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kiwamizamurai/recommendation-tutorial.ipynb

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recommendation-tutorial.ipynb
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"name": "Recommendation-tutorial.ipynb",
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"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
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"source": [
"<a href=\"https://colab.research.google.com/gist/kiwamizamurai/3362bb1b4ae7a7440585659c93a8e6a1/recommendation-tutorial.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"metadata": {
"id": "sIv5gaxz_tyY",
"colab_type": "code",
"colab": {}
},
"source": [
"# from google.colab import files\n",
"# files.upload()"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "YhUzdbo7Rus5",
"colab_type": "text"
},
"source": [
"## Dataset\n",
"\n",
"- https://www.kaggle.com/kanncaa1/recommendation-systems-tutorial/data"
]
},
{
"cell_type": "code",
"metadata": {
"id": "se7CZSlWSLNS",
"colab_type": "code",
"colab": {}
},
"source": [
"import pandas as pd"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "hXSwlnolRtqI",
"colab_type": "code",
"colab": {}
},
"source": [
"df_movie = pd.read_csv('movie.csv')\n",
"df_rating = pd.read_csv('rating.csv')"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "ZOHvTNvkRtsr",
"colab_type": "code",
"colab": {
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"height": 424
},
"outputId": "0a028b1c-71fd-4127-b1c2-a94d59b28092"
},
"source": [
"df_movie"
],
"execution_count": 5,
"outputs": [
{
"output_type": "execute_result",
"data": {
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" <td>Comedy</td>\n",
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" <tr>\n",
" <th>27274</th>\n",
" <td>131256</td>\n",
" <td>Feuer, Eis &amp; Dosenbier (2002)</td>\n",
" <td>Comedy</td>\n",
" </tr>\n",
" <tr>\n",
" <th>27275</th>\n",
" <td>131258</td>\n",
" <td>The Pirates (2014)</td>\n",
" <td>Adventure</td>\n",
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" movieId ... genres\n",
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"3 4 ... Comedy|Drama|Romance\n",
"4 5 ... Comedy\n",
"... ... ... ...\n",
"27273 131254 ... Comedy\n",
"27274 131256 ... Comedy\n",
"27275 131258 ... Adventure\n",
"27276 131260 ... (no genres listed)\n",
"27277 131262 ... Adventure|Fantasy|Horror\n",
"\n",
"[27278 rows x 3 columns]"
]
},
"metadata": {
"tags": []
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"execution_count": 5
}
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{
"cell_type": "code",
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"colab_type": "code",
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"height": 424
},
"outputId": "150106d8-aef1-4707-bc88-7fa9141d3ffb"
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"source": [
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"execution_count": 6,
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{
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" userId movieId rating timestamp\n",
"0 1 2 3.5 2005-04-02 23:53:47\n",
"1 1 29 3.5 2005-04-02 23:31:16\n",
"2 1 32 3.5 2005-04-02 23:33:39\n",
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"32973 258 2012 5.0 2008-09-10 23:31:26\n",
"32974 258 2028 4.0 2007-06-09 03:47:4\n",
"\n",
"[32975 rows x 4 columns]"
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"metadata": {
"tags": []
},
"execution_count": 6
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "nH00RvF-ScWh",
"colab_type": "code",
"colab": {
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"height": 424
},
"outputId": "8b8271ed-b021-43e7-e6eb-2d127ca7264a"
},
"source": [
"merge_movie_rating = pd.merge(df_rating, df_movie, on='movieId')\n",
"merge_movie_rating"
],
"execution_count": 7,
"outputs": [
{
"output_type": "execute_result",
"data": {
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],
"text/plain": [
" userId ... genres\n",
"0 1 ... Adventure|Children|Fantasy\n",
"1 5 ... Adventure|Children|Fantasy\n",
"2 13 ... Adventure|Children|Fantasy\n",
"3 29 ... Adventure|Children|Fantasy\n",
"4 34 ... Adventure|Children|Fantasy\n",
"... ... ... ...\n",
"32970 252 ... Action|Crime|Drama|Film-Noir|Thriller\n",
"32971 252 ... Crime|Drama|Thriller\n",
"32972 254 ... Animation|Drama|War\n",
"32973 255 ... Comedy|Romance\n",
"32974 258 ... Documentary\n",
"\n",
"[32975 rows x 6 columns]"
]
},
"metadata": {
"tags": []
},
"execution_count": 7
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "W8Q4JpELSlNO",
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"height": 424
},
"outputId": "e3ab8cec-49a1-4625-cd42-1a8c88f2f03c"
},
"source": [
"data = merge_movie_rating[['movieId', 'title', 'userId', 'rating']]\n",
"data"
],
"execution_count": 8,
"outputs": [
{
"output_type": "execute_result",
"data": {
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" <td>Perfect Candidate, A (1996)</td>\n",
" <td>258</td>\n",
" <td>0.5</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>32975 rows × 4 columns</p>\n",
"</div>"
],
"text/plain": [
" movieId title userId rating\n",
"0 2 Jumanji (1995) 1 3.5\n",
"1 2 Jumanji (1995) 5 3.0\n",
"2 2 Jumanji (1995) 13 3.0\n",
"3 2 Jumanji (1995) 29 3.0\n",
"4 2 Jumanji (1995) 34 3.0\n",
"... ... ... ... ...\n",
"32970 26117 Killers, The (1964) 252 3.5\n",
"32971 26704 State of Grace (1990) 252 3.5\n",
"32972 5690 Grave of the Fireflies (Hotaru no haka) (1988) 254 3.0\n",
"32973 1854 Kissing a Fool (1998) 255 3.0\n",
"32974 1123 Perfect Candidate, A (1996) 258 0.5\n",
"\n",
"[32975 rows x 4 columns]"
]
},
"metadata": {
"tags": []
},
"execution_count": 8
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "cc6_2Ql3S9TR",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 652
},
"outputId": "04ec5c3d-ec85-4706-e937-97679cb7f1b5"
},
"source": [
"pivot_table = data.pivot_table(index=[\"userId\"], columns=[\"title\"], values=\"rating\").fillna(0)\n",
"print(pivot_table.shape)\n",
"pivot_table.head(10)"
],
"execution_count": 9,
"outputs": [
{
"output_type": "stream",
"text": [
"(258, 5477)\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
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" <th>title</th>\n",
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" <th>'burbs, The (1989)</th>\n",
" <th>'night Mother (1986)</th>\n",
" <th>(500) Days of Summer (2009)</th>\n",
" <th>*batteries not included (1987)</th>\n",
" <th>...And Justice for All (1979)</th>\n",
" <th>10 Things I Hate About You (1999)</th>\n",
" <th>10,000 BC (2008)</th>\n",
" <th>100 Girls (2000)</th>\n",
" <th>101 Dalmatians (1996)</th>\n",
" <th>101 Dalmatians (One Hundred and One Dalmatians) (1961)</th>\n",
" <th>102 Dalmatians (2000)</th>\n",
" <th>11:14 (2003)</th>\n",
" <th>11th Hour, The (2007)</th>\n",
" <th>12 Angry Men (1957)</th>\n",
" <th>12 Years a Slave (2013)</th>\n",
" <th>127 Hours (2010)</th>\n",
" <th>13 Assassins (Jûsan-nin no shikaku) (2010)</th>\n",
" <th>13 Ghosts (1960)</th>\n",
" <th>13 Going on 30 (2004)</th>\n",
" <th>13th Warrior, The (1999)</th>\n",
" <th>14 Blades (Jin yi wei) (2010)</th>\n",
" <th>1408 (2007)</th>\n",
" <th>15 Minutes (2001)</th>\n",
" <th>16 Blocks (2006)</th>\n",
" <th>17 Again (2009)</th>\n",
" <th>18 Again! (1988)</th>\n",
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" <th>1941 (1979)</th>\n",
" <th>1984 (Nineteen Eighty-Four) (1984)</th>\n",
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" <th>2 Fast 2 Furious (Fast and the Furious 2, The) (2003)</th>\n",
" <th>2 ou 3 choses que je sais d'elle (2 or 3 Things I Know About Her) (1967)</th>\n",
" <th>20 Dates (1998)</th>\n",
" <th>20 Feet from Stardom (Twenty Feet from Stardom) (2013)</th>\n",
" <th>20,000 Leagues Under the Sea (1954)</th>\n",
" <th>200 Cigarettes (1999)</th>\n",
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" <th>...</th>\n",
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" <th>You Don't Know Jack (2010)</th>\n",
" <th>You Don't Mess with the Zohan (2008)</th>\n",
" <th>You Got Served (2004)</th>\n",
" <th>You Only Live Twice (1967)</th>\n",
" <th>You've Got Mail (1998)</th>\n",
" <th>You, Me and Dupree (2006)</th>\n",
