{"cells": [{"cell_type": "markdown", "metadata": {}, "source": ["# R\u00e9duction des dimensions\n", "\n", "On peut souhaiter r\u00e9duire de nombre de dimensions d'un jeu de donn\u00e9es :\n", "\n", "- pour le compresser : diminution le volume d'informations utiles \u00e0 stocker et par la m\u00eame occasion la dur\u00e9e d'ex\u00e9cution d'un algorithme d'apprentisssage (car l'espace \u00e0 explorer est plus petit)\n", "- pour n'en conserver que les caract\u00e9ristiques (features) discriminantes et \u00e9viter ainsi le surapprentissage (apprentissage du bruit dans les donn\u00e9es)"]}, {"cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [{"data": {"text/html": ["
\n", ""], "text/plain": [""]}, "execution_count": 2, "metadata": {}, "output_type": "execute_result"}], "source": ["from jyquickhelper import add_notebook_menu\n", "add_notebook_menu()"]}, {"cell_type": "code", "execution_count": 2, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:21.749414Z", "start_time": "2017-10-22T18:15:20.532846Z"}}, "outputs": [], "source": ["%matplotlib inline\n", "\n", "import matplotlib.pyplot as plt # tra\u00e7age de graphiques\n", "import numpy as np # traitement des arrays num\u00e9riques\n", "import pandas as pd\n", "\n", "from sklearn import datasets # datasets classiques\n", "from sklearn import preprocessing # normalisation les donn\u00e9es\n", "from sklearn import decomposition # PCA et NMF\n", "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis # LDA\n", "\n", "np.random.seed = 2017 # pour des r\u00e9sultats reproductibles"]}, {"cell_type": "markdown", "metadata": {}, "source": ["# 1. PCA - L'analyse en composante principale"]}, {"cell_type": "markdown", "metadata": {}, "source": ["## 1.1 Algorithme\n", "**L'analyse en composante principale pour des donn\u00e9es num\u00e9riques en n dimensions est un algorithme non supervis\u00e9 d'identification des dimensions de variance d\u00e9croissante et de changement de base pour ne conserver que les k dimensions de plus grande variance.**\n", "\n", "Il consiste \u00e0 :\n", "\n", "0. *Optionnel : Normaliser les donn\u00e9es (important si les donn\u00e9es n'ont par exemple pas \u00e9t\u00e9 mesur\u00e9es aux m\u00eames \u00e9chelles)*\n", "0. Construire la matrice de covariance entre les variables :\n", "$\\Sigma = \\frac{1}{n-1}\\sum_{i=1}^{n}{((X - \\bar{x})'(X - \\bar{x}))}$\n", "0. Trouver les valeurs propres $\\lambda_i$ et vecteurs propres $v_i$ :\n", "$\\Sigma v_i = \\lambda_iv_i$, ces vecteurs propres forment un rep\u00e8re orthogonal de l'espace des donn\u00e9es (en tant que vecteurs propres d'une matrice symm\u00e9trique qu'on supposera de rang n)\n", "0. Classer les valeurs propres (et les vecteurs associ\u00e9s) de fa\u00e7on d\u00e9croissante : $\\{\\lambda_{(n)}, \\lambda_{(n-1)}...\\lambda_{(1)} \\}$ o\u00f9 $\\lambda_{(i)}$ est la i-\u00e8me variance dans l'ordre croissant\n", "0. Ne conserver que les k ($k \\leqslant n$) premiers vecteurs : $\\{v_{(n)}, v_{(n-1)}...v_{(n-k+1)} \\}$\n", "0. Construire la matrice de projection dans l'espace de ces vecteurs (changement de base si n=k)\n", "0. Projeter les donn\u00e9es initiales dans cet espace de dimension *k*\n", "\n", "Tout cela peut bien sur \u00eatre impl\u00e9ment\u00e9 from scratch avec Numpy mais nous utiliserons ici scikit-learn pour raccourcir l'impl\u00e9mentation et nous concentrer sur la visualisation des r\u00e9sultats.