    def forward(self, users, movies, minmax=None):\n",
    "        features = torch.cat([self.u(users), self.m(movies)], dim=1)\n",
    "        x = self.drop(features)\n",
    "        x = self.hidden(x)\n",
    "        out = torch.sigmoid(self.fc(x))\n",
    "        if minmax is not None:\n",
    "            min_rating, max_rating = minmax\n",
    "            out = out*(max_rating - min_rating + 1) + min_rating - 0.5\n",
    "        return out\n",
    "    \n",
    "    def _init(self):\n",
    "        \"\"\"\n",
    "        Setup embeddings and hidden layers with reasonable initial values.\n",
    "        \"\"\"\n",
    "        \n",
    "        def init(m):\n",
    "            if type(m) == nn.Linear:\n",
    "                torch.nn.init.xavier_uniform_(m.weight)\n",
    "                m.bias.data.fill_(0.01)\n",
    "                \n",
    "        self.u.weight.data.uniform_(-0.05, 0.05)\n",
    "        self.m.weight.data.uniform_(-0.05, 0.05)\n",
    "        self.hidden.apply(init)\n",
    "        init(self.fc)\n",
    "    \n",
    "    \n",
    "def get_list(n):\n",
    "    if isinstance(n, (int, float)):\n",
    "        return [n]\n",
    "    elif hasattr(n, '__iter__'):\n",
    "        return list(n)\n",
    "    raise TypeError('layers configuraiton should be a single number or a list of numbers')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, if we want to create a network with a single hidden layer and dropout, we can use the following code snippet:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EmbeddingNet(\n",
       "  (u): Embedding(6040, 150)\n",
       "  (m): Embedding(3706, 150)\n",
       "  (drop): Dropout(p=0.02)\n",
       "  (hidden): Sequential(\n",
       "    (0): Linear(in_features=300, out_features=100, bias=True)\n",
       "    (1): ReLU()\n",
       "    (2): Dropout(p=0.5)\n",
       "  )\n",
       "  (fc): Linear(in_features=100, out_features=1, bias=True)\n",
       ")"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "EmbeddingNet(n, m, n_factors=150, hidden=100, dropouts=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If case if something more involved is required, pass a list of values instead:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EmbeddingNet(\n",
       "  (u): Embedding(6040, 150)\n",
       "  (m): Embedding(3706, 150)\n",
       "  (drop): Dropout(p=0.02)\n",
       "  (hidden): Sequential(\n",
       "    (0): Linear(in_features=300, out_features=100, bias=True)\n",
       "    (1): ReLU()\n",
       "    (2): Dropout(p=0.25)\n",
       "    (3): Linear(in_features=100, out_features=200, bias=True)\n",
       "    (4): ReLU()\n",
       "    (5): Dropout(p=0.5)\n",
       "    (6): Linear(in_features=200, out_features=300, bias=True)\n",
       "    (7): ReLU()\n",
       "  )\n",
       "  (fc): Linear(in_features=300, out_features=1, bias=True)\n",
       ")"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "EmbeddingNet(n, m, n_factors=150, hidden=[100, 200, 300], dropouts=[0.25, 0.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Cyclical Learning Rate (CLR)\n",
    "\n",
    "One of the `fastai` library features is the cyclical learning rate scheduler. We can implement something similar inheriting the `_LRScheduler` class from the `torch` library. Following the [original paper's](https://arxiv.org/abs/1506.01186) pseudocode, this [CLR Keras callback implementation](https://github.com/bckenstler/CLR), and making a couple of adjustments to support [cosine annealing](https://pytorch.org/docs/stable/optim.html#torch.optim.lr_scheduler.CosineAnnealingLR) with restarts, let's create our own CLR scheduler.\n",
    "\n",
    "The implementation of this idea is quite simple. The [base PyTorch scheduler class](https://pytorch.org/docs/stable/_modules/torch/optim/lr_scheduler.html) has the `get_lr()` method that is invoked each time when we call the `step()` method. The method should return a list of learning rates depending on the current training epoch. In our case, we have the same learning rate for all of the layers, and therefore, we return a list with a single value. \n",
    "\n",
    "The next cell defines a `CyclicLR` class that expectes a single callback function. This function should accept the current training epoch and the base value of learning rate, and return a new learning rate value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "class CyclicLR(_LRScheduler):\n",