" <th>Young Adult (2011)</th>\n",
" <th>Young Americans, The (1993)</th>\n",
" <th>Young Doctors in Love (1982)</th>\n",
" <th>Young Einstein (1988)</th>\n",
" <th>Young Frankenstein (1974)</th>\n",
" <th>Young Guns (1988)</th>\n",
" <th>Young Guns II (1990)</th>\n",
" <th>Young Lions, The (1958)</th>\n",
" <th>Young Poisoner's Handbook, The (1995)</th>\n",
" <th>Young Sherlock Holmes (1985)</th>\n",
" <th>Young and the Damned, The (Olvidados, Los) (1950)</th>\n",
" <th>Young at Heart (a.k.a. Young@Heart) (2007)</th>\n",
" <th>Youngblood (1986)</th>\n",
" <th>Your Friends and Neighbors (1998)</th>\n",
" <th>Your Highness (2011)</th>\n",
" <th>Youth in Revolt (2009)</th>\n",
" <th>Z (1969)</th>\n",
" <th>Zachariah (1971)</th>\n",
" <th>Zack and Miri Make a Porno (2008)</th>\n",
" <th>Zelig (1983)</th>\n",
" <th>Zero Dark Thirty (2012)</th>\n",
" <th>Zero Effect (1998)</th>\n",
" <th>Zeus and Roxanne (1997)</th>\n",
" <th>Zodiac (2007)</th>\n",
" <th>Zombieland (2009)</th>\n",
" <th>Zookeeper (2011)</th>\n",
" <th>Zoolander (2001)</th>\n",
" <th>Zorro, the Gay Blade (1981)</th>\n",
" <th>Zulu (1964)</th>\n",
" <th>eXistenZ (1999)</th>\n",
" <th>xXx (2002)</th>\n",
" <th>¡Three Amigos! (1986)</th>\n",
" </tr>\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",
" <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>...</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",
" <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",
" <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",
" <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>6</th>\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",
" <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",
" <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",
" <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",
" <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",
" <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",
" <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",
" <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>7</th>\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",
" <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",
" <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",
" <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>3.0</td>\n",
" <td>3.0</td>\n",
" <td>0.0</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>3.0</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",
" <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",
" <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",
" <td>0.0</td>\n",
" <td>0.0</td>\n",
" <td>0.0</td>\n",
" <td>2.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\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",
" <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",
" <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",
" <td>0.0</td>\n",
" <td>0.0</td>\n",
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" <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>...</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",
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" <td>0.0</td>\n",
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" <td>0.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\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",
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" <td>0.0</td>\n",
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" <td>0.0</td>\n",
" <td>0.0</td>\n",
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" <td>0.0</td>\n",
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" <td>0.0</td>\n",
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" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>0.0</td>\n",
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" <td>0.0</td>\n",
" <td>0.0</td>\n",
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" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>10 rows × 5477 columns</p>\n",
"</div>"
],
"text/plain": [
"title 'Til There Was You (1997) ... ¡Three Amigos! (1986)\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",
"6 0.0 ... 0.0\n",
"7 0.0 ... 2.0\n",
"8 0.0 ... 0.0\n",
"9 0.0 ... 0.0\n",
"10 0.0 ... 0.0\n",
"\n",
"[10 rows x 5477 columns]"
]
},
"metadata": {
"tags": []
},
"execution_count": 9
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "_t5R98IeyBN9",
"colab_type": "text"
},
"source": [
"## By Correlation\n",
"\n",
"First in first, I'm gonna use just Correlation of the matrix, thereby recommending movies based on the similarity of movies.\n",
"\n",
"This means that this recommendation cannot recommend movies with respect to each user. \n",
"\n",
"We have similarities of movies, but we do not have expected rating of each user."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "xapWjNSs9SO2",
"colab_type": "text"
},
"source": [
"まず一つ目は相関を用いたレコメンデーションです。\n",
"\n",
"これは上記のピポット行列の相関から係数の高い物をレコメンドするだけなので\n",
"\n",
"ユーザー用というよりはクラスタリングに近いです。"
]
},
{
"cell_type": "code",
"metadata": {
"id": "bTZ7mm22j9WV",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 138
},
"outputId": "96b506e3-af40-44da-d14e-dca2f1314cf7"
},
"source": [
"movie_watched = pivot_table[\"Jumanji (1995)\"]\n",
"similarity_with_other_movies = pivot_table.corrwith(movie_watched) # find correlation between \"Bad Boys (1995)\" and other movies\n",
"similarity_with_other_movies = similarity_with_other_movies.sort_values(ascending=False)\n",
"similarity_with_other_movies.head()"
],
"execution_count": 10,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"title\n",
"Jumanji (1995) 1.000000\n",
"Operation Dumbo Drop (1995) 0.491024\n",
"Cops and Robbersons (1994) 0.445863\n",
"Dunston Checks In (1996) 0.437373\n",
"Toys (1992) 0.431135\n",
"dtype: float64"
]
},
"metadata": {
"tags": []
},
"execution_count": 10
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "_QyWf5X6kUS2",
"colab_type": "code",
"colab": {}
},
"source": [
"import seaborn as sns\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "cn7fUZ4qlpRF",
"colab_type": "code",
"colab": {}
},
"source": [
"tmp = pivot_table.iloc[:, :100]"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "c0hSrj_Wlpmx",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 918
},
"outputId": "ca601a57-d72e-4cb7-aa65-9eb5b81669a0"
},
"source": [
"corr = tmp.corr()\n",
"\n",
"# Generate a mask for the upper triangle\n",
"mask = np.zeros_like(corr, dtype=np.bool)\n",
"mask[np.triu_indices_from(mask)] = True\n",
"\n",
"# Set up the matplotlib figure\n",
"f, ax = plt.subplots(figsize=(18, 9))\n",
"\n",
"# Generate a custom diverging colormap\n",
"cmap = sns.diverging_palette(220, 10, as_cmap=True)\n",
"\n",
"# Draw the heatmap with the mask and correct aspect ratio\n",
"sns.heatmap(corr, mask=mask, cmap=cmap, vmax=.3, center=0,\n",
" square=True, linewidths=.5, cbar_kws={\"shrink\": .5})"
],
"execution_count": 13,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7f8a59821e48>"
]
},
"metadata": {
"tags": []
},
"execution_count": 13
},
{
"output_type": "display_data",
"data": {
"image/png": 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RTSsCVwNdgKeAH0fEF5KOAH4JTAUmAYdFxHOS1gJ+V10tuoR/cZuZmbVd3qPb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\nCCGEEMLCpLNnXY5kVCGEdiFpeeBioC8pWdIo2yPzvu8Bw4EvARvYHlv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Q1wshhBBCqGs+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\n",
"text/plain": [
"<Figure size 1296x648 with 2 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "UF60ogp6x8KJ",
"colab_type": "text"
},
"source": [
"## By SVD\n",
"\n",
"As I said above, correlation method cannot provide each user with foreseeable ratings.\n",
"\n",
"In this section, I'm gonna introduce you other way to reccommend. \n",
"\n",
"The keyword is **Singular value decomposition**.\n",
"\n",
"- https://en.wikipedia.org/wiki/Singular_value_decomposition\n",
"\n",
"> Suppose M is an m × n matrix whose entries come from the field K, which is either the field of real numbers or the field of complex numbers. Then the singular value decomposition of M exists, and is a factorization of the form\n",
"$$ \n",
"\\mathbf{M}=\\mathbf{U} \\boldsymbol{\\Sigma} \\mathbf{V}^{*}\n",