\n", "Cf. https://fr.wikipedia.org/wiki/Analyse_en_composantes_principales et http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html"]}, {"cell_type": "markdown", "metadata": {}, "source": ["## 1.2 Impl\u00e9mentation avec scikit-learn\n", "### 1.2.1 Donn\u00e9es\n", "Nous partirons classiquement du dataset Iris (classification de 3 fleurs sur la base de certaines de leurs mesures) :"]}, {"cell_type": "code", "execution_count": 3, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:21.765450Z", "start_time": "2017-10-22T18:15:21.749414Z"}}, "outputs": [], "source": ["iris = datasets.load_iris()\n", "X_iris = iris.data\n", "y_iris = iris.target"]}, {"cell_type": "code", "execution_count": 4, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:22.170018Z", "start_time": "2017-10-22T18:15:21.769427Z"}}, "outputs": [{"name": "stdout", "output_type": "stream", "text": ["Dimensions de l'espace de d\u00e9part : 4\n", "Repr\u00e9sentation des donn\u00e9es dans ces dimensions :\n"]}, {"data": {"image/png": 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CUgzw7I0vU7i6qBUiMsY0FVVdtn70V1WLcevP11zG6mjgJXV9D+TGE2pjTBXq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\nb3UW7VUpz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"text/plain": [""]}, "metadata": {}, "output_type": "display_data"}], "source": ["print(\"Dimensions de l'espace de d\u00e9part : {}\".format(X_iris.shape[1]))\n", "print(\"Repr\u00e9sentation des donn\u00e9es dans ces dimensions :\")\n", "\n", "plt.figure(figsize=(12,4))\n", "plt.subplot(1, 2, 1)\n", "plt.title(\"Dimensions 0 et 1:\")\n", "plt.scatter(X_iris[:, 0], X_iris[:, 1], c=y_iris)\n", "plt.subplot(1, 2, 2)\n", "plt.title(\"Dimensions 2 et 3:\")\n", "plt.scatter(X_iris[:, 2], X_iris[:, 3], c=y_iris)\n", "plt.plot([1,7],[0.05,2.5])\n", "plt.show()"]}, {"cell_type": "markdown", "metadata": {}, "source": ["### 1.2.2 Premier exemple de PCA\n", "Graphiquement, on peut se dire que les 2 derni\u00e8res dimensions sont tr\u00e8s corr\u00e9l\u00e9es et donc redondantes. Dans un strict but de classification, on pourrait d'ailleurs presque se contenter de la dimension indiqu\u00e9e par la ligne bleue pour correctement discriminer les 3 types de fleurs (*nous verrons par la suite qu'il s'agit d'un cas particulier non g\u00e9n\u00e9ralisable*).\n", "\n", "Effectuons une PCA avec scikit-learn avec un changemment de base conservant les 4 dimensions pour illustrer leurs diff\u00e9rences :"]}, {"cell_type": "code", "execution_count": 5, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:22.181527Z", "start_time": "2017-10-22T18:15:22.172527Z"}}, "outputs": [], "source": ["# Gardons toutes les composantes pour le moment\n", "# Nous pourrons toujours en retirer ensuite puisqu'elles seront tri\u00e9es par significativit\u00e9\n", "pca = decomposition.PCA(n_components=4)\n", "\n", "X_iris_PCA = pca.fit(X_iris).transform(X_iris) "]}, {"cell_type": "code", "execution_count": 6, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:22.818817Z", "start_time": "2017-10-22T18:15:22.185025Z"}}, "outputs": [{"data": {"image/png": 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tuB/dOtZ5FR1FtOqVNtu/McYYY4zpWMkUDktV9Q1V3aqq22tf7R7ZbqBL9zyu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"text/plain": [""]}, "metadata": {}, "output_type": "display_data"}], "source": ["def graph_acp2(X_PC2, y):\n", " plt.figure(figsize=(15,4))\n", " plt.subplot(1, 3, 1)\n", " plt.xlabel('Principal