    "    \n",
    "    def __init__(self, optimizer, schedule, last_epoch=-1):\n",
    "        assert callable(schedule)\n",
    "        self.schedule = schedule\n",
    "        super().__init__(optimizer, last_epoch)\n",
    "\n",
    "    def get_lr(self):\n",
    "        return [self.schedule(self.last_epoch, lr) for lr in self.base_lrs]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our scheduler is very similar to [LambdaLR](https://pytorch.org/docs/stable/optim.html#torch.optim.lr_scheduler.LambdaLR) one but expects a bit different callback signature. \n",
    "\n",
    "So now we only need to define appropriate scheduling functions. We're createing a couple of functions that accept scheduling parameters and return a _new function_ with the appropriate signature:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def triangular(step_size, max_lr, method='triangular', gamma=0.99):\n",
    "    \n",
    "    def scheduler(epoch, base_lr):\n",
    "        period = 2 * step_size\n",
    "        cycle = math.floor(1 + epoch/period)\n",
    "        x = abs(epoch/step_size - 2*cycle + 1)\n",
    "        delta = (max_lr - base_lr)*max(0, (1 - x))\n",
    "\n",
    "        if method == 'triangular':\n",
    "            pass  # we've already done\n",
    "        elif method == 'triangular2':\n",
    "            delta /= float(2 ** (cycle - 1))\n",
    "        elif method == 'exp_range':\n",
    "            delta *= (gamma**epoch)\n",
    "        else:\n",
    "            raise ValueError('unexpected method: %s' % method)\n",
    "            \n",
    "        return base_lr + delta\n",
    "        \n",
    "    return scheduler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cosine(t_max, eta_min=0):\n",
    "    \n",
    "    def scheduler(epoch, base_lr):\n",
    "        t = epoch % t_max\n",
    "        return eta_min + (base_lr - eta_min)*(1 + math.cos(math.pi*t/t_max))/2\n",
    "    \n",
    "    return scheduler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To understand how the created functions work, and to check the correctness of our implementation, let's create a couple of plots visualizing learning rates changes depending on the number of epoch:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_lr(schedule):\n",
    "    ts = list(range(1000))\n",
    "    y = [schedule(t, 0.001) for t in ts]\n",
    "    plt.plot(ts, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f566c588860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_lr(triangular(250, 0.005))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f565a608c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_lr(triangular(250, 0.005, 'triangular2'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f566986fb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_lr(triangular(250, 0.005, 'exp_range', gamma=0.999))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f566b56aeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_lr(cosine(t_max=500, eta_min=0.0005))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that cosine annealing scheduler is a bit different from other schedules as soon as it starts with `base_lr` and gradually decreases it to the minimal value while triangle schedulers increase the original rate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Training Loop\n",
    "\n",
    "Now we're ready to start the training process. First of all, let's split the original dataset using [train_test_split](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html) function from the `scikit-learn` library. (Though you can use anything else instead, like, [get_cv_idxs](https://github.com/fastai/fastai/blob/921777feb46f215ed2b5f5dcfcf3e6edd299ea92/fastai/dataset.py#L6-L22) from `fastai`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_valid, y_train, y_valid = train_test_split(X, y, test_size=0.2, random_state=RANDOM_STATE)\n",
    "datasets = {'train': (X_train, y_train), 'val': (X_valid, y_valid)}\n",
    "dataset_sizes = {'train': len(X_train), 'val': len(X_valid)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0, 5.0)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "minmax = ratings.rating.min().astype(float), ratings.rating.max().astype(float)\n",
    "minmax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "net = EmbeddingNet(\n",
    "    n_users=n, n_movies=m, \n",