"$$ \n",
"> where\n",
"- $U$ is an $m \\times m$ unitary matrix over $K$ (if $K = \\mathbb {R} $, unitary matrices are orthogonal matrices),\n",
"- $\\Sigma$ is a diagonal $m \\times n$ matrix with non-negative real numbers on the diagonal,\n",
"- $V$ is an $n \\times n$ unitary matrix over $K$, and $V^*$ is the conjugate transpose of V.\n",
"\n",
"In this picture, \n",
"\n",
"- $m$ is the number of users\n",
"- $n$ is the number of movies\n",
"\n",
"![svd](https://miro.medium.com/max/1720/1*NQBN1LbJEqjkaPEetAHa2g.jpeg)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "g4T9JnPU778H",
"colab_type": "text"
},
"source": [
"In addition, this method is closely related with PCA(Principal Component Analysis). \n",
"\n",
"I'm gonna just summarize it here (if you are interested in it, please go to the references below.)\n",
"\n",
"- $U$ is composed of eigenvectors of $AA^T$\n",
"- $V$ is composed of eigenvectors of $A^TA$\n",
"\n",
"\n",
"($AA^T$ is famous for a variance-covariance matrix)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "MD64JnjL6zIa",
"colab_type": "text"
},
"source": [
"However, other problem occured.\n",
"\n",
"The thing is that $X$ (user x movie \\[rating\\]) is a sparse matrix in most situations."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "M4FhHrng9sZz",
"colab_type": "text"
},
"source": [
"二つ目はSVDです。詳しくは参考文献を見てください。\n",
"\n",
"SVDは次元削減の手法の一つでPCAの進化版的なイメージです。\n",
"\n",
"$$ \n",
"\\mathbf{M}=\\mathbf{U} \\boldsymbol{\\Sigma} \\mathbf{V}^{*}\n",
"$$ \n",
"\n",
"こんなふうに分解できます。"
]
},
{
"cell_type": "code",
"metadata": {
"id": "zUBi0G_LnjSy",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "fde46501-0f2a-4c3b-e3d9-a3fe6b56a6a4"
},
"source": [
"R = tmp.values\n",
"print(tmp.shape, R.shape)"
],
"execution_count": 14,
"outputs": [
{
"output_type": "stream",
"text": [
"(258, 100) (258, 100)\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "-BDCZcN-qRcq",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "d38971e5-4a61-4acf-8ddf-c78933900082"
},
"source": [
"user_ratings_mean = np.mean(R, axis = 1)\n",
"user_ratings_mean.shape"
],
"execution_count": 15,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(258,)"
]
},
"metadata": {
"tags": []
},
"execution_count": 15
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Ud9qJ3WtPqNQ",
"colab_type": "text"
},
"source": [
"別に引かなくていい"
]
},
{
"cell_type": "code",
"metadata": {
"id": "Y4dAWRDtqRhe",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 138
},
"outputId": "1e62c69c-f07b-458b-9b2a-bbd83f101e78"
},
"source": [
"R_demeaned = R - user_ratings_mean.reshape(-1, 1)\n",
"R_demeaned"
],
"execution_count": 16,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[-0.11, -0.11, -0.11, ..., -0.11, -0.11, -0.11],\n",
" [-0.13, -0.13, -0.13, ..., -0.13, 4.87, -0.13],\n",
" [-0.18, -0.18, -0.18, ..., -0.18, -0.18, -0.18],\n",
" ...,\n",
" [ 0. , 0. , 0. , ..., 0. , 0. , 0. ],\n",
" [ 0. , 0. , 0. , ..., 0. , 0. , 0. ],\n",
" [-0.02, -0.02, -0.02, ..., -0.02, -0.02, -0.02]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 16
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "TRg4jJQOsJm2",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 676
},
"outputId": "1c0ec2b4-f8f5-425d-8fde-e05da9c40a1f"
},
"source": [
"from scipy.sparse.linalg import svds\n",
"U, sigma, Vt = svds(R_demeaned, k = 50)\n",
"print('U\\n', U)\n",
"\n",
"print('S\\n', sigma)\n",
"\n",
"print('Vt\\n', Vt)"
],
"execution_count": 17,
"outputs": [
{
"output_type": "stream",
"text": [
"U\n",
" [[ 0.29462601 0.02746939 0.13377665 ... -0.00149963 -0.02962719\n",
" -0.11572325]\n",
" [ 0.05740164 -0.04504849 -0.00574595 ... -0.0450934 -0.08720129\n",
" -0.10823364]\n",
" [ 0.15109075 -0.04190446 0.03442851 ... -0.07569589 -0.11211274\n",
" -0.13100078]\n",
" ...\n",
" [ 0. 0. 0. ... 0. 0.\n",
" 0. ]\n",
" [ 0. 0. 0. ... 0. 0.\n",
" 0. ]\n",
" [-0.02733864 -0.01590649 -0.05015199 ... -0.01760493 0.00720953\n",
" -0.00058377]]\n",
"S\n",
" [ 3.82414903 3.9307335 4.00631577 4.18941633 4.34602148 4.43491611\n",
" 4.61536038 4.70058567 4.72130258 4.91254791 4.95037205 5.04144252\n",
" 5.19107116 5.26636606 5.46404332 5.56749486 5.8452363 5.85230379\n",
" 5.93431519 6.0663563 6.38080311 6.60452016 6.96415155 7.13865675\n",
" 7.42872954 7.52002378 8.1837815 8.30869773 8.80978768 9.05164282\n",
" 9.30017761 9.62136154 9.96606478 10.62989582 11.02497877 11.28271122\n",
" 11.49663818 11.7424932 12.37205411 12.52704224 13.3219029 14.0722323\n",
" 14.96749843 15.3605474 16.07566938 17.15629329 17.89121713 21.177078\n",
" 25.14706959 29.7853957 ]\n",
"Vt\n",
" [[-0.05446532 0.05183917 0.06758519 ... 0.02603748 0.07347523\n",
" -0.07739756]\n",
" [-0.00889387 -0.19945824 -0.14511254 ... 0.00211987 -0.0792355\n",
" -0.0209753 ]\n",
" [-0.07926175 0.18735308 -0.06752051 ... 0.00680863 -0.09207248\n",
" -0.10605307]\n",
" ...\n",
" [-0.04957941 -0.06965043 0.03415722 ... 0.02317819 0.00846311\n",
" -0.07615297]\n",
" [-0.03684841 -0.05362304 -0.04240651 ... 0.04927711 -0.02583689\n",
" -0.04279539]\n",
" [ 0.07204848 0.06833627 0.04547167 ... 0.0377437 0.01903552\n",
" 0.07567201]]\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "Go3Bimg0sJrC",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "4a8c7b59-763d-4c8c-ddbf-e00b6dc2193c"
},
"source": [
"Sigma = np.diag(sigma)\n",
"all_user_predicted_ratings = np.dot(np.dot(U, Sigma), Vt) + user_ratings_mean.reshape(-1, 1)\n",
"all_user_predicted_ratings.shape"
],
"execution_count": 18,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(258, 100)"
]
},
"metadata": {
"tags": []
},
"execution_count": 18
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "FQ2oTK0rsJws",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 446
},
"outputId": "ebc9f576-bdee-4924-c127-adefc203356f"
},
"source": [
"preds_df = pd.DataFrame(all_user_predicted_ratings, columns = pivot_table.columns[:100])\n",
"preds_df.head()"
],
"execution_count": 19,
"outputs": [
{
"output_type": "execute_result",
"data": {
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"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th>title</th>\n",
" <th>'Til There Was You (1997)</th>\n",
" <th>'burbs, The (1989)</th>\n",
" <th>'night Mother (1986)</th>\n",
" <th>(500) Days of Summer (2009)</th>\n",
" <th>*batteries not included (1987)</th>\n",
" <th>...And Justice for All (1979)</th>\n",
" <th>10 Things I Hate About You (1999)</th>\n",
" <th>10,000 BC (2008)</th>\n",
" <th>100 Girls (2000)</th>\n",
" <th>101 Dalmatians (1996)</th>\n",
" <th>101 Dalmatians (One Hundred and One Dalmatians) (1961)</th>\n",
" <th>102 Dalmatians (2000)</th>\n",
" <th>11:14 (2003)</th>\n",
" <th>11th Hour, The (2007)</th>\n",
" <th>12 Angry Men (1957)</th>\n",
" <th>12 Years a Slave (2013)</th>\n",
" <th>127 Hours (2010)</th>\n",
" <th>13 Assassins (Jûsan-nin no shikaku) (2010)</th>\n",
" <th>13 Ghosts (1960)</th>\n",
" <th>13 Going on 30 (2004)</th>\n",
" <th>13th Warrior, The (1999)</th>\n",
" <th>14 Blades (Jin yi wei) (2010)</th>\n",
" <th>1408 (2007)</th>\n",
" <th>15 Minutes (2001)</th>\n",
" <th>16 Blocks (2006)</th>\n",
" <th>17 Again (2009)</th>\n",
" <th>18 Again! (1988)</th>\n",
" <th>187 (One Eight Seven) (1997)</th>\n",
" <th>1941 (1979)</th>\n",
" <th>1984 (Nineteen Eighty-Four) (1984)</th>\n",
" <th>2 Days in the Valley (1996)</th>\n",
" <th>2 Fast 2 Furious (Fast and the Furious 2, The) (2003)</th>\n",
" <th>2 ou 3 choses que je sais d'elle (2 or 3 Things I Know About Her) (1967)</th>\n",
" <th>20 Dates (1998)</th>\n",
" <th>20 Feet from Stardom (Twenty Feet from Stardom) (2013)</th>\n",
" <th>20,000 Leagues Under the Sea (1954)</th>\n",
" <th>200 Cigarettes (1999)</th>\n",
" <th>2001: A Space Odyssey (1968)</th>\n",
" <th>2010: The Year We Make Contact (1984)</th>\n",
" <th>2012 (2009)</th>\n",
" <th>...</th>\n",
" <th>300 (2007)</th>\n",
" <th>3000 Miles to Graceland (2001)</th>\n",
" <th>300: Rise of an Empire (2014)</th>\n",
" <th>35 Up (1991)</th>\n",
" <th>39 Steps, The (1935)</th>\n",
" <th>3:10 to Yuma (2007)</th>\n",
" <th>4 Months, 3 Weeks and 2 Days (4 luni, 3 saptamâni si 2 zile) (2007)</th>\n",
" <th>40 Days and 40 Nights (2002)</th>\n",
" <th>40-Year-Old Virgin, The (2005)</th>\n",