Component 1')\n", " plt.ylabel('Principal Component 2')\n", " plt.scatter(X_PC2[:, 0], X_PC2[:, 1], c=y)\n", " plt.subplot(1, 3, 2)\n", " plt.title(\"Dimension de la plus grande variance :\")\n", " plt.scatter(X_PC2[:, 0], np.ones(X_PC2.shape[0]), c=y)\n", " plt.subplot(1, 3, 3)\n", " plt.title(\"Dimension de 2nde variance :\")\n", " plt.scatter(X_PC2[:, 1], np.ones(X_PC2.shape[0]), c=y)\n", " plt.show()\n", "\n", "graph_acp2(X_iris_PCA, y_iris)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["## 1.3 Quelques r\u00e9serves\n", "Comme \u00e9voqu\u00e9 dans la pr\u00e9sentation, il est \u00e0 noter qu'il s'agit d'un **algorithme non supervis\u00e9**, qui ne tient donc pas compte des \u00e9tiquettes des donn\u00e9es.\n", "Dans le cas ci-dessus, nous avons eu la chance que les donn\u00e9es soient lin\u00e9airement s\u00e9parables sur la dimension de plus grande variance. Dans le cas contraire, l'ACP aurait pu ne pas nous aider et nous aurions m\u00eame pu perdre les dimensions selon lesquelles discriminer les donn\u00e9es correctement.\n", "\n", "A noter \u00e9galement que dans le cas de donn\u00e9es de variance assez homog\u00e8ne selon toutes les dimensions, une ACP ne nous apporte rien.\n", "\n", "**L'ACP peut donc \u00eatre inutile voire contreproductive dans un objectif de classification.**\n", "\n", "Ci-apr\u00e8s 2 contre-exemples :"]}, {"cell_type": "markdown", "metadata": {}, "source": ["### 1.3.1 ACP et discrimination selon dimension de moindre variance"]}, {"cell_type": "code", "execution_count": 7, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:22.843738Z", "start_time": "2017-10-22T18:15:22.818817Z"}}, "outputs": [], "source": ["X11 = np.random.rand(30)*10\n", "X21 = X11 + 1\n", "X12 = np.random.rand(20)*10\n", "X22 = X12 + 2\n", "X = np.array([np.concatenate((X11,X12)),\n", " np.concatenate((X21,X22))]).T\n", "y = np.concatenate((np.zeros(30), np.ones(20)))\n", "X = preprocessing.scale(X, with_mean=True, with_std=True)"]}, {"cell_type": "code", "execution_count": 8, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:23.069777Z", "start_time": "2017-10-22T18:15:22.847739Z"}}, "outputs": [{"data": {"image/png": 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/oWTUwBGpby6P1TfQe6BGAIl0RCoEklHfufobhMuKm2wrLi3m0G8eSEWv8jxl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\nAElFTkSuQmCC\n", "text/plain": [""]}, "metadata": {}, "output_type": "display_data"}], "source": ["plt.scatter(X[:, 0], X[:, 1], c=y)\n", "plt.show()"]}, {"cell_type": "code", "execution_count": 9, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:23.532892Z", "start_time": "2017-10-22T18:15:23.073294Z"}}, "outputs": [{"data": {"image/png": 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J3yVJNgHOj4il3R2jmZmZmZnZlqhkolhgX0nnARPT9gIiIrbd2IVHxI3Aje3K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\n4/bn7ZkWBQAAAABJRU5ErkJggg==\n", "text/plain": [""]}, "metadata": {}, "output_type": "display_data"}], "source": ["pca = decomposition.PCA(n_components=2)\n", "X_PC2 = pca.fit(X).transform(X)\n", "graph_acp2(X_PC2, y)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Ici une ACP ne retenant que la dimension de plus grande variance nous aurait donc fait perdre toute possibilit\u00e9 de discrimination."]