    "    n_factors=150, hidden=[500, 500, 500], \n",
    "    embedding_dropout=0.05, dropouts=[0.5, 0.5, 0.25])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next cell is preparing and running the training loop with cyclical learning rate, validation and early stopping. We use `Adam` optimizer with cosine-annealing learnign rate. The rate is decreased on each batch during `2` epochs, and then is reset to the original value.\n",
    "\n",
    "Note that our loop has two phases. One of them is called `train`. During this phase, we update our network's weights and change the learning rate. The another one is called `val` and is used to check the model's performence. When the loss value decreases, we save model parameters to restore them later. If there is no improvements after `10` sequential training epochs, we exit from the loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss improvement on epoch: 1\n",
      "[001/100] train: 0.8876 - val: 0.8223\n",
      "loss improvement on epoch: 2\n",
      "[002/100] train: 0.7970 - val: 0.8076\n",
      "loss improvement on epoch: 3\n",
      "[003/100] train: 0.8001 - val: 0.7984\n",
      "loss improvement on epoch: 4\n",
      "[004/100] train: 0.7595 - val: 0.7867\n",
      "loss improvement on epoch: 5\n",
      "[005/100] train: 0.7671 - val: 0.7864\n",
      "loss improvement on epoch: 6\n",
      "[006/100] train: 0.7290 - val: 0.7833\n",
      "[007/100] train: 0.7418 - val: 0.7842\n",
      "[008/100] train: 0.6966 - val: 0.7904\n",
      "[009/100] train: 0.7095 - val: 0.7885\n",
      "[010/100] train: 0.6547 - val: 0.7993\n",
      "[011/100] train: 0.6701 - val: 0.7925\n",
      "[012/100] train: 0.6138 - val: 0.8075\n",
      "[013/100] train: 0.6348 - val: 0.8025\n",
      "[014/100] train: 0.5822 - val: 0.8153\n",
      "[015/100] train: 0.6054 - val: 0.8147\n",
      "[016/100] train: 0.5586 - val: 0.8214\n",
      "early stopping after epoch 016\n"
     ]
    }
   ],
   "source": [
    "lr = 1e-3\n",
    "wd = 1e-5\n",
    "bs = 2000\n",
    "n_epochs = 100\n",
    "patience = 10\n",
    "no_improvements = 0\n",
    "best_loss = np.inf\n",
    "best_weights = None\n",
    "history = []\n",
    "lr_history = []\n",
    "\n",
    "device = torch.device('cuda:0' if torch.cuda.is_available() else 'cpu')\n",
    "\n",
    "net.to(device)\n",
    "criterion = nn.MSELoss(reduction='sum')\n",
    "optimizer = optim.Adam(net.parameters(), lr=lr, weight_decay=wd)\n",
    "iterations_per_epoch = int(math.ceil(dataset_sizes['train'] // bs))\n",
    "scheduler = CyclicLR(optimizer, cosine(t_max=iterations_per_epoch * 2, eta_min=lr/10))\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    stats = {'epoch': epoch + 1, 'total': n_epochs}\n",
    "    \n",
    "    for phase in ('train', 'val'):\n",
    "        training = phase == 'train'\n",
    "        running_loss = 0.0\n",
    "        n_batches = 0\n",
    "        \n",
    "        for batch in batches(*datasets[phase], shuffle=training, bs=bs):\n",
    "            x_batch, y_batch = [b.to(device) for b in batch]\n",
    "            optimizer.zero_grad()\n",
    "        \n",
    "            # compute gradients only during 'train' phase\n",
    "            with torch.set_grad_enabled(training):\n",
    "                outputs = net(x_batch[:, 1], x_batch[:, 0], minmax)\n",
    "                loss = criterion(outputs, y_batch)\n",
    "                \n",
    "                # don't update weights and rates when in 'val' phase\n",
    "                if training:\n",
    "                    scheduler.step()\n",
    "                    loss.backward()\n",
    "                    optimizer.step()\n",
    "                    lr_history.extend(scheduler.get_lr())\n",
    "                    \n",
    "            running_loss += loss.item()\n",
    "            \n",
    "        epoch_loss = running_loss / dataset_sizes[phase]\n",
    "        stats[phase] = epoch_loss\n",
    "        \n",
    "        # early stopping: save weights of the best model so far\n",
    "        if phase == 'val':\n",
    "            if epoch_loss < best_loss:\n",
    "                print('loss improvement on epoch: %d' % (epoch + 1))\n",
    "                best_loss = epoch_loss\n",
    "                best_weights = copy.deepcopy(net.state_dict())\n",
    "                no_improvements = 0\n",
    "            else:\n",
    "                no_improvements += 1\n",