" <th>400 Blows, The (Les quatre cents coups) (1959)</th>\n",
" <th>42 Up (1998)</th>\n",
" <th>47 Samurai (Chûshingura) (Loyal 47 Ronin, The) (1962)</th>\n",
" <th>48 Hrs. (1982)</th>\n",
" <th>49 Up (2005)</th>\n",
" <th>50 First Dates (2004)</th>\n",
" <th>50/50 (2011)</th>\n",
" <th>52 Pick-Up (1986)</th>\n",
" <th>54 (1998)</th>\n",
" <th>56 Up (2012)</th>\n",
" <th>5th Musketeer, The (a.k.a. Fifth Musketeer, The) (1979)</th>\n",
" <th>6th Day, The (2000)</th>\n",
" <th>6th Man, The (Sixth Man, The) (1997)</th>\n",
" <th>7th Voyage of Sinbad, The (1958)</th>\n",
" <th>8 1/2 (8½) (1963)</th>\n",
" <th>8 Heads in a Duffel Bag (1997)</th>\n",
" <th>8 Mile (2002)</th>\n",
" <th>8 Seconds (1994)</th>\n",
" <th>8 Women (2002)</th>\n",
" <th>84 Charing Cross Road (1987)</th>\n",
" <th>8MM (1999)</th>\n",
" <th>9 1/2 Weeks (Nine 1/2 Weeks) (1986)</th>\n",
" <th>9 Songs (2004)</th>\n",
" <th>9/11 (2002)</th>\n",
" <th>A-Team, The (2010)</th>\n",
" <th>A.I. Artificial Intelligence (2001)</th>\n",
" <th>AVP: Alien vs. Predator (2004)</th>\n",
" <th>AVPR: Aliens vs. Predator - Requiem (2007)</th>\n",
" <th>Abandoned, The (2006)</th>\n",
" <th>Abbott and Costello Meet Frankenstein (1948)</th>\n",
" <th>Abominable Dr. Phibes, The (1971)</th>\n",
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" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>-0.055563</td>\n",
" <td>-0.076438</td>\n",
" <td>-0.088263</td>\n",
" <td>0.004166</td>\n",
" <td>0.097933</td>\n",
" <td>0.023231</td>\n",
" <td>-0.066088</td>\n",
" <td>0.094263</td>\n",
" <td>0.100613</td>\n",
" <td>-0.025201</td>\n",
" <td>0.048217</td>\n",
" <td>-0.223578</td>\n",
" <td>0.273693</td>\n",
" <td>-0.042069</td>\n",
" <td>-0.031204</td>\n",
" <td>-0.088864</td>\n",
" <td>-0.154398</td>\n",
" <td>0.341822</td>\n",
" <td>-0.093166</td>\n",
" <td>-0.037045</td>\n",
" <td>-0.022822</td>\n",
" <td>0.310632</td>\n",
" <td>0.125384</td>\n",
" <td>0.040891</td>\n",
" <td>0.037492</td>\n",
" <td>0.040263</td>\n",
" <td>-0.055563</td>\n",
" <td>0.110077</td>\n",
" <td>0.088700</td>\n",
" <td>0.016980</td>\n",
" <td>-0.106205</td>\n",
" <td>0.082535</td>\n",
" <td>0.056367</td>\n",
" <td>0.088181</td>\n",
" <td>-0.068734</td>\n",
" <td>-0.203214</td>\n",
" <td>0.304270</td>\n",
" <td>3.593550</td>\n",
" <td>-0.003444</td>\n",
" <td>0.081281</td>\n",
" <td>...</td>\n",
" <td>0.066166</td>\n",
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" <td>-0.008830</td>\n",
" <td>-0.088864</td>\n",
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" <td>0.167479</td>\n",
" <td>0.051235</td>\n",
" <td>0.024838</td>\n",
" <td>-0.053271</td>\n",
" <td>0.505168</td>\n",
" <td>0.507633</td>\n",
" <td>0.448924</td>\n",
" <td>-0.068734</td>\n",
" <td>-0.030419</td>\n",
" <td>-0.136177</td>\n",
" <td>0.205673</td>\n",
" <td>-0.193665</td>\n",
" <td>-0.068734</td>\n",
" <td>-0.288932</td>\n",
" <td>-0.038360</td>\n",
" <td>0.179509</td>\n",
" <td>2.786996</td>\n",
" <td>-0.043713</td>\n",
" <td>-0.021140</td>\n",
" <td>-0.036945</td>\n",
" <td>0.241955</td>\n",
" <td>0.022783</td>\n",
" <td>-0.028475</td>\n",
" <td>-0.132010</td>\n",
" <td>-0.126126</td>\n",
" <td>0.101536</td>\n",
" <td>-0.089837</td>\n",
" <td>0.327534</td>\n",
" <td>-0.068362</td>\n",
" <td>-0.291883</td>\n",
" <td>-0.080604</td>\n",
" <td>0.097843</td>\n",
" <td>-0.189676</td>\n",
" <td>-0.104851</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.054560</td>\n",
" <td>-0.150978</td>\n",
" <td>0.015145</td>\n",
" <td>-0.034608</td>\n",
" <td>-0.028957</td>\n",
" <td>0.014763</td>\n",
" <td>0.114136</td>\n",
" <td>-0.042509</td>\n",
" <td>-0.036862</td>\n",
" <td>0.047712</td>\n",
" <td>0.005032</td>\n",
" <td>-0.010041</td>\n",
" <td>0.034829</td>\n",
" <td>0.149570</td>\n",
" <td>-0.027513</td>\n",
" <td>0.013371</td>\n",
" <td>-0.065501</td>\n",
" <td>0.068190</td>\n",
" <td>-0.247236</td>\n",
" <td>-0.418257</td>\n",
" <td>0.023287</td>\n",
" <td>0.069825</td>\n",
" <td>-0.110760</td>\n",
" <td>0.074997</td>\n",
" <td>-0.011391</td>\n",
" <td>0.079365</td>\n",
" <td>0.054560</td>\n",
" <td>-0.082533</td>\n",
" <td>0.102307</td>\n",
" <td>-0.187655</td>\n",
" <td>-0.017957</td>\n",
" <td>0.546489</td>\n",
" <td>0.059778</td>\n",
" <td>0.080587</td>\n",
" <td>0.020916</td>\n",
" <td>-0.002355</td>\n",
" <td>0.102196</td>\n",
" <td>5.018342</td>\n",
" <td>0.141193</td>\n",
" <td>0.026542</td>\n",
" <td>...</td>\n",
" <td>0.010109</td>\n",
" <td>-0.030113</td>\n",
" <td>-0.005765</td>\n",
" <td>0.013371</td>\n",
" <td>0.043262</td>\n",
" <td>-0.023653</td>\n",
" <td>0.068593</td>\n",
" <td>-0.175257</td>\n",
" <td>-0.011872</td>\n",
" <td>-0.017981</td>\n",
" <td>0.065864</td>\n",
" <td>0.109328</td>\n",
" <td>-0.019497</td>\n",
" <td>0.020916</td>\n",
" <td>0.064048</td>\n",
" <td>-0.008578</td>\n",
" <td>0.036162</td>\n",
" <td>-0.321544</td>\n",
" <td>0.020916</td>\n",
" <td>-0.018797</td>\n",
" <td>-0.110977</td>\n",
" <td>-0.032175</td>\n",
" <td>-0.089775</td>\n",
" <td>0.003462</td>\n",
" <td>-0.125585</td>\n",
" <td>0.089598</td>\n",
" <td>-0.187455</td>\n",
" <td>-0.243987</td>\n",
" <td>0.036006</td>\n",
" <td>0.036846</td>\n",
" <td>0.024008</td>\n",
" <td>-0.049989</td>\n",
" <td>0.074587</td>\n",
" <td>-0.178566</td>\n",
" <td>-0.083115</td>\n",
" <td>0.143622</td>\n",
" <td>-0.056677</td>\n",
" <td>0.002517</td>\n",
" <td>4.587499</td>\n",
" <td>0.045655</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.006738</td>\n",
" <td>-0.211388</td>\n",
" <td>0.007455</td>\n",
" <td>-0.043048</td>\n",
" <td>0.009676</td>\n",
" <td>0.406935</td>\n",
" <td>-0.035012</td>\n",
" <td>0.127787</td>\n",
" <td>-0.009285</td>\n",
" <td>-0.047256</td>\n",
" <td>0.035356</td>\n",
" <td>0.040906</td>\n",
" <td>0.092431</td>\n",
" <td>-0.098287</td>\n",
" <td>-0.022246</td>\n",
" <td>0.011629</td>\n",
" <td>-0.001597</td>\n",
" <td>0.006026</td>\n",
" <td>0.007365</td>\n",
" <td>-0.023928</td>\n",
" <td>-0.011853</td>\n",
" <td>-0.001631</td>\n",
" <td>-0.083977</td>\n",
" <td>0.083427</td>\n",
" <td>0.074022</td>\n",
" <td>-0.041495</td>\n",
" <td>0.006738</td>\n",
" <td>0.521388</td>\n",
" <td>-0.041373</td>\n",
" <td>5.000251</td>\n",
" <td>-0.101690</td>\n",
" <td>0.001710</td>\n",
" <td>0.020708</td>\n",
" <td>-0.034691</td>\n",
" <td>0.004200</td>\n",
" <td>0.303877</td>\n",
" <td>0.325298</td>\n",
" <td>5.022796</td>\n",
" <td>3.833104</td>\n",
" <td>-0.055652</td>\n",
" <td>...</td>\n",
" <td>-0.015525</td>\n",
" <td>-0.208069</td>\n",
" <td>0.005439</td>\n",
" <td>0.011629</td>\n",
" <td>0.020552</td>\n",
" <td>0.007615</td>\n",
" <td>-0.309079</td>\n",
" <td>-0.043074</td>\n",
" <td>0.000236</td>\n",
" <td>0.052319</td>\n",
" <td>-0.142458</td>\n",
" <td>-0.159651</td>\n",
" <td>-0.005113</td>\n",
" <td>0.004200</td>\n",
" <td>0.041174</td>\n",
" <td>0.077356</td>\n",
" <td>0.154985</td>\n",
" <td>-0.120276</td>\n",
" <td>0.004200</td>\n",
" <td>-0.046625</td>\n",
" <td>-0.116957</td>\n",
" <td>-0.212972</td>\n",
" <td>-0.044177</td>\n",
" <td>-0.048295</td>\n",
" <td>0.043978</td>\n",
" <td>0.139435</td>\n",
" <td>-0.169810</td>\n",
" <td>0.005205</td>\n",
" <td>-0.010657</td>\n",
" <td>3.799285</td>\n",
" <td>-0.024940</td>\n",
" <td>-0.004180</td>\n",
" <td>-0.007162</td>\n",
" <td>0.049378</td>\n",
" <td>-0.015397</td>\n",
" <td>-0.065631</td>\n",
" <td>0.043888</td>\n",
" <td>-0.024600</td>\n",
" <td>-0.081787</td>\n",
" <td>0.027393</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
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" <td>0.000000</td>\n",
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" <td>0.000000</td>\n",
" <td>...</td>\n",
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" <td>0.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.000000</td>\n",
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],
"text/plain": [
"title 'Til There Was You (1997) ... Abominable Dr. Phibes, The (1971)\n",
"0 -0.055563 ... -0.104851\n",
"1 0.054560 ... 0.045655\n",
"2 0.006738 ... 0.027393\n",
"3 0.000000 ... 0.000000\n",
"4 0.000000 ... 0.000000\n",
"\n",
"[5 rows x 100 columns]"
]
},
"metadata": {
"tags": []
},
"execution_count": 19