}, {"cell_type": "markdown", "metadata": {}, "source": ["### 1.3.2 ACP sur des donn\u00e9es de variance homog\u00e8ne"]}, {"cell_type": "code", "execution_count": 10, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:23.554901Z", "start_time": "2017-10-22T18:15:23.535895Z"}}, "outputs": [], "source": ["X11 = np.random.normal(0, 10, 500)\n", "X21 = abs(np.random.normal(0, 10, 500))\n", "X12 = np.random.normal(0, 10, 500)\n", "X22 = -abs(np.random.normal(0, 10, 500))\n", "X = np.array([np.concatenate((X11,X12)),\n", " np.concatenate((X21,X22))]).T\n", "y = np.concatenate((np.zeros(500), np.ones(500)))\n", "y = y.astype(int)"]}, {"cell_type": "code", "execution_count": 11, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:23.849958Z", "start_time": "2017-10-22T18:15:23.558895Z"}}, "outputs": [{"data": {"image/png": 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NEPHkFCWV5DHsFBMOh4PJHWe5ZMaYIy3YA0N44B+IRqt2Cx9pDTqKVStC0J3H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\n4VssFssswTp8i8VimSX8f/MFPFQnu78lAAAAAElFTkSuQmCC\n", "text/plain": [""]}, "metadata": {}, "output_type": "display_data"}], "source": ["plt.figure(figsize=(6,6))\n", "plt.scatter(X[:, 0], X[:, 1], c=y)\n", "plt.show()"]}, {"cell_type": "code", "execution_count": 12, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:23.862943Z", "start_time": "2017-10-22T18:15:23.852943Z"}}, "outputs": [], "source": ["pca = decomposition.PCA(n_components=2)\n", "pca.fit(X)\n", "X_PC2 = pca.transform(X)"]}, {"cell_type": "code", "execution_count": 13, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:24.542475Z", "start_time": "2017-10-22T18:15:23.866944Z"}}, "outputs": [{"data": {"image/png": 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R0HrIkNuQ4MhCh2aMMcYYY0wG6wNoTCdp4jOovgy0FrQeiEHyc7RqIu4HXGOMMcYYY3oX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u55u1/EUa7szGz6txnMyrlrjkl8TreDjte3p1ylJBbP+KvwA4pABOZO+ROAzrdckFcU/dAOgdG1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\nahJdmwAAAABJRU5ErkJggg==\n", "text/plain": [""]}, "metadata": {}, "output_type": "display_data"}], "source": ["graph_acp2(X_PC2, y) "]}, {"cell_type": "markdown", "metadata": {}, "source": ["Ici une ACP est inutile car la variance des donn\u00e9es est homog\u00e8ne selon les dimensions initiales (cf. orientation diagonale entre les 2 classes)."]}, {"cell_type": "markdown", "metadata": {}, "source": ["# 2. Autres m\u00e9thodes\n", "D'autres m\u00e9thodes, que nous d\u00e9taillerons moins pour le moment, peuvent \u00eatre plus pertinentes que l'ACP dans certains contextes :"]}, {"cell_type": "markdown", "metadata": {}, "source": ["## 2.1 L'[analyse discriminante lin\u00e9aire ou quadratique](http://scikit-learn.org/stable/modules/lda_qda.html) (LDA/QDA)\n", "Plut\u00f4t que de maximiser la variance sur des dimensions des donn\u00e9es, on va ici chercher \u00e0 maximiser la variance inter-classes par rapport \u00e0 celle intra classe. Cette m\u00e9thode transformera donc l'espace d'origine en un espace plus adapt\u00e9 que l'ACP dans un objectif de classification."]}, {"cell_type": "code", "execution_count": 14, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:25.605113Z", "start_time": "2017-10-22T18:15:24.545473Z"}}, "outputs": [{"name": "stdout", "output_type": "stream", "text": ["Rappel des composantes identifi\u00e9es par le PCA :\n"]}, {"data": {"image/png": 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tuB/dOtZ5FR1FtOqVNtu/McYYY4zpWMkUDktV9Q1V3aqq22tf7R7ZbqBL9zyu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"text/plain": [""]}, "metadata": {}, "output_type": "display_data"}, {"name": "stdout", "output_type": "stream", "text": ["Composantes