    "                \n",
    "    history.append(stats)\n",
    "    print('[{epoch:03d}/{total:03d}] train: {train:.4f} - val: {val:.4f}'.format(**stats))\n",
    "    if no_improvements >= patience:\n",
    "        print('early stopping after epoch {epoch:03d}'.format(**stats))\n",
    "        break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Metrics\n",
    "\n",
    "To visualize the training process and to check the correctness of the learning rate scheduling, let's create a couple of plots using collected stats:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ax = pd.DataFrame(history).drop(columns='total').plot(x='epoch')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7faa4381c978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.plot(lr_history[:2*iterations_per_epoch])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the learning rate is updated in accordance with cosine annealing schedule."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The training process was terminated after _16 epochs_. Now we're going to restore the best weights saved during training, and apply the model to the validation subset of the data to see the final model's performance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "net.load_state_dict(best_weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "groud_truth, predictions = [], []\n",
    "\n",
    "with torch.no_grad():\n",
    "    for batch in batches(*datasets['val'], shuffle=False, bs=bs):\n",
    "        x_batch, y_batch = [b.to(device) for b in batch]\n",
    "        outputs = net(x_batch[:, 1], x_batch[:, 0], minmax)\n",
    "        groud_truth.extend(y_batch.tolist())\n",
    "        predictions.extend(outputs.tolist())\n",
    "\n",
    "groud_truth = np.asarray(groud_truth).ravel()\n",
    "predictions = np.asarray(predictions).ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final RMSE: 0.8854\n"
     ]
    }
   ],
   "source": [
    "final_loss = np.sqrt(np.mean((predictions - groud_truth)**2))\n",
    "print(f'Final RMSE: {final_loss:.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('best.weights', 'wb') as file:\n",
    "    pickle.dump(best_weights, file)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Bonus: Embeddings Visualization\n",
    "\n",
    "Finally, we can create a couple of visualizations to show how various movies are encoded in embeddings space. Again, we're repeting the approach shown in the original post and apply the [Principal Components Analysis](http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html) to reduce the dimentionality of embeddings and show some of them with bar plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Loading previously saved weights:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('best.weights', 'rb') as file:\n",
    "    best_weights = pickle.load(file)\n",
    "net.load_state_dict(best_weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def to_numpy(tensor):\n",
    "    return tensor.cpu().numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating the mappings between original users's and movies's IDs, and new contiguous values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "_, _, (user_id_map, movie_id_map) = create_dataset(ratings)\n",
    "embed_to_original = {v: k for k, v in movie_id_map.items()}\n",
    "popular_movies = ratings.groupby('movieId').movieId.count().sort_values(ascending=False).values[:1000]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reducing the dimensionality of movie embeddings vectors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, 1000)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "embed = to_numpy(net.m.weight.data)\n",
    "pca = PCA(n_components=5)\n",
    "components = pca.fit(embed[popular_movies].T).components_\n",
    "components.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, creating a joined data frame with projected embeddings and movies they represent:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "components_df = pd.DataFrame(components.T, columns=[f'fc{i}' for i in range(pca.n_components_)])\n",
    "movie_ids = [embed_to_original[idx] for idx in components_df.index]\n",
    "meta = movies.set_index('movieId')\n",
    "components_df['movie_id'] = movie_ids\n",
    "components_df['title'] = meta.loc[movie_ids].title.values\n",