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "wEJCDVZyxpGs",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 477
},
"outputId": "456ecec4-35a8-4920-98f4-3eb9013f50c7"
},
"source": [
"pd.DataFrame(tmp, columns = pivot_table.columns[:100]).head()"
],
"execution_count": 20,
"outputs": [
{
"output_type": "execute_result",
"data": {
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" <th>title</th>\n",
" <th>'Til There Was You (1997)</th>\n",
" <th>'burbs, The (1989)</th>\n",
" <th>'night Mother (1986)</th>\n",
" <th>(500) Days of Summer (2009)</th>\n",
" <th>*batteries not included (1987)</th>\n",
" <th>...And Justice for All (1979)</th>\n",
" <th>10 Things I Hate About You (1999)</th>\n",
" <th>10,000 BC (2008)</th>\n",
" <th>100 Girls (2000)</th>\n",
" <th>101 Dalmatians (1996)</th>\n",
" <th>101 Dalmatians (One Hundred and One Dalmatians) (1961)</th>\n",
" <th>102 Dalmatians (2000)</th>\n",
" <th>11:14 (2003)</th>\n",
" <th>11th Hour, The (2007)</th>\n",
" <th>12 Angry Men (1957)</th>\n",
" <th>12 Years a Slave (2013)</th>\n",
" <th>127 Hours (2010)</th>\n",
" <th>13 Assassins (Jûsan-nin no shikaku) (2010)</th>\n",
" <th>13 Ghosts (1960)</th>\n",
" <th>13 Going on 30 (2004)</th>\n",
" <th>13th Warrior, The (1999)</th>\n",
" <th>14 Blades (Jin yi wei) (2010)</th>\n",
" <th>1408 (2007)</th>\n",
" <th>15 Minutes (2001)</th>\n",
" <th>16 Blocks (2006)</th>\n",
" <th>17 Again (2009)</th>\n",
" <th>18 Again! (1988)</th>\n",
" <th>187 (One Eight Seven) (1997)</th>\n",
" <th>1941 (1979)</th>\n",
" <th>1984 (Nineteen Eighty-Four) (1984)</th>\n",
" <th>2 Days in the Valley (1996)</th>\n",
" <th>2 Fast 2 Furious (Fast and the Furious 2, The) (2003)</th>\n",
" <th>2 ou 3 choses que je sais d'elle (2 or 3 Things I Know About Her) (1967)</th>\n",
" <th>20 Dates (1998)</th>\n",
" <th>20 Feet from Stardom (Twenty Feet from Stardom) (2013)</th>\n",
" <th>20,000 Leagues Under the Sea (1954)</th>\n",
" <th>200 Cigarettes (1999)</th>\n",
" <th>2001: A Space Odyssey (1968)</th>\n",
" <th>2010: The Year We Make Contact (1984)</th>\n",
" <th>2012 (2009)</th>\n",
" <th>...</th>\n",
" <th>300 (2007)</th>\n",
" <th>3000 Miles to Graceland (2001)</th>\n",
" <th>300: Rise of an Empire (2014)</th>\n",
" <th>35 Up (1991)</th>\n",
" <th>39 Steps, The (1935)</th>\n",
" <th>3:10 to Yuma (2007)</th>\n",
" <th>4 Months, 3 Weeks and 2 Days (4 luni, 3 saptamâni si 2 zile) (2007)</th>\n",
" <th>40 Days and 40 Nights (2002)</th>\n",
" <th>40-Year-Old Virgin, The (2005)</th>\n",
" <th>400 Blows, The (Les quatre cents coups) (1959)</th>\n",
" <th>42 Up (1998)</th>\n",
" <th>47 Samurai (Chûshingura) (Loyal 47 Ronin, The) (1962)</th>\n",
" <th>48 Hrs. (1982)</th>\n",
" <th>49 Up (2005)</th>\n",
" <th>50 First Dates (2004)</th>\n",
" <th>50/50 (2011)</th>\n",
" <th>52 Pick-Up (1986)</th>\n",
" <th>54 (1998)</th>\n",
" <th>56 Up (2012)</th>\n",
" <th>5th Musketeer, The (a.k.a. Fifth Musketeer, The) (1979)</th>\n",
" <th>6th Day, The (2000)</th>\n",
" <th>6th Man, The (Sixth Man, The) (1997)</th>\n",
" <th>7th Voyage of Sinbad, The (1958)</th>\n",
" <th>8 1/2 (8½) (1963)</th>\n",
" <th>8 Heads in a Duffel Bag (1997)</th>\n",
" <th>8 Mile (2002)</th>\n",
" <th>8 Seconds (1994)</th>\n",
" <th>8 Women (2002)</th>\n",
" <th>84 Charing Cross Road (1987)</th>\n",
" <th>8MM (1999)</th>\n",
" <th>9 1/2 Weeks (Nine 1/2 Weeks) (1986)</th>\n",
" <th>9 Songs (2004)</th>\n",
" <th>9/11 (2002)</th>\n",
" <th>A-Team, The (2010)</th>\n",
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" <th>AVP: Alien vs. Predator (2004)</th>\n",
" <th>AVPR: Aliens vs. Predator - Requiem (2007)</th>\n",
" <th>Abandoned, The (2006)</th>\n",
" <th>Abbott and Costello Meet Frankenstein (1948)</th>\n",
" <th>Abominable Dr. Phibes, The (1971)</th>\n",
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" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 100 columns</p>\n",
"</div>"
],
"text/plain": [
"title 'Til There Was You (1997) ... Abominable Dr. Phibes, The (1971)\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",
"[5 rows x 100 columns]"
]
},
"metadata": {
"tags": []
},
"execution_count": 20
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "c2xXz1t-tsTT",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 446
},
"outputId": "4024803f-7212-4a06-ff00-469d3e798229"
},
"source": [
"pd.DataFrame(np.round(all_user_predicted_ratings, decimals=3), columns = pivot_table.columns[:100]).head()"
],
"execution_count": 21,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/html": [
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"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th>title</th>\n",
" <th>'Til There Was You (1997)</th>\n",
" <th>'burbs, The (1989)</th>\n",
" <th>'night Mother (1986)</th>\n",
" <th>(500) Days of Summer (2009)</th>\n",
" <th>*batteries not included (1987)</th>\n",
" <th>...And Justice for All (1979)</th>\n",
" <th>10 Things I Hate About You (1999)</th>\n",
" <th>10,000 BC (2008)</th>\n",
" <th>100 Girls (2000)</th>\n",
" <th>101 Dalmatians (1996)</th>\n",
" <th>101 Dalmatians (One Hundred and One Dalmatians) (1961)</th>\n",
" <th>102 Dalmatians (2000)</th>\n",
" <th>11:14 (2003)</th>\n",
" <th>11th Hour, The (2007)</th>\n",
" <th>12 Angry Men (1957)</th>\n",
" <th>12 Years a Slave (2013)</th>\n",
" <th>127 Hours (2010)</th>\n",
" <th>13 Assassins (Jûsan-nin no shikaku) (2010)</th>\n",
" <th>13 Ghosts (1960)</th>\n",
" <th>13 Going on 30 (2004)</th>\n",
" <th>13th Warrior, The (1999)</th>\n",
" <th>14 Blades (Jin yi wei) (2010)</th>\n",
" <th>1408 (2007)</th>\n",
" <th>15 Minutes (2001)</th>\n",
" <th>16 Blocks (2006)</th>\n",
" <th>17 Again (2009)</th>\n",
" <th>18 Again! (1988)</th>\n",
" <th>187 (One Eight Seven) (1997)</th>\n",
" <th>1941 (1979)</th>\n",
" <th>1984 (Nineteen Eighty-Four) (1984)</th>\n",
" <th>2 Days in the Valley (1996)</th>\n",
" <th>2 Fast 2 Furious (Fast and the Furious 2, The) (2003)</th>\n",
" <th>2 ou 3 choses que je sais d'elle (2 or 3 Things I Know About Her) (1967)</th>\n",
" <th>20 Dates (1998)</th>\n",
" <th>20 Feet from Stardom (Twenty Feet from Stardom) (2013)</th>\n",
" <th>20,000 Leagues Under the Sea (1954)</th>\n",
" <th>200 Cigarettes (1999)</th>\n",
" <th>2001: A Space Odyssey (1968)</th>\n",
" <th>2010: The Year We Make Contact (1984)</th>\n",
" <th>2012 (2009)</th>\n",
" <th>...</th>\n",
" <th>300 (2007)</th>\n",
" <th>3000 Miles to Graceland (2001)</th>\n",
" <th>300: Rise of an Empire (2014)</th>\n",
" <th>35 Up (1991)</th>\n",
" <th>39 Steps, The (1935)</th>\n",
" <th>3:10 to Yuma (2007)</th>\n",
" <th>4 Months, 3 Weeks and 2 Days (4 luni, 3 saptamâni si 2 zile) (2007)</th>\n",
" <th>40 Days and 40 Nights (2002)</th>\n",
" <th>40-Year-Old Virgin, The (2005)</th>\n",
" <th>400 Blows, The (Les quatre cents coups) (1959)</th>\n",
" <th>42 Up (1998)</th>\n",
" <th>47 Samurai (Chûshingura) (Loyal 47 Ronin, The) (1962)</th>\n",
" <th>48 Hrs. (1982)</th>\n",
" <th>49 Up (2005)</th>\n",
" <th>50 First Dates (2004)</th>\n",
" <th>50/50 (2011)</th>\n",
" <th>52 Pick-Up (1986)</th>\n",
" <th>54 (1998)</th>\n",
" <th>56 Up (2012)</th>\n",
" <th>5th Musketeer, The (a.k.a. Fifth Musketeer, The) (1979)</th>\n",
" <th>6th Day, The (2000)</th>\n",
" <th>6th Man, The (Sixth Man, The) (1997)</th>\n",
" <th>7th Voyage of Sinbad, The (1958)</th>\n",
" <th>8 1/2 (8½) (1963)</th>\n",
" <th>8 Heads in a Duffel Bag (1997)</th>\n",
" <th>8 Mile (2002)</th>\n",
" <th>8 Seconds (1994)</th>\n",
" <th>8 Women (2002)</th>\n",
" <th>84 Charing Cross Road (1987)</th>\n",
" <th>8MM (1999)</th>\n",
" <th>9 1/2 Weeks (Nine 1/2 Weeks) (1986)</th>\n",
" <th>9 Songs (2004)</th>\n",
" <th>9/11 (2002)</th>\n",
" <th>A-Team, The (2010)</th>\n",
" <th>A.I. Artificial Intelligence (2001)</th>\n",
" <th>AVP: Alien vs. Predator (2004)</th>\n",
" <th>AVPR: Aliens vs. Predator - Requiem (2007)</th>\n",
" <th>Abandoned, The (2006)</th>\n",
" <th>Abbott and Costello Meet Frankenstein (1948)</th>\n",
" <th>Abominable Dr. Phibes, The (1971)</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>-0.056</td>\n",
" <td>-0.076</td>\n",
" <td>-0.088</td>\n",
" <td>0.004</td>\n",
" <td>0.098</td>\n",
" <td>0.023</td>\n",
" <td>-0.066</td>\n",
" <td>0.094</td>\n",
" <td>0.101</td>\n",
" <td>-0.025</td>\n",
