{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Факторизация матриц с SVD\n", "\n", "$$\\begin{equation}\n", "R = U\\Sigma V^{T}\n", "\\end{equation}$$\n", "\n", "где R это матрица рейтингов юзеров, $U$ это матрица фичей юзеров, $\\Sigma$ диагональная матрица сингулярных значений (весов), и $V^{T}$ матрица фичей фильмов. $U$ и $V^{T}$ ортогональны. $U$ показывает скольким юзерам нравится фича и $V^{T}$ показывает как фича относится(релевантна) фильму.\n", "\n", "Чтобы получить низкоранговую аппроксимацию, мы берем эти матрицы и оставляем только топ $k$ фичей, которые отражают скрытые предпочтения и вкусы. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "\n", "ratings_list = [i.strip().split(\"::\") for i in open('/users/muzalevskiy/Downloads/ml-1m/ratings.dat', 'r').readlines()]\n", "users_list = [i.strip().split(\"::\") for i in open('/users/muzalevskiy/Downloads/ml-1m/users.dat', 'r').readlines()]\n", "movies_list = [i.strip().split(\"::\") for i in open('/users/muzalevskiy/Downloads/ml-1m/movies.dat', 'r').readlines()]" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "ratings = np.array(ratings_list)\n", "users = np.array(users_list)\n", "movies = np.array(movies_list)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "ratings_df = pd.DataFrame(ratings_list, columns = ['UserID', 'MovieID', 'Rating', 'Timestamp'], dtype = int)\n", "movies_df = pd.DataFrame(movies_list, columns = ['MovieID', 'Title', 'Genres'])\n", "movies_df['MovieID'] = movies_df['MovieID'].apply(pd.to_numeric)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
MovieIDTitleGenres
01Toy Story (1995)Animation|Children's|Comedy
12Jumanji (1995)Adventure|Children's|Fantasy
23Grumpier Old Men (1995)Comedy|Romance
34Waiting to Exhale (1995)Comedy|Drama
45Father of the Bride Part II (1995)Comedy
\n", "
" ], "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" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "movies_df.head()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
UserIDMovieIDRatingTimestamp
0111935978300760
116613978302109
219143978301968
3134084978300275
4123555978824291
\n", "
" ], "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" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ratings_df.head()" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
MovieID12345678910...3943394439453946394739483949395039513952
UserID
15.00.00.00.00.00.00.00.00.00.0...0.00.00.00.00.00.00.00.00.00.0
20.00.00.00.00.00.00.00.00.00.0...0.00.00.00.00.00.00.00.00.00.0
30.00.00.00.00.00.00.00.00.00.0...0.00.00.00.00.00.00.00.00.00.0
40.00.00.00.00.00.00.00.00.00.0...0.00.00.00.00.00.00.00.00.00.0
50.00.00.00.00.02.00.00.00.00.0...0.00.00.00.00.00.00.00.00.00.0
\n", "

5 rows × 3706 columns

\n", "
" ], "text/plain": [ "MovieID 1 2 3 4 5 6 7 8 9 10 ... \\\n", "UserID ... \n", "1 5.0 0.0 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 0.0 0.0 ... \n", "3 0.0 0.0 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 0.0 0.0 ... \n", "5 0.0 0.0 0.0 0.0 0.0 2.0 0.0 0.0 0.0 0.0 ... \n", "\n", "MovieID 3943 3944 3945 3946 3947 3948 3949 3950 3951 3952 \n", "UserID \n", "1 0.0 0.0 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 0.0 0.0 \n", "3 0.0 0.0 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 0.0 0.0 \n", "5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 \n", "\n", "[5 rows x 3706 columns]" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R_df = ratings_df.pivot(index = 'UserID', columns ='MovieID', values = 'Rating').fillna(0)\n", "R_df.head()" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [], "source": [ "R = R_df.as_matrix()\n", "user_ratings_mean = np.mean(R, axis = 1)\n", "R_demeaned = R - user_ratings_mean.reshape(-1, 1)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "from scipy.sparse.linalg import svds\n", "U, sigma, Vt = svds(R_demeaned, k = 50)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": true }, "outputs": [], "source": [ "sigma = np.diag(sigma)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": true }, "outputs": [], "source": [ "all_user_predicted_ratings = np.dot(np.dot(U, sigma), Vt) + user_ratings_mean.reshape(-1, 1)" ] }, { "cell_type": "code", "execution_count": 202, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