    "components_df['genres'] = meta.loc[movie_ids].genres.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fc0</th>\n",
       "      <th>fc1</th>\n",
       "      <th>fc2</th>\n",
       "      <th>fc3</th>\n",
       "      <th>fc4</th>\n",
       "      <th>movie_id</th>\n",
       "      <th>title</th>\n",
       "      <th>genres</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>221</th>\n",
       "      <td>-0.019097</td>\n",
       "      <td>-0.028055</td>\n",
       "      <td>0.037613</td>\n",
       "      <td>-0.018125</td>\n",
       "      <td>-0.025174</td>\n",
       "      <td>39</td>\n",
       "      <td>Clueless (1995)</td>\n",
       "      <td>Comedy|Romance</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>375</th>\n",
       "      <td>0.032642</td>\n",
       "      <td>0.005979</td>\n",
       "      <td>-0.009179</td>\n",
       "      <td>-0.018974</td>\n",
       "      <td>-0.058169</td>\n",
       "      <td>353</td>\n",
       "      <td>Crow, The (1994)</td>\n",
       "      <td>Action|Romance|Thriller</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>803</th>\n",
       "      <td>-0.035493</td>\n",
       "      <td>0.027022</td>\n",
       "      <td>-0.021069</td>\n",
       "      <td>0.000926</td>\n",
       "      <td>0.009471</td>\n",
       "      <td>342</td>\n",
       "      <td>Muriel's Wedding (1994)</td>\n",
       "      <td>Comedy|Romance</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>585</th>\n",
       "      <td>0.035508</td>\n",
       "      <td>-0.014357</td>\n",
       "      <td>-0.016352</td>\n",
       "      <td>0.014617</td>\n",
       "      <td>-0.004404</td>\n",
       "      <td>1269</td>\n",
       "      <td>Arsenic and Old Lace (1944)</td>\n",
       "      <td>Comedy|Mystery|Thriller</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          fc0       fc1       fc2       fc3       fc4  movie_id  \\\n",
       "221 -0.019097 -0.028055  0.037613 -0.018125 -0.025174        39   \n",
       "375  0.032642  0.005979 -0.009179 -0.018974 -0.058169       353   \n",
       "803 -0.035493  0.027022 -0.021069  0.000926  0.009471       342   \n",
       "585  0.035508 -0.014357 -0.016352  0.014617 -0.004404      1269   \n",
       "\n",
       "                           title                   genres  \n",
       "221              Clueless (1995)           Comedy|Romance  \n",
       "375             Crow, The (1994)  Action|Romance|Thriller  \n",
       "803      Muriel's Wedding (1994)           Comedy|Romance  \n",
       "585  Arsenic and Old Lace (1944)  Comedy|Mystery|Thriller  "
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "components_df.sample(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_components(components, component, ascending=False):\n",
    "    fig, ax = plt.subplots(figsize=(18, 12))\n",
    "    \n",
    "    subset = components.sort_values(by=component, ascending=ascending).iloc[:12]\n",
    "    columns = components_df.columns\n",
    "    features = columns[columns.str.startswith('fc')].tolist()\n",
    "    \n",
    "    fc = subset[features]\n",
    "    titles = ['\\n'.join(wrap(t, width=10)) for t in subset.title]\n",
    "    genres = subset.genres.str.replace('|', '\\n')\n",
    "    labels = [f'{t}\\n\\n{g}' for t, g in zip(titles, genres)]\n",
    "    \n",
    "    fc.plot(ax=ax, kind='bar')\n",
    "    y_ticks = [f'{t:2.2f}' for t in ax.get_yticks()]\n",
    "    ax.set_xticklabels(labels, rotation=0, fontsize=14)\n",
    "    ax.set_yticklabels(y_ticks, fontsize=14)\n",
    "    ax.legend(loc='best', fontsize=14)\n",
    "    \n",
    "    plot_title = f\"Movies with {['highest', 'lowest'][ascending]} '{component}' component values\" \n",
    "    ax.set_title(plot_title, fontsize=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f565dfd6710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_components(components_df, 'fc0', ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f566088ce80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_components(components_df, 'fc0', ascending=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the visualizations above, we could make a guess that the `red` component mostly reflects the rate of \"seriousness\" in the movie. Comedies, animations and adventures mostly have the negative values of this feature while more \"dramatical\" movies have high levels of this component."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}