" <td>0.048</td>\n",
" <td>-0.224</td>\n",
" <td>0.274</td>\n",
" <td>-0.042</td>\n",
" <td>-0.031</td>\n",
" <td>-0.089</td>\n",
" <td>-0.154</td>\n",
" <td>0.342</td>\n",
" <td>-0.093</td>\n",
" <td>-0.037</td>\n",
" <td>-0.023</td>\n",
" <td>0.311</td>\n",
" <td>0.125</td>\n",
" <td>0.041</td>\n",
" <td>0.037</td>\n",
" <td>0.040</td>\n",
" <td>-0.056</td>\n",
" <td>0.110</td>\n",
" <td>0.089</td>\n",
" <td>0.017</td>\n",
" <td>-0.106</td>\n",
" <td>0.083</td>\n",
" <td>0.056</td>\n",
" <td>0.088</td>\n",
" <td>-0.069</td>\n",
" <td>-0.203</td>\n",
" <td>0.304</td>\n",
" <td>3.594</td>\n",
" <td>-0.003</td>\n",
" <td>0.081</td>\n",
" <td>...</td>\n",
" <td>0.066</td>\n",
" <td>0.079</td>\n",
" <td>-0.009</td>\n",
" <td>-0.089</td>\n",
" <td>-0.053</td>\n",
" <td>-0.105</td>\n",
" <td>0.167</td>\n",
" <td>0.051</td>\n",
" <td>0.025</td>\n",
" <td>-0.053</td>\n",
" <td>0.505</td>\n",
" <td>0.508</td>\n",
" <td>0.449</td>\n",
" <td>-0.069</td>\n",
" <td>-0.030</td>\n",
" <td>-0.136</td>\n",
" <td>0.206</td>\n",
" <td>-0.194</td>\n",
" <td>-0.069</td>\n",
" <td>-0.289</td>\n",
" <td>-0.038</td>\n",
" <td>0.180</td>\n",
" <td>2.787</td>\n",
" <td>-0.044</td>\n",
" <td>-0.021</td>\n",
" <td>-0.037</td>\n",
" <td>0.242</td>\n",
" <td>0.023</td>\n",
" <td>-0.028</td>\n",
" <td>-0.132</td>\n",
" <td>-0.126</td>\n",
" <td>0.102</td>\n",
" <td>-0.090</td>\n",
" <td>0.328</td>\n",
" <td>-0.068</td>\n",
" <td>-0.292</td>\n",
" <td>-0.081</td>\n",
" <td>0.098</td>\n",
" <td>-0.190</td>\n",
" <td>-0.105</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.055</td>\n",
" <td>-0.151</td>\n",
" <td>0.015</td>\n",
" <td>-0.035</td>\n",
" <td>-0.029</td>\n",
" <td>0.015</td>\n",
" <td>0.114</td>\n",
" <td>-0.043</td>\n",
" <td>-0.037</td>\n",
" <td>0.048</td>\n",
" <td>0.005</td>\n",
" <td>-0.010</td>\n",
" <td>0.035</td>\n",
" <td>0.150</td>\n",
" <td>-0.028</td>\n",
" <td>0.013</td>\n",
" <td>-0.066</td>\n",
" <td>0.068</td>\n",
" <td>-0.247</td>\n",
" <td>-0.418</td>\n",
" <td>0.023</td>\n",
" <td>0.070</td>\n",
" <td>-0.111</td>\n",
" <td>0.075</td>\n",
" <td>-0.011</td>\n",
" <td>0.079</td>\n",
" <td>0.055</td>\n",
" <td>-0.083</td>\n",
" <td>0.102</td>\n",
" <td>-0.188</td>\n",
" <td>-0.018</td>\n",
" <td>0.546</td>\n",
" <td>0.060</td>\n",
" <td>0.081</td>\n",
" <td>0.021</td>\n",
" <td>-0.002</td>\n",
" <td>0.102</td>\n",
" <td>5.018</td>\n",
" <td>0.141</td>\n",
" <td>0.027</td>\n",
" <td>...</td>\n",
" <td>0.010</td>\n",
" <td>-0.030</td>\n",
" <td>-0.006</td>\n",
" <td>0.013</td>\n",
" <td>0.043</td>\n",
" <td>-0.024</td>\n",
" <td>0.069</td>\n",
" <td>-0.175</td>\n",
" <td>-0.012</td>\n",
" <td>-0.018</td>\n",
" <td>0.066</td>\n",
" <td>0.109</td>\n",
" <td>-0.019</td>\n",
" <td>0.021</td>\n",
" <td>0.064</td>\n",
" <td>-0.009</td>\n",
" <td>0.036</td>\n",
" <td>-0.322</td>\n",
" <td>0.021</td>\n",
" <td>-0.019</td>\n",
" <td>-0.111</td>\n",
" <td>-0.032</td>\n",
" <td>-0.090</td>\n",
" <td>0.003</td>\n",
" <td>-0.126</td>\n",
" <td>0.090</td>\n",
" <td>-0.187</td>\n",
" <td>-0.244</td>\n",
" <td>0.036</td>\n",
" <td>0.037</td>\n",
" <td>0.024</td>\n",
" <td>-0.050</td>\n",
" <td>0.075</td>\n",
" <td>-0.179</td>\n",
" <td>-0.083</td>\n",
" <td>0.144</td>\n",
" <td>-0.057</td>\n",
" <td>0.003</td>\n",
" <td>4.587</td>\n",
" <td>0.046</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.007</td>\n",
" <td>-0.211</td>\n",
" <td>0.007</td>\n",
" <td>-0.043</td>\n",
" <td>0.010</td>\n",
" <td>0.407</td>\n",
" <td>-0.035</td>\n",
" <td>0.128</td>\n",
" <td>-0.009</td>\n",
" <td>-0.047</td>\n",
" <td>0.035</td>\n",
" <td>0.041</td>\n",
" <td>0.092</td>\n",
" <td>-0.098</td>\n",
" <td>-0.022</td>\n",
" <td>0.012</td>\n",
" <td>-0.002</td>\n",
" <td>0.006</td>\n",
" <td>0.007</td>\n",
" <td>-0.024</td>\n",
" <td>-0.012</td>\n",
" <td>-0.002</td>\n",
" <td>-0.084</td>\n",
" <td>0.083</td>\n",
" <td>0.074</td>\n",
" <td>-0.041</td>\n",
" <td>0.007</td>\n",
" <td>0.521</td>\n",
" <td>-0.041</td>\n",
" <td>5.000</td>\n",
" <td>-0.102</td>\n",
" <td>0.002</td>\n",
" <td>0.021</td>\n",
" <td>-0.035</td>\n",
" <td>0.004</td>\n",
" <td>0.304</td>\n",
" <td>0.325</td>\n",
" <td>5.023</td>\n",
" <td>3.833</td>\n",
" <td>-0.056</td>\n",
" <td>...</td>\n",
" <td>-0.016</td>\n",
" <td>-0.208</td>\n",
" <td>0.005</td>\n",
" <td>0.012</td>\n",
" <td>0.021</td>\n",
" <td>0.008</td>\n",
" <td>-0.309</td>\n",
" <td>-0.043</td>\n",
" <td>0.000</td>\n",
" <td>0.052</td>\n",
" <td>-0.142</td>\n",
" <td>-0.160</td>\n",
" <td>-0.005</td>\n",
" <td>0.004</td>\n",
" <td>0.041</td>\n",
" <td>0.077</td>\n",
" <td>0.155</td>\n",
" <td>-0.120</td>\n",
" <td>0.004</td>\n",
" <td>-0.047</td>\n",
" <td>-0.117</td>\n",
" <td>-0.213</td>\n",
" <td>-0.044</td>\n",
" <td>-0.048</td>\n",
" <td>0.044</td>\n",
" <td>0.139</td>\n",
" <td>-0.170</td>\n",
" <td>0.005</td>\n",
" <td>-0.011</td>\n",
" <td>3.799</td>\n",
" <td>-0.025</td>\n",
" <td>-0.004</td>\n",
" <td>-0.007</td>\n",
" <td>0.049</td>\n",
" <td>-0.015</td>\n",
" <td>-0.066</td>\n",
" <td>0.044</td>\n",
" <td>-0.025</td>\n",
" <td>-0.082</td>\n",
" <td>0.027</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>...</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>...</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 100 columns</p>\n",
"</div>"
],
"text/plain": [
"title 'Til There Was You (1997) ... Abominable Dr. Phibes, The (1971)\n",
"0 -0.056 ... -0.105\n",
"1 0.055 ... 0.046\n",
"2 0.007 ... 0.027\n",
"3 0.000 ... 0.000\n",
"4 0.000 ... 0.000\n",
"\n",
"[5 rows x 100 columns]"
]
},
"metadata": {
"tags": []
},
"execution_count": 21
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "dvkYeOQ-sJ1z",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 138
},
"outputId": "4f1f505c-96f4-453e-c99a-7d0b90977f1b"
},
"source": [
"# preds_df\n",
"# userID\n",
"# movies_df\n",
"# original_ratings_df\n",
"# num_recommendations=5)\n",
"\n",
"userID = 2\n",
"user_row_number = userID - 1\n",
"sorted_user_predictions = preds_df.iloc[user_row_number].sort_values(ascending=False) \n",
"sorted_user_predictions.head()"
],
"execution_count": 22,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"title\n",
"2001: A Space Odyssey (1968) 5.018342\n",
"Abbott and Costello Meet Frankenstein (1948) 4.587499\n",
"28 Days (2000) 3.117094\n",
"2 Fast 2 Furious (Fast and the Furious 2, The) (2003) 0.546489\n",
"27 Dresses (2008) 0.329421\n",
"Name: 1, dtype: float64"
]
},
"metadata": {
"tags": []
},
"execution_count": 22
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "_SqD8f1Z1xC4",
"colab_type": "text"
},
"source": [
"## By Matrix Factorization\n",
"\n",
"The final algorithmi is called **Matrix Factorization(MF)**\n",
"\n",
"This one solves the issue made by SVD by using Gradient Descent method.\n",
"\n",
"MF uses only existed elements of the matrix, whereby we can ignore the values of zero (not-observed)\n",
"\n",
"![a](https://miro.medium.com/max/1800/1*F5RM9oMnJcWi1oxaEhF0mg.png)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "5EpiJTmPIeKi",
"colab_type": "text"
},
"source": [
"MFではユーザー行列とアイテム行列（movie）の二つの行列で元の行列を近似します。\n",
"\n",
"この学習において勾配法を用います。"
]
},
{
"cell_type": "code",
"metadata": {
"id": "4UYqe9qrzWKR",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 69
},
"outputId": "9d839624-4c13-4084-d01f-ccef4f64f6b2"
},
"source": [
"from scipy.spatial.distance import cosine\n",
"\n",
"user1 = np.array([4, 5, 0, 1, 0])\n",
"user2 = np.array([3, 0, 1, 5, 0])\n",
"user3 = np.array([4, 0, 0, 3, 5])\n",
"print(cosine(user1, user2))\n",
"print(cosine(user2, user3))\n",
"print(cosine(user2, user2))"
],
"execution_count": 25,
"outputs": [
{
"output_type": "stream",
"text": [
"0.5566055486862941\n",
"0.3545765509594274\n",
"0.0\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "_3XXpzYozWQO",
"colab_type": "code",
"colab": {}
},
"source": [
"from tqdm import tqdm_notebook as tqdm\n",
"\n",
"def get_rating_error(r, p, q):\n",
" ########## v{ui} - prediction\n",
" return r - np.dot(p, q)\n",
"\n",
"\n",
"def get_error(R, P, Q, beta):\n",
" error = 0.0\n",
" for i in range(len(R)):\n",
" for j in range(len(R[i])):\n",
" if R[i][j] == 0:\n",
" continue\n",
" error += pow(get_rating_error(R[i][j], P[:,i], Q[:,j]), 2)\n",