identifi\u00e9es par le LDA (on remarque une meilleure s\u00e9paration des classes sur la 1\u00e8re composante) :\n"]}, {"data": {"image/png": 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MdBRa+w7xDacRX3cY8fLr0djqzZn+PUHyk+yV586u2QLeUpLOxile8HRrWVnG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"text/plain": [""]}, "metadata": {}, "output_type": "display_data"}], "source": ["lda = LinearDiscriminantAnalysis(n_components=2)\n", "X_iris_LDA = lda.fit(X_iris, y_iris).transform(X_iris)\n", "\n", "print(\"Rappel des composantes identifi\u00e9es par le PCA :\")\n", "graph_acp2(X_iris_PCA, y_iris) \n", "print(\"Composantes identifi\u00e9es par le LDA (on remarque une meilleure s\u00e9paration des classes sur la 1\u00e8re composante) :\")\n", "graph_acp2(X_iris_LDA, y_iris) "]}, {"cell_type": "markdown", "metadata": {}, "source": ["# 2.1La [factorisation de matrices](http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.NMF.html)\n", "On va ici chercher \u00e0 approcher une matrice **V de dimensions m\\*n**, de grande taille souvent creuse et positive (e.g. les \u00e9valuations de tous les clients sur tous les produits dans un site marchand), par un **produit d'une matrice W de dimensions m\\*k** (e.g. le profils de tous les clients) **avec une matrice H de dimensions k\\*n** (e.g. les \u00e9valuations moyennes pour ces profils). Nous chercherons ainsi \u00e0 avoir (m\\*k + k\\*n) << m\\*n pour diminuer l'espace de repr\u00e9sentation de nos donn\u00e9es, tout en conservant le maximum d'information.\n", "\n", "$$\n", "\\begin{bmatrix}\n", " v_{11} & v_{12} & v_{13} & \\dots & v_{1n} \\\\\n", " v_{21} & v_{22} & v_{23} & \\dots & v_{2n} \\\\\n", " v_{31} & V_{32} & v_{33} & \\dots & v_{3n} \\\\\n", " \\vdots & \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", " v_{m1} & V_{m2} & v_{m3} & \\dots & v_{mn}\n", "\\end{bmatrix}\n", "=\n", "\\begin{bmatrix}\n", " w_{11} & \\dots & w_{1k} \\\\\n", " w_{21} & \\dots & w_{2k} \\\\\n", " w_{31} & \\dots & w_{3k} \\\\\n", " \\vdots & \\ddots & \\vdots \\\\\n", " w_{m1} & \\dots & w_{mk}\n", "\\end{bmatrix}\n", "*\n", "\\begin{bmatrix}\n", " h_{11} & h_{12} & h_{13} & \\dots & h_{1n} \\\\\n", " \\vdots & \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", " h_{k1} & h_{k2} & h_{k3} & \\dots & h_{kn}\n", "\\end{bmatrix}\n", "$$\n", "\n", "Sans entrer dans les d\u00e9tails, ces algorithmes consisteront \u00e0 trouver W et H qui minimisent $||V - W*H ||_F^2$. Il est \u00e0 noter que la solution minimisant cette norme peut ne pas \u00eatre unique. De plus ces algorithmes sont multiples, souvent de complexit\u00e9 computationnelle \u00e9lev\u00e9e et requi\u00e8rent des r\u00e9gularisations.\n", "\n", "A titre d'exemple construisons une matrice de notations de films par des utilisateurs que nous allons t\u00e2cher de factoriser en une matrice de profils (les go\u00fbts de chaque utilisateurs) et une autre de cat\u00e9gories de films (les profils auxquels ces films sont susceptibles de plaire). Ces notations vont de 1 \u00e0 9 et on d\u00e9signera par 0 l'absence de note. Cet exemple est volontairement simpliste et ne peut pas passer \u00e0 l'\u00e9chelle ni \u00eatre g\u00e9n\u00e9ralis\u00e9 trivialement."]}, {"cell_type": "code", "execution_count": 15, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:25.676638Z", "start_time": "2017-10-22T18:15:25.608116Z"}}, "outputs": [{"data": {"text/html": ["\n", "\n", "