MovieID12345678910...3943394439453946394739483949395039513952
04.2888610.143055-0.195080-0.0188430.012232-0.176604-0.0741200.141358-0.059553-0.195950...0.0278070.0016400.026395-0.022024-0.0854150.4035290.1055790.0319120.0504500.088910
10.7447160.1696590.3354180.0007580.0224751.3530500.0514260.0712580.1616011.567246...-0.056502-0.013733-0.0105800.062576-0.0162480.155790-0.418737-0.101102-0.054098-0.140188
21.8188240.4561360.090978-0.043037-0.025694-0.158617-0.1317780.0989770.0305510.735470...0.040481-0.0053010.0128320.0293490.0208660.1215320.0762050.0123450.015148-0.109956
30.408057-0.0729600.0396420.0893630.0419500.237753-0.0494260.0094670.045469-0.111370...0.008571-0.005425-0.008500-0.003417-0.0839820.0945120.057557-0.0260500.014841-0.034224
41.5742720.021239-0.0513000.246884-0.0324061.552281-0.199630-0.014920-0.0604980.450512...0.1101510.0460100.006934-0.015940-0.050080-0.0525390.5071890.0338300.1257060.199244
\n", "

5 rows × 3706 columns

\n", "
" ], "text/plain": [ "MovieID 1 2 3 4 5 6 7 \\\n", "0 4.288861 0.143055 -0.195080 -0.018843 0.012232 -0.176604 -0.074120 \n", "1 0.744716 0.169659 0.335418 0.000758 0.022475 1.353050 0.051426 \n", "2 1.818824 0.456136 0.090978 -0.043037 -0.025694 -0.158617 -0.131778 \n", "3 0.408057 -0.072960 0.039642 0.089363 0.041950 0.237753 -0.049426 \n", "4 1.574272 0.021239 -0.051300 0.246884 -0.032406 1.552281 -0.199630 \n", "\n", "MovieID 8 9 10 ... 3943 3944 3945 \\\n", "0 0.141358 -0.059553 -0.195950 ... 0.027807 0.001640 0.026395 \n", "1 0.071258 0.161601 1.567246 ... -0.056502 -0.013733 -0.010580 \n", "2 0.098977 0.030551 0.735470 ... 0.040481 -0.005301 0.012832 \n", "3 0.009467 0.045469 -0.111370 ... 0.008571 -0.005425 -0.008500 \n", "4 -0.014920 -0.060498 0.450512 ... 0.110151 0.046010 0.006934 \n", "\n", "MovieID 3946 3947 3948 3949 3950 3951 3952 \n", "0 -0.022024 -0.085415 0.403529 0.105579 0.031912 0.050450 0.088910 \n", "1 0.062576 -0.016248 0.155790 -0.418737 -0.101102 -0.054098 -0.140188 \n", "2 0.029349 0.020866 0.121532 0.076205 0.012345 0.015148 -0.109956 \n", "3 -0.003417 -0.083982 0.094512 0.057557 -0.026050 0.014841 -0.034224 \n", "4 -0.015940 -0.050080 -0.052539 0.507189 0.033830 0.125706 0.199244 \n", "\n", "[5 rows x 3706 columns]" ] }, "execution_count": 202, "metadata": {}, "output_type": "execute_result" } ], "source": [ "preds_df = pd.DataFrame(all_user_predicted_ratings, columns = R_df.columns)\n", "preds_df.head()" ] }, { "cell_type": "code", "execution_count": 259, "metadata": {}, "outputs": [], "source": [ "def recommend_movies(predictions_df, userID, movies_df, original_ratings_df, num_recommendations=5):\n", " \n", " user_row_number = userID - 1 \n", " sorted_user_predictions = preds_df.iloc[user_row_number].sort_values(ascending=False) \n", " \n", " user_data = original_ratings_df[original_ratings_df.UserID == (userID)]\n", " user_full = (user_data.merge(movies_df, how = 'left', left_on = 'MovieID', right_on = 'MovieID').\n", " sort_values(['Rating'], ascending=False)\n", " )\n", "\n", " print 'User {0} has already rated {1} movies.'.format(userID, user_full.shape[0])\n", " print 'Recommending highest {0} predicted ratings movies not already rated.'.format(num_recommendations)\n", " \n", " recommendations = (movies_df[~movies_df['MovieID'].isin(user_full['MovieID'])].\n", " merge(pd.DataFrame(sorted_user_predictions).reset_index(), how = 'left',\n", " left_on = 'MovieID',\n", " right_on = 'MovieID').