" error += beta/2.0 * (np.linalg.norm(P) + np.linalg.norm(Q))\n",
" return error\n",
"\n",
"\n",
"def matrix_factorization(R, K, steps=5000, alpha=0.0002, beta=0.02, threshold=0.001):\n",
" ########## initialize each matrix\n",
" P = np.random.rand(K, len(R))\n",
" Q = np.random.rand(K, len(R[0]))\n",
"\n",
" for step in tqdm(range(steps)):\n",
" for i in range(len(R)):\n",
" for j in range(len(R[i])):\n",
" if R[i][j] == 0:\n",
" continue\n",
" err = get_rating_error(R[i][j], P[:, i], Q[:, j])\n",
"\n",
" ########## update\n",
" for k in range(K):\n",
" delta_p = alpha * (2 * err * Q[k][j])\n",
" delta_q = alpha * (2 * err * P[k][i])\n",
" P[k][i] += delta_p\n",
" Q[k][j] += delta_q\n",
"\n",
" error = get_error(R, P, Q, beta)\n",
" if error < threshold:\n",
" break\n",
" return P, Q"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "Et1SXuZGzWbY",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 121,
"referenced_widgets": [
"9fa04dc5f75043beae49b6e269707d51"
]
},
"outputId": "28945285-3ae2-44ba-ad75-2773e131a1fe"
},
"source": [
"R = np.array([\n",
" [5, 3, 0, 1],\n",
" [4, 0, 0, 1],\n",
" [1, 1, 0, 5],\n",
" [1, 0, 0, 4],\n",
" [0, 1, 5, 4],\n",
" ]\n",
" )\n",
"nP, nQ = matrix_factorization(R, 2)\n",
"nR = np.round(np.dot(nP.T, nQ), decimals=2)\n",
"nR"
],
"execution_count": 48,
"outputs": [
{
"output_type": "display_data",
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "9fa04dc5f75043beae49b6e269707d51",
"version_minor": 0,
"version_major": 2
},
"text/plain": [
"HBox(children=(IntProgress(value=0, max=5000), HTML(value='')))"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "stream",
"text": [
"\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[5.01, 2.98, 3.23, 1. ],\n",
" [3.99, 2.39, 2.79, 1. ],\n",
" [1.04, 0.91, 5.79, 4.99],\n",
" [0.98, 0.81, 4.69, 3.99],\n",
" [1.48, 1.11, 4.96, 4.04]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 48
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "_O6uSGNxP0aG",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "c4bf1233-6a75-4ba3-e804-e45698e2c6d4"
},
"source": [
"tmp.shape"
],
"execution_count": 46,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(258, 100)"
]
},
"metadata": {
"tags": []
},
"execution_count": 46
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "BtiKkH1bzWkb",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 69,
"referenced_widgets": [
"9d350ceeb1f746cdaa2957695e654ff6"
]
},
"outputId": "5dbc7bc0-7e50-4ce4-e092-546da8299721"
},
"source": [
"%%time\n",
"\n",
"nP, nQ = matrix_factorization(tmp.values, K=4, steps=500, alpha=0.002, beta=0.02, threshold=0.01)\n",
"nR = np.round(np.dot(nP.T, nQ), decimals=2)"
],
"execution_count": 49,
"outputs": [
{
"output_type": "display_data",
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "9d350ceeb1f746cdaa2957695e654ff6",
"version_minor": 0,
"version_major": 2
},
"text/plain": [
"HBox(children=(IntProgress(value=0, max=500), HTML(value='')))"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "stream",
"text": [
"\n",
"CPU times: user 27.6 s, sys: 1.5 s, total: 29.1 s\n",
"Wall time: 27.2 s\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "cwJILysoQkP9",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "a2260103-0b3a-4cc5-b80f-875347ce3f6e"
},
"source": [
"print(nP.shape, nQ.shape)"
],
"execution_count": 51,
"outputs": [
{
"output_type": "stream",
"text": [
"(4, 258) (4, 100)\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "b6KtR9LNQlk6",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 446
},
"outputId": "0f73feca-6b6b-4d7c-d301-4d1780cd2694"
},
"source": [
"pd.DataFrame(nR, columns = pivot_table.columns[:100]).head()"
],
"execution_count": 52,
"outputs": [
{
"output_type": "execute_result",
"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>title</th>\n",
" <th>'Til There Was You (1997)</th>\n",
" <th>'burbs, The (1989)</th>\n",
" <th>'night Mother (1986)</th>\n",
" <th>(500) Days of Summer (2009)</th>\n",
" <th>*batteries not included (1987)</th>\n",
" <th>...And Justice for All (1979)</th>\n",
" <th>10 Things I Hate About You (1999)</th>\n",
" <th>10,000 BC (2008)</th>\n",
" <th>100 Girls (2000)</th>\n",
" <th>101 Dalmatians (1996)</th>\n",
" <th>101 Dalmatians (One Hundred and One Dalmatians) (1961)</th>\n",
" <th>102 Dalmatians (2000)</th>\n",
" <th>11:14 (2003)</th>\n",
" <th>11th Hour, The (2007)</th>\n",
" <th>12 Angry Men (1957)</th>\n",
" <th>12 Years a Slave (2013)</th>\n",
" <th>127 Hours (2010)</th>\n",
" <th>13 Assassins (Jûsan-nin no shikaku) (2010)</th>\n",
" <th>13 Ghosts (1960)</th>\n",
" <th>13 Going on 30 (2004)</th>\n",
" <th>13th Warrior, The (1999)</th>\n",
" <th>14 Blades (Jin yi wei) (2010)</th>\n",
" <th>1408 (2007)</th>\n",
" <th>15 Minutes (2001)</th>\n",
" <th>16 Blocks (2006)</th>\n",
" <th>17 Again (2009)</th>\n",
" <th>18 Again! (1988)</th>\n",
" <th>187 (One Eight Seven) (1997)</th>\n",
" <th>1941 (1979)</th>\n",
" <th>1984 (Nineteen Eighty-Four) (1984)</th>\n",
" <th>2 Days in the Valley (1996)</th>\n",
" <th>2 Fast 2 Furious (Fast and the Furious 2, The) (2003)</th>\n",
" <th>2 ou 3 choses que je sais d'elle (2 or 3 Things I Know About Her) (1967)</th>\n",
" <th>20 Dates (1998)</th>\n",
" <th>20 Feet from Stardom (Twenty Feet from Stardom) (2013)</th>\n",
" <th>20,000 Leagues Under the Sea (1954)</th>\n",
" <th>200 Cigarettes (1999)</th>\n",
" <th>2001: A Space Odyssey (1968)</th>\n",
" <th>2010: The Year We Make Contact (1984)</th>\n",
" <th>2012 (2009)</th>\n",
" <th>...</th>\n",
" <th>300 (2007)</th>\n",
" <th>3000 Miles to Graceland (2001)</th>\n",
" <th>300: Rise of an Empire (2014)</th>\n",
" <th>35 Up (1991)</th>\n",
" <th>39 Steps, The (1935)</th>\n",
" <th>3:10 to Yuma (2007)</th>\n",
" <th>4 Months, 3 Weeks and 2 Days (4 luni, 3 saptamâni si 2 zile) (2007)</th>\n",
" <th>40 Days and 40 Nights (2002)</th>\n",
" <th>40-Year-Old Virgin, The (2005)</th>\n",
" <th>400 Blows, The (Les quatre cents coups) (1959)</th>\n",
" <th>42 Up (1998)</th>\n",
" <th>47 Samurai (Chûshingura) (Loyal 47 Ronin, The) (1962)</th>\n",
" <th>48 Hrs. (1982)</th>\n",
" <th>49 Up (2005)</th>\n",
" <th>50 First Dates (2004)</th>\n",
" <th>50/50 (2011)</th>\n",
" <th>52 Pick-Up (1986)</th>\n",
" <th>54 (1998)</th>\n",
" <th>56 Up (2012)</th>\n",
" <th>5th Musketeer, The (a.k.a. Fifth Musketeer, The) (1979)</th>\n",
" <th>6th Day, The (2000)</th>\n",
" <th>6th Man, The (Sixth Man, The) (1997)</th>\n",
" <th>7th Voyage of Sinbad, The (1958)</th>\n",
" <th>8 1/2 (8½) (1963)</th>\n",
" <th>8 Heads in a Duffel Bag (1997)</th>\n",
" <th>8 Mile (2002)</th>\n",
" <th>8 Seconds (1994)</th>\n",
" <th>8 Women (2002)</th>\n",
" <th>84 Charing Cross Road (1987)</th>\n",
" <th>8MM (1999)</th>\n",
" <th>9 1/2 Weeks (Nine 1/2 Weeks) (1986)</th>\n",
" <th>9 Songs (2004)</th>\n",
" <th>9/11 (2002)</th>\n",
" <th>A-Team, The (2010)</th>\n",
" <th>A.I. Artificial Intelligence (2001)</th>\n",
" <th>AVP: Alien vs. Predator (2004)</th>\n",
" <th>AVPR: Aliens vs. Predator - Requiem (2007)</th>\n",
" <th>Abandoned, The (2006)</th>\n",
" <th>Abbott and Costello Meet Frankenstein (1948)</th>\n",
" <th>Abominable Dr. Phibes, The (1971)</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1.65</td>\n",
" <td>3.13</td>\n",
" <td>2.96</td>\n",
" <td>1.82</td>\n",
" <td>2.98</td>\n",
" <td>3.75</td>\n",
" <td>2.57</td>\n",
" <td>2.47</td>\n",
" <td>3.01</td>\n",
" <td>2.44</td>\n",
" <td>1.74</td>\n",
" <td>1.98</td>\n",
" <td>3.32</td>\n",
" <td>2.83</td>\n",
" <td>3.73</td>\n",
" <td>3.98</td>\n",
" <td>3.59</td>\n",
" <td>2.70</td>\n",
" <td>2.72</td>\n",
" <td>2.97</td>\n",
" <td>2.29</td>\n",
" <td>2.33</td>\n",
" <td>2.17</td>\n",
" <td>3.70</td>\n",
" <td>1.49</td>\n",
" <td>0.34</td>\n",
" <td>2.34</td>\n",
" <td>3.42</td>\n",
" <td>2.68</td>\n",
" <td>3.35</td>\n",
" <td>2.76</td>\n",
" <td>2.39</td>\n",
" <td>2.96</td>\n",
" <td>1.30</td>\n",
" <td>2.61</td>\n",
" <td>1.88</td>\n",
" <td>2.00</td>\n",
" <td>3.50</td>\n",
" <td>3.19</td>\n",
" <td>1.36</td>\n",
" <td>...</td>\n",
" <td>1.75</td>\n",
" <td>3.34</td>\n",
" <td>1.78</td>\n",
" <td>3.87</td>\n",
" <td>3.30</td>\n",
" <td>2.82</td>\n",
" <td>3.19</td>\n",
" <td>2.19</td>\n",
" <td>3.89</td>\n",
" <td>3.10</td>\n",