\n", " \n", " \n", " Movies | \n", " Charming prince | \n", " First date | \n", " Lovely love | \n", " Guns are cool | \n", " Ultra badass 4 | \n", " My fist in your face | \n", " Guns & roses | \n", "
\n", " \n", " Users | \n", " | \n", " | \n", " | \n", " | \n", " | \n", " | \n", " | \n", "
\n", " \n", " \n", " \n", " allmoviesrock | \n", " 7 | \n", " 8 | \n", " 0 | \n", " 0 | \n", " 7 | \n", " 8 | \n", " 7 | \n", "
\n", " \n", " big_guns | \n", " 1 | \n", " 2 | \n", " 1 | \n", " 8 | \n", " 9 | \n", " 8 | \n", " 9 | \n", "
\n", " \n", " chuck_norris_fan | \n", " 0 | \n", " 2 | \n", " 0 | \n", " 9 | \n", " 0 | \n", " 9 | \n", " 8 | \n", "
\n", " \n", " easily_pleased | \n", " 0 | \n", " 8 | \n", " 8 | \n", " 0 | \n", " 7 | \n", " 9 | \n", " 7 | \n", "
\n", " \n", " girlygirl | \n", " 9 | \n", " 0 | \n", " 8 | \n", " 1 | \n", " 0 | \n", " 0 | \n", " 7 | \n", "
\n", " \n", " loves_everything | \n", " 9 | \n", " 9 | \n", " 9 | \n", " 9 | \n", " 9 | \n", " 9 | \n", " 0 | \n", "
\n", " \n", " loves_flowers | \n", " 7 | \n", " 8 | \n", " 0 | \n", " 0 | \n", " 0 | \n", " 0 | \n", " 8 | \n", "
\n", " \n", " machoman | \n", " 0 | \n", " 1 | \n", " 0 | \n", " 8 | \n", " 7 | \n", " 9 | \n", " 8 | \n", "
\n", " \n", " more_guns_please | \n", " 0 | \n", " 2 | \n", " 0 | \n", " 9 | \n", " 8 | \n", " 0 | \n", " 7 | \n", "
\n", " \n", " mylittleponey98 | \n", " 7 | \n", " 0 | \n", " 7 | \n", " 0 | \n", " 1 | \n", " 0 | \n", " 8 | \n", "
\n", " \n", " romance_addict | \n", " 9 | \n", " 8 | \n", " 0 | \n", " 0 | \n", " 0 | \n", " 1 | \n", " 0 | \n", "
\n", " \n", " testosterone guy | \n", " 0 | \n", " 0 | \n", " 1 | \n", " 9 | \n", " 9 | \n", " 9 | \n", " 7 | \n", "
\n", " \n", " yeah_guns666 | \n", " 1 | \n", " 0 | \n", " 3 | \n", " 0 | \n", " 9 | \n", " 9 | \n", " 0 | \n", "
\n", " \n", "
\n", "
"], "text/plain": ["Movies Charming prince First date Lovely love Guns are cool \\\n", "Users \n", "allmoviesrock 7 8 0 0 \n", "big_guns 1 2 1 8 \n", "chuck_norris_fan 0 2 0 9 \n", "easily_pleased 0 8 8 0 \n", "girlygirl 9 0 8 1 \n", "loves_everything 9 9 9 9 \n", "loves_flowers 7 8 0 0 \n", "machoman 0 1 0 8 \n", "more_guns_please 0 2 0 9 \n", "mylittleponey98 7 0 7 0 \n", "romance_addict 9 8 0 0 \n", "testosterone guy 0 0 1 9 \n", "yeah_guns666 1 0 3 0 \n", "\n", "Movies Ultra badass 4 My fist in your face Guns & roses \n", "Users \n", "allmoviesrock 7 8 7 \n", "big_guns 9 8 9 \n", "chuck_norris_fan 0 9 8 \n", "easily_pleased 7 9 7 \n", "girlygirl 0 0 7 \n", "loves_everything 9 9 0 \n", "loves_flowers 0 0 8 \n", "machoman 7 9 8 \n", "more_guns_please 8 0 7 \n", "mylittleponey98 1 0 8 \n", "romance_addict 0 1 0 \n", "testosterone guy 9 9 7 \n", "yeah_guns666 9 9 0 "]}, "execution_count": 16, "metadata": {}, "output_type": "execute_result"}], "source": ["df = pd.DataFrame.from_dict({'loves_everything': [9,9,9,9,9,9,0],\n", " 'big_guns': [1,2,1,8,9,8,9],\n", " 'testosterone guy': [0,0,1,9,9,9,7],\n", " 'girlygirl': [9,0,8,1,0,0,7],\n", " 'romance_addict': [9,8,0,0,0,1,0],\n", " 'machoman': [0,1,0,8,7,9,8],\n", " 'loves_flowers': [7,8,0,0,0,0,8],\n", " 'easily_pleased': [0,8,8,0,7,9,7],\n", " 'chuck_norris_fan': [0,2,0,9,0,9,8],\n", " 'mylittleponey98': [7,0,7,0,1,0,8],\n", " 'allmoviesrock': [7,8,0,0,7,8,7],\n", " 'more_guns_please': [0,2,0,9,8,0,7],\n", " 'yeah_guns666': [1,0,3,0,9,9,0]},\n", " ).transpose()\n", "df.index.name = \"Users\"\n", "df.columns = ['Charming prince', 'First date', 'Lovely love', 'Guns are cool', 'Ultra badass 4', 'My fist in your face', 'Guns & roses']\n", "df.columns.name = \"Movies\"\n", "df"]}, {"cell_type": "code", "execution_count": 16, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:25.715652Z", "start_time": "2017-10-22T18:15:25.681638Z"}}, "outputs": [], "source": ["nmf = decomposition.NMF(n_components=2,\n", " random_state=1,\n", " alpha=.1,\n", " l1_ratio=.5).fit(df)"]}, {"cell_type": "code", "execution_count": 17, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:25.736666Z", "start_time": "2017-10-22T18:15:25.718633Z"}}, "outputs": [{"data": {"text/html": ["\n", "\n", "
\n", " \n", " \n", " Categories | \n", " action lover | \n", " romcom lover | \n", "
\n", " \n", " Users | \n", " | \n", " | \n", "
\n", " \n", " \n", " \n", " allmoviesrock | \n", " 1.364464 | \n", " 1.788403 | \n", "
\n", " \n", " big_guns | \n", " 2.542310 | \n", " 0.229329 | \n", "
\n", " \n", " chuck_norris_fan | \n", " 1.945916 | \n", " 0.072006 | \n", "
\n", " \n", " easily_pleased | \n", " 1.649300 | \n", " 1.397724 | \n", "
\n", " \n", " girlygirl | \n", " 0.031053 | \n", " 2.159935 | \n", "
\n", " \n", " loves_everything | \n", " 1.847780 | \n", " 2.263489 | \n", "
\n", " \n", " loves_flowers | \n", " 0.092489 | \n", " 2.079689 | \n", "
\n", " \n", " machoman | \n", " 2.436259 | \n", " 0.000000 | \n", "
\n", " \n", " more_guns_please | \n", " 1.755344 | \n", " 0.047097 | \n", "
\n", " \n", " mylittleponey98 | \n", " 0.168292 | \n", " 1.849657 | \n", "
\n", " \n", " romance_addict | \n", " 0.000000 | \n", " 1.917144 | \n", "
\n", " \n", " testosterone guy | \n", " 2.602998 | \n", " 0.000000 | \n", "
\n", " \n", " yeah_guns666 | \n", " 1.519834 | \n", " 0.074898 | \n", "
\n", " \n", "
\n", "
"], "text/plain": ["Categories action lover romcom lover\n", "Users \n", "allmoviesrock 1.364464 1.788403\n", "big_guns 2.542310 0.229329\n", "chuck_norris_fan 1.945916 0.072006\n", "easily_pleased 1.649300 1.397724\n", "girlygirl 0.031053 2.159935\n", "loves_everything 1.847780 2.263489\n", "loves_flowers 0.092489 2.079689\n", "machoman 2.436259 0.000000\n", "more_guns_please 1.755344 0.047097\n", "mylittleponey98 0.168292 1.849657\n", "romance_addict 0.000000 1.917144\n", "testosterone guy 2.602998 0.000000\n", "yeah_guns666 1.519834 0.074898"]}, "execution_count": 18, "metadata": {}, "output_type": "execute_result"}], "source": ["profiles = pd.DataFrame(nmf.transform(df),\n", " index=df.index,\n", " columns=['action lover', 'romcom lover'])\n", "profiles.columns.name = 'Categories'\n", "profiles"]}, {"cell_type": "code", "execution_count": 18, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:25.763685Z", "start_time": "2017-10-22T18:15:25.740652Z"}}, "outputs": [{"data": {"text/html": ["\n", "\n", "
\n", " \n", " \n", " Categories | \n", " action lover | \n", " romcom lover | \n", "
\n", " \n", " Users | \n", " | \n", " | \n", "
\n", " \n", " \n", " \n", " allmoviesrock | \n", " True | \n", " True | \n", "
\n", " \n", " big_guns | \n", " True | \n", " False | \n", "
\n", " \n", " chuck_norris_fan | \n", " True | \n", " False | \n", "
\n", " \n", " easily_pleased | \n", " True | \n", " True | \n", "
\n", " \n", " girlygirl | \n", " False | \n", " True | \n", "
\n", " \n", " loves_everything | \n", " True | \n", " True | \n", "
\n", " \n", " loves_flowers | \n", " False | \n", " True | \n", "