\n", " rename(columns = {user_row_number: 'Predictions'}).\n", " sort_values('Predictions', ascending = False).\n", " iloc[:num_recommendations, :-1]\n", " )\n", "\n", " return user_full, recommendations" ] }, { "cell_type": "code", "execution_count": 256, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "User 837 has already rated 69 movies.\n", "Recommending highest 10 predicted ratings movies not already rated.\n" ] } ], "source": [ "already_rated, predictions = recommend_movies(preds_df, 837, movies_df, ratings_df, 10)" ] }, { "cell_type": "code", "execution_count": 257, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
UserIDMovieIDRatingTimestampTitleGenres
368378585975360036Godfather, The (1972)Action|Crime|Drama
3583713875975360036Jaws (1975)Action|Horror
6583720285975360089Saving Private Ryan (1998)Action|Drama|War
6383712215975360036Godfather: Part II, The (1974)Action|Crime|Drama
118379135975359921Maltese Falcon, The (1941)Film-Noir|Mystery
2083734175975360893Crimson Pirate, The (1952)Adventure|Comedy|Sci-Fi
3483721864975359955Strangers on a Train (1951)Film-Noir|Thriller
5583727914975360893Airplane! (1980)Comedy
3183711884975360920Strictly Ballroom (1992)Comedy|Romance
2883713044975360058Butch Cassidy and the Sundance Kid (1969)Action|Comedy|Western
\n", "
" ], "text/plain": [ " UserID MovieID Rating Timestamp \\\n", "36 837 858 5 975360036 \n", "35 837 1387 5 975360036 \n", "65 837 2028 5 975360089 \n", "63 837 1221 5 975360036 \n", "11 837 913 5 975359921 \n", "20 837 3417 5 975360893 \n", "34 837 2186 4 975359955 \n", "55 837 2791 4 975360893 \n", "31 837 1188 4 975360920 \n", "28 837 1304 4 975360058 \n", "\n", " Title Genres \n", "36 Godfather, The (1972) Action|Crime|Drama \n", "35 Jaws (1975) Action|Horror \n", "65 Saving Private Ryan (1998) Action|Drama|War \n", "63 Godfather: Part II, The (1974) Action|Crime|Drama \n", "11 Maltese Falcon, The (1941) Film-Noir|Mystery \n", "20 Crimson Pirate, The (1952) Adventure|Comedy|Sci-Fi \n", "34 Strangers on a Train (1951) Film-Noir|Thriller \n", "55 Airplane! (1980) Comedy \n", "31 Strictly Ballroom (1992) Comedy|Romance \n", "28 Butch Cassidy and the Sundance Kid (1969) Action|Comedy|Western " ] }, "execution_count": 257, "metadata": {}, "output_type": "execute_result" } ], "source": [ "already_rated.head(10)" ] }, { "cell_type": "code", "execution_count": 258, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
MovieIDTitleGenres
516527Schindler's List (1993)Drama|War
18481953French Connection, The (1971)Action|Crime|Drama|Thriller
596608Fargo (1996)Crime|Drama|Thriller
12351284Big Sleep, The (1946)Film-Noir|Mystery
20852194Untouchables, The (1987)Action|Crime|Drama
11881230Annie Hall (1977)Comedy|Romance
11981242Glory (1989)Action|Drama|War
897922Sunset Blvd. (a.k.a. Sunset Boulevard) (1950)Film-Noir
18491954Rocky (1976)Action|Drama
581593Silence of the Lambs, The (1991)Drama|Thriller
\n", "
" ], "text/plain": [ " MovieID Title \\\n", "516 527 Schindler's List (1993) \n", "1848 1953 French Connection, The (1971) \n", "596 608 Fargo (1996) \n", "1235 1284 Big Sleep, The (1946) \n", "2085 2194 Untouchables, The (1987) \n", "1188 1230 Annie Hall (1977) \n", "1198 1242 Glory (1989) \n", "897 922 Sunset Blvd. (a.k.a. Sunset Boulevard) (1950) \n", "1849 1954 Rocky (1976) \n", "581 593 Silence of the Lambs, The (1991) \n", "\n", " Genres \n", "516 Drama|War \n", "1848 Action|Crime|Drama|Thriller \n", "596 Crime|Drama|Thriller \n", "1235 Film-Noir|Mystery \n", "2085 Action|Crime|Drama \n", "1188 Comedy|Romance \n", "1198 Action|Drama|War \n", "897 Film-Noir \n", "1849 Action|Drama \n", "581 Drama|Thriller " ] }, "execution_count": 258, "metadata": {}, "output_type": "execute_result" } ], "source": [ "predictions" ] } ], "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": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 1 }