" <td>2.86</td>\n",
" <td>1.50</td>\n",
" <td>2.21</td>\n",
" <td>3.21</td>\n",
" <td>2.62</td>\n",
" <td>3.99</td>\n",
" <td>2.38</td>\n",
" <td>2.41</td>\n",
" <td>3.09</td>\n",
" <td>2.77</td>\n",
" <td>2.49</td>\n",
" <td>2.96</td>\n",
" <td>3.95</td>\n",
" <td>1.24</td>\n",
" <td>3.46</td>\n",
" <td>2.85</td>\n",
" <td>2.47</td>\n",
" <td>2.77</td>\n",
" <td>2.71</td>\n",
" <td>3.63</td>\n",
" <td>2.35</td>\n",
" <td>2.69</td>\n",
" <td>1.89</td>\n",
" <td>3.75</td>\n",
" <td>2.78</td>\n",
" <td>1.94</td>\n",
" <td>2.96</td>\n",
" <td>1.82</td>\n",
" <td>1.94</td>\n",
" <td>2.52</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1.77</td>\n",
" <td>2.61</td>\n",
" <td>4.00</td>\n",
" <td>5.32</td>\n",
" <td>3.59</td>\n",
" <td>2.98</td>\n",
" <td>3.75</td>\n",
" <td>2.84</td>\n",
" <td>2.43</td>\n",
" <td>2.45</td>\n",
" <td>2.61</td>\n",
" <td>2.25</td>\n",
" <td>4.58</td>\n",
" <td>2.49</td>\n",
" <td>4.02</td>\n",
" <td>3.41</td>\n",
" <td>2.12</td>\n",
" <td>3.47</td>\n",
" <td>3.57</td>\n",
" <td>1.69</td>\n",
" <td>2.58</td>\n",
" <td>3.25</td>\n",
" <td>2.18</td>\n",
" <td>1.20</td>\n",
" <td>1.58</td>\n",
" <td>0.81</td>\n",
" <td>2.42</td>\n",
" <td>2.73</td>\n",
" <td>2.87</td>\n",
" <td>4.23</td>\n",
" <td>3.24</td>\n",
" <td>0.93</td>\n",
" <td>3.45</td>\n",
" <td>2.44</td>\n",
" <td>3.63</td>\n",
" <td>3.32</td>\n",
" <td>2.72</td>\n",
" <td>5.01</td>\n",
" <td>3.00</td>\n",
" <td>1.40</td>\n",
" <td>...</td>\n",
" <td>4.73</td>\n",
" <td>3.19</td>\n",
" <td>3.31</td>\n",
" <td>3.38</td>\n",
" <td>5.14</td>\n",
" <td>5.32</td>\n",
" <td>2.57</td>\n",
" <td>3.33</td>\n",
" <td>2.37</td>\n",
" <td>3.72</td>\n",
" <td>4.38</td>\n",
" <td>3.07</td>\n",
" <td>3.94</td>\n",
" <td>2.90</td>\n",
" <td>3.64</td>\n",
" <td>4.40</td>\n",
" <td>1.11</td>\n",
" <td>2.24</td>\n",
" <td>3.31</td>\n",
" <td>3.59</td>\n",
" <td>3.99</td>\n",
" <td>3.54</td>\n",
" <td>3.02</td>\n",
" <td>5.15</td>\n",
" <td>3.46</td>\n",
" <td>3.44</td>\n",
" <td>2.70</td>\n",
" <td>2.94</td>\n",
" <td>2.80</td>\n",
" <td>2.49</td>\n",
" <td>2.68</td>\n",
" <td>3.56</td>\n",
" <td>3.59</td>\n",
" <td>4.47</td>\n",
" <td>2.87</td>\n",
" <td>3.49</td>\n",
" <td>3.45</td>\n",
" <td>1.62</td>\n",
" <td>4.90</td>\n",
" <td>3.33</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>2.57</td>\n",
" <td>3.48</td>\n",
" <td>5.24</td>\n",
" <td>4.88</td>\n",
" <td>4.13</td>\n",
" <td>4.34</td>\n",
" <td>4.19</td>\n",
" <td>3.58</td>\n",
" <td>3.51</td>\n",
" <td>3.44</td>\n",
" <td>3.81</td>\n",
" <td>3.10</td>\n",
" <td>5.01</td>\n",
" <td>3.08</td>\n",
" <td>5.23</td>\n",
" <td>4.90</td>\n",
" <td>3.74</td>\n",
" <td>3.95</td>\n",
" <td>4.15</td>\n",
" <td>2.91</td>\n",
" <td>4.02</td>\n",
" <td>3.77</td>\n",
" <td>2.38</td>\n",
" <td>3.17</td>\n",
" <td>1.26</td>\n",
" <td>0.69</td>\n",
" <td>3.06</td>\n",
" <td>3.80</td>\n",
" <td>3.64</td>\n",
" <td>5.01</td>\n",
" <td>4.26</td>\n",
" <td>1.58</td>\n",
" <td>4.05</td>\n",
" <td>2.77</td>\n",
" <td>4.33</td>\n",
" <td>3.37</td>\n",
" <td>2.97</td>\n",
" <td>5.03</td>\n",
" <td>3.97</td>\n",
" <td>1.59</td>\n",
" <td>...</td>\n",
" <td>4.54</td>\n",
" <td>4.05</td>\n",
" <td>3.52</td>\n",
" <td>4.70</td>\n",
" <td>5.46</td>\n",
" <td>5.26</td>\n",
" <td>3.61</td>\n",
" <td>3.48</td>\n",
" <td>3.81</td>\n",
" <td>4.68</td>\n",
" <td>4.45</td>\n",
" <td>2.92</td>\n",
" <td>4.03</td>\n",
" <td>3.95</td>\n",
" <td>3.84</td>\n",
" <td>5.70</td>\n",
" <td>2.32</td>\n",
" <td>3.14</td>\n",
" <td>4.22</td>\n",
" <td>4.29</td>\n",
" <td>3.87</td>\n",
" <td>4.03</td>\n",
" <td>4.31</td>\n",
" <td>3.94</td>\n",
" <td>4.27</td>\n",
" <td>4.14</td>\n",
" <td>3.44</td>\n",
" <td>3.77</td>\n",
" <td>3.51</td>\n",
" <td>3.98</td>\n",
" <td>3.50</td>\n",
" <td>4.02</td>\n",
" <td>3.67</td>\n",
" <td>5.44</td>\n",
" <td>3.81</td>\n",
" <td>2.64</td>\n",
" <td>4.12</td>\n",
" <td>2.14</td>\n",
" <td>4.64</td>\n",
" <td>3.65</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.98</td>\n",
" <td>1.49</td>\n",
" <td>1.86</td>\n",
" <td>1.34</td>\n",
" <td>1.56</td>\n",
" <td>1.86</td>\n",
" <td>1.49</td>\n",
" <td>1.62</td>\n",
" <td>1.56</td>\n",
" <td>1.58</td>\n",
" <td>1.30</td>\n",
" <td>1.26</td>\n",
" <td>1.91</td>\n",
" <td>1.41</td>\n",
" <td>1.80</td>\n",
" <td>2.13</td>\n",
" <td>1.39</td>\n",
" <td>1.22</td>\n",
" <td>1.32</td>\n",
" <td>1.54</td>\n",
" <td>1.62</td>\n",
" <td>1.13</td>\n",
" <td>1.19</td>\n",
" <td>1.61</td>\n",
" <td>0.25</td>\n",
" <td>0.21</td>\n",
" <td>1.33</td>\n",
" <td>1.84</td>\n",
" <td>1.35</td>\n",
" <td>2.02</td>\n",
" <td>1.79</td>\n",
" <td>0.80</td>\n",
" <td>1.48</td>\n",
" <td>0.90</td>\n",
" <td>1.51</td>\n",
" <td>1.50</td>\n",
" <td>0.96</td>\n",
" <td>2.19</td>\n",
" <td>1.51</td>\n",
" <td>0.61</td>\n",
" <td>...</td>\n",
" <td>1.65</td>\n",
" <td>1.53</td>\n",
" <td>1.16</td>\n",
" <td>1.91</td>\n",
" <td>1.82</td>\n",
" <td>1.84</td>\n",
" <td>1.37</td>\n",
" <td>1.20</td>\n",
" <td>1.64</td>\n",
" <td>1.75</td>\n",
" <td>1.56</td>\n",
" <td>0.93</td>\n",
" <td>1.32</td>\n",
" <td>1.46</td>\n",
" <td>1.45</td>\n",
" <td>2.13</td>\n",
" <td>1.10</td>\n",
" <td>1.60</td>\n",
" <td>1.57</td>\n",
" <td>1.40</td>\n",
" <td>1.49</td>\n",
" <td>1.44</td>\n",
" <td>1.79</td>\n",
" <td>1.17</td>\n",
" <td>1.84</td>\n",
" <td>1.51</td>\n",
" <td>1.39</td>\n",
" <td>1.59</td>\n",
" <td>1.46</td>\n",
" <td>1.64</td>\n",
" <td>1.27</td>\n",
" <td>1.62</td>\n",
" <td>1.27</td>\n",
" <td>2.26</td>\n",
" <td>1.71</td>\n",
" <td>0.90</td>\n",
" <td>1.64</td>\n",
" <td>0.98</td>\n",
" <td>1.42</td>\n",
" <td>1.27</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1.28</td>\n",
" <td>1.86</td>\n",
" <td>2.30</td>\n",
" <td>1.00</td>\n",
" <td>1.73</td>\n",
" <td>2.43</td>\n",
" <td>1.58</td>\n",
" <td>1.62</td>\n",
" <td>1.94</td>\n",
" <td>1.72</td>\n",
" <td>1.73</td>\n",
" <td>1.48</td>\n",
" <td>1.89</td>\n",
" <td>1.55</td>\n",
" <td>2.50</td>\n",
" <td>2.65</td>\n",
" <td>2.45</td>\n",
" <td>1.61</td>\n",
" <td>1.70</td>\n",
" <td>1.91</td>\n",
" <td>2.04</td>\n",
" <td>1.51</td>\n",
" <td>1.04</td>\n",
" <td>2.58</td>\n",
" <td>0.42</td>\n",
" <td>0.13</td>\n",
" <td>1.45</td>\n",
" <td>2.09</td>\n",
" <td>1.71</td>\n",
" <td>2.10</td>\n",
" <td>1.96</td>\n",
" <td>1.24</td>\n",
" <td>1.75</td>\n",
" <td>0.96</td>\n",
" <td>1.76</td>\n",
" <td>1.04</td>\n",
" <td>1.13</td>\n",
" <td>1.70</td>\n",
" <td>2.01</td>\n",
" <td>0.71</td>\n",
" <td>...</td>\n",
" <td>1.05</td>\n",
" <td>2.01</td>\n",
" <td>1.14</td>\n",
" <td>2.50</td>\n",
" <td>1.91</td>\n",
" <td>1.53</td>\n",
" <td>2.00</td>\n",
" <td>1.20</td>\n",
" <td>2.43</td>\n",
" <td>2.09</td>\n",
" <td>1.49</td>\n",
" <td>0.77</td>\n",
" <td>1.26</td>\n",
" <td>2.06</td>\n",
" <td>1.40</td>\n",
" <td>2.68</td>\n",
" <td>1.67</td>\n",
" <td>1.62</td>\n",
" <td>1.99</td>\n",
" <td>1.80</td>\n",
" <td>1.18</td>\n",
" <td>1.69</td>\n",
" <td>2.45</td>\n",
" <td>0.25</td>\n",
" <td>2.03</td>\n",
" <td>1.80</td>\n",
" <td>1.60</td>\n",
" <td>1.78</td>\n",
" <td>1.66</td>\n",
" <td>2.42</td>\n",
" <td>1.64</td>\n",
" <td>1.59</td>\n",
" <td>1.11</td>\n",
" <td>2.37</td>\n",
" <td>1.85</td>\n",
" <td>0.44</td>\n",
" <td>1.80</td>\n",
" <td>1.10</td>\n",
" <td>1.09</td>\n",
" <td>1.42</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 100 columns</p>\n",
"</div>"
],
"text/plain": [
"title 'Til There Was You (1997) ... Abominable Dr. Phibes, The (1971)\n",
"0 1.65 ... 2.52\n",
"1 1.77 ... 3.33\n",
"2 2.57 ... 3.65\n",
"3 0.98 ... 1.27\n",
"4 1.28 ... 1.42\n",
"\n",
"[5 rows x 100 columns]"
]
},
"metadata": {
"tags": []
},
"execution_count": 52
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "9EqKq8Lrnu8K",
"colab_type": "text"
},
"source": [
"## Reference\n",
"\n",
"- https://www.kaggle.com/kanncaa1/recommendation-systems-tutorial/data\n",
"- https://heartbeat.fritz.ai/recommender-systems-with-python-part-iii-collaborative-filtering-singular-value-decomposition-5b5dcb3f242b\n",
"- http://nicolas-hug.com/blog/matrix_facto_2\n",
"- https://qiita.com/ysekky/items/c81ff24da0390a74fc6c\n",
"- https://www.cs.cmu.edu/~mgormley/courses/10601-s17/slides/lecture25-mf.pdf"
]
}
]
}
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