\n", " \n", " machoman | \n", " True | \n", " False | \n", "
\n", " \n", " more_guns_please | \n", " True | \n", " False | \n", "
\n", " \n", " mylittleponey98 | \n", " False | \n", " True | \n", "
\n", " \n", " romance_addict | \n", " False | \n", " True | \n", "
\n", " \n", " testosterone guy | \n", " True | \n", " False | \n", "
\n", " \n", " yeah_guns666 | \n", " True | \n", " False | \n", "
\n", " \n", "
\n", "
"], "text/plain": ["Categories action lover romcom lover\n", "Users \n", "allmoviesrock True True\n", "big_guns True False\n", "chuck_norris_fan True False\n", "easily_pleased True True\n", "girlygirl False True\n", "loves_everything True True\n", "loves_flowers False True\n", "machoman True False\n", "more_guns_please True False\n", "mylittleponey98 False True\n", "romance_addict False True\n", "testosterone guy True False\n", "yeah_guns666 True False"]}, "execution_count": 19, "metadata": {}, "output_type": "execute_result"}], "source": ["profiles = profiles > 1\n", "profiles"]}, {"cell_type": "code", "execution_count": 19, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:25.783680Z", "start_time": "2017-10-22T18:15:25.767678Z"}}, "outputs": [], "source": ["movie_cat = pd.DataFrame(nmf.components_,\n", " columns=df.columns,\n", " index=['action lover', 'romcom lover'])\n", "movie_cat.index.name = 'Categories'\n", "movie_cat = movie_cat > 1"]}, {"cell_type": "code", "execution_count": 20, "metadata": {"ExecuteTime": {"end_time": "2017-10-22T18:15:25.812688Z", "start_time": "2017-10-22T18:15:25.786668Z"}}, "outputs": [{"data": {"text/html": ["\n", "\n", "
\n", " \n", " \n", " Movies | \n", " Charming prince | \n", " First date | \n", " Lovely love | \n", " Guns are cool | \n", " Ultra badass 4 | \n", " My fist in your face | \n", " Guns & roses | \n", "
\n", " \n", " Categories | \n", " | \n", " | \n", " | \n", " | \n", " | \n", " | \n", " | \n", "
\n", " \n", " \n", " \n", " action lover | \n", " False | \n", " False | \n", " False | \n", " True | \n", " True | \n", " True | \n", " True | \n", "
\n", " \n", " romcom lover | \n", " True | \n", " True | \n", " True | \n", " False | \n", " False | \n", " False | \n", " True | \n", "
\n", " \n", "
\n", "
"], "text/plain": ["Movies Charming prince First date Lovely love Guns are cool \\\n", "Categories \n", "action lover False False False True \n", "romcom lover True True True False \n", "\n", "Movies Ultra badass 4 My fist in your face Guns & roses \n", "Categories \n", "action lover True True True \n", "romcom lover False False True "]}, "execution_count": 21, "metadata": {}, "output_type": "execute_result"}], "source": ["movie_cat"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Nous avons donc bien obtenu une matrice de profils et une autre de cat\u00e9gories de films dont la multiplication nous donnera approximativement les go\u00fbts des utilisateurs pour chaque film, y compris ceux qu'ils n'ont pas vus ou \u00e9valu\u00e9s."]}], "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": "3.6.1"}, "varInspector": {"cols": {"lenName": 16, "lenType": 16, "lenVar": 40}, "kernels_config": {"python": {"delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())"}, "r": {"delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) "}}, "types_to_exclude": ["module", "function", "builtin_function_or_method", "instance", "_Feature"], "window_display": false}}, "nbformat": 4, "nbformat_minor": 2}