{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "

Tabla de contenidos

\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Introducción\n", "\n", "Con esta técnica lo que se consigue es reducir la dimensión del conjunto de features o variables, mediante la obtención de una serie de ejes llamados factoriales, que son ortogonales y además preservan la mayor parte de la variabilidad de las variables originales. Este método en su conjunto **es una transformación lineal no supervisada**.\n", "\n", "La idea general es la siguiente. Si tenemos una matriz de datos X (n,d), con este método lo que se busca es una W (d,k) de tal manera, que se obtenga un vector Z (n,k) con k\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
012345678910111213
count178.000178.000178.000178.000178.000178.000178.000178.000178.000178.000178.000178.000178.000178.000
mean1.93813.0012.3362.36719.49599.7422.2952.0290.3621.5915.0580.9572.612746.893
std0.7750.8121.1170.2743.34014.2820.6260.9990.1240.5722.3180.2290.710314.907
min1.00011.0300.7401.36010.60070.0000.9800.3400.1300.4101.2800.4801.270278.000
25%1.00012.3621.6032.21017.20088.0001.7421.2050.2701.2503.2200.7821.938500.500
50%2.00013.0501.8652.36019.50098.0002.3552.1350.3401.5554.6900.9652.780673.500
75%3.00013.6783.0832.55821.500107.0002.8002.8750.4381.9506.2001.1203.170985.000
max3.00014.8305.8003.23030.000162.0003.8805.0800.6603.58013.0001.7104.0001680.000
\n", "" ], "text/plain": [ " 0 1 2 3 4 5 6 7 \\\n", "count 178.000 178.000 178.000 178.000 178.000 178.000 178.000 178.000 \n", "mean 1.938 13.001 2.336 2.367 19.495 99.742 2.295 2.029 \n", "std 0.775 0.812 1.117 0.274 3.340 14.282 0.626 0.999 \n", "min 1.000 11.030 0.740 1.360 10.600 70.000 0.980 0.340 \n", "25% 1.000 12.362 1.603 2.210 17.200 88.000 1.742 1.205 \n", "50% 2.000 13.050 1.865 2.360 19.500 98.000 2.355 2.135 \n", "75% 3.000 13.678 3.083 2.558 21.500 107.000 2.800 2.875 \n", "max 3.000 14.830 5.800 3.230 30.000 162.000 3.880 5.080 \n", "\n", " 8 9 10 11 12 13 \n", "count 178.000 178.000 178.000 178.000 178.000 178.000 \n", "mean 0.362 1.591 5.058 0.957 2.612 746.893 \n", "std 0.124 0.572 2.318 0.229 0.710 314.907 \n", "min 0.130 0.410 1.280 0.480 1.270 278.000 \n", "25% 0.270 1.250 3.220 0.782 1.938 500.500 \n", "50% 0.340 1.555 4.690 0.965 2.780 673.500 \n", "75% 0.438 1.950 6.200 1.120 3.170 985.000 \n", "max 0.660 3.580 13.000 1.710 4.000 1680.000 " ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "win= pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data', header=None)\n", "print(win.head())\n", "pd.set_option(\"display.precision\", 3)\n", "win.describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A continuación dividimos los datos en un conjunto train y otro test y también estandarizamos los datos" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "D:\\programas\\Anaconda\\lib\\site-packages\\sklearn\\cross_validation.py:41: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. Also note that the interface of the new CV iterators are different from that of this module. This module will be removed in 0.20.\n", " \"This module will be removed in 0.20.\", DeprecationWarning)\n" ] } ], "source": [ "from sklearn.cross_validation import train_test_split\n", "from sklearn.preprocessing import StandardScaler\n", "X, y = win.iloc[:, 1:].values, win.iloc[:, 0].values\n", "# Generamos conjunto train y test\n", "X_train, X_test, y_train, y_test = train_test_split(X, y,test_size=0.3, random_state=0)\n", "# Ahora estandarizamos\n", "sc = StandardScaler()\n", "X_train_std = sc.fit_transform(X_train)\n", "X_test_std = sc.fit_transform(X_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Siguiendo los pasos indicados en el comienzo de este post, vamos a continuación a calcular la matriz de varianzas y covarianzas, así como los valores y los vectores propios. Para calcular valores y vectores propios se utiliza la función *inealg.eig* de la librería NumPy. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Valores propios: \n", " [4.8923083 2.46635032 1.42809973 1.01233462 0.84906459 0.60181514\n", " 0.52251546 0.08414846 0.33051429 0.29595018 0.16831254 0.21432212\n", " 0.2399553 ]\n" ] } ], "source": [ "cov=np.cov(X_train_std.T)\n", "eigen_vals,eigen_vect=np.linalg.eig(cov)\n", "print(\"Valores propios: \\n\",eigen_vals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sabemos que los valores expresados en porcentaje nos van a facilitar el porcentaje de variabilidad expresado por ese factor. Más en concreto, ese porcentaje de explicación se obtiene mediante la fórmula siguiente:\n", "\n", "\\\\[ \\frac{\\lambda_j}{\\sum_{j=1}^d \\lambda_j} \\\\]\n", "\n", "Calculemos esos valores con el código siguiente:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Variabilidad de cada eje: \n", " [0.3732964772349068, 0.18818926106599576, 0.10896790724757799, 0.07724389477124867, 0.06478594601826185, 0.04592013811478144, 0.039869355976347116, 0.025219142607261543, 0.022581806817679684, 0.01830924471952688, 0.016353362655051457, 0.012842705837492727, 0.006420756933868302]\n", "Variabilidad acumulada: \n", " [0.37329648 0.56148574 0.67045365 0.74769754 0.81248349 0.85840362\n", " 0.89827298 0.92349212 0.94607393 0.96438317 0.98073654 0.99357924\n", " 1. ]\n" ] } ], "source": [ "tot=sum(eigen_vals)\n", "variabilidad=[(i/tot) for i in sorted(eigen_vals, reverse=True)]\n", "print(\"Variabilidad de cada eje: \\n\",variabilidad)\n", "cum_variabilidad=np.cumsum(variabilidad)\n", "print(\"Variabilidad acumulada: \\n\",cum_variabilidad)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ponemos ahora en un gráfico estos valores:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "import matplotlib.pyplot as plt\n", "plt.figure(figsize=(10,5))\n", "plt.bar(range(1,14), variabilidad, alpha=0.5, align='center', label='Varianza explicada individual')\n", "plt.step(range(1,14), cum_variabilidad, where='mid', label='Varianza explicada acumulada')\n", "plt.ylabel('Ratio de varianza explicada')\n", "plt.xlabel('Componentes principales')\n", "plt.legend(loc='best')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Con el gráfico y los datos obtenidos anteriormente, se puede comprobar que si nos quedamos con los os primeros componentes tendremos explicado aproximadamente el 60 por ciento de la variabilidad del sistema.\n", "\n", "A continuación vamos a ver cómo se consiguen las *puntuaciones factoriales*, es decir las coordenadas de los valores originales en los nuevos ejes.\n", "\n", "Primero construimos los pares formados por los valores propios y los vectores propios, después ordenamos en orden decreciente de los valores propios." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "pares=[(np.abs(eigen_vals[i]),eigen_vect[:,i]) for i in range(len(eigen_vals))]\n", "pares.sort(reverse=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A efectos didácticos a continuación nos quedamos con los dos primeros factores que explican el 60 por ciento de la variabilidad total. Porcentaje algo bajo pero suficiente para el propósito didáctico que se pretende. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Matriz W:\n", " [[ 0.14669811 0.50417079]\n", " [-0.24224554 0.24216889]\n", " [-0.02993442 0.28698484]\n", " [-0.25519002 -0.06468718]\n", " [ 0.12079772 0.22995385]\n", " [ 0.38934455 0.09363991]\n", " [ 0.42326486 0.01088622]\n", " [-0.30634956 0.01870216]\n", " [ 0.30572219 0.03040352]\n", " [-0.09869191 0.54527081]\n", " [ 0.30032535 -0.27924322]\n", " [ 0.36821154 -0.174365 ]\n", " [ 0.29259713 0.36315461]]\n" ] } ], "source": [ "w= np.hstack((pares[0][1][:, np.newaxis], pares[1][1][:, np.newaxis]))\n", "print('Matriz W:\\n',w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ahora los valores proyectados sobre los ejes factoriales estarían dados por la siguiente fórmula:\n", "\n", "\\\\[ x^{'}=xW \\\\]\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 2.59891628, 0.00484089],\n", " [ 0.15819134, -2.26659577]])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_train_std[0:2].dot(w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ahora procedemos a dibujar el resultado obtenido sobre dos factores:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X_train_pca = X_train_std.dot(w)\n", "colors = ['r', 'b', 'g']\n", "markers = ['s', 'x', 'o']\n", "plt.figure(figsize=(10,8))\n", "for l, c, m in zip(np.unique(y_train), colors, markers):\n", " plt.scatter(X_train_pca[y_train==l, 0],\n", " X_train_pca[y_train==l, 1],\n", " c=c, label=l, marker=m)\n", "plt.xlabel('PC 1')\n", "plt.ylabel('PC 2')\n", "plt.legend(loc='lower right')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Regresión Logit\n", "\n", "A continuación vamos a montar un ejemplo en el que utilizamos scikit-learn para primero hacer una reducción con PCA y después aplicar una regresión logit sobre las coordenadas en los ejes factoriales. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from matplotlib.colors import ListedColormap\n", "\n", "def plot_decision_regions(X, y, classifier, resolution=0.02):\n", " # definimos generación del marker y el color map\n", " markers = ('s', 'x', 'o', '^', 'v')\n", " colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')\n", " cmap = ListedColormap(colors[:len(np.unique(y))])\n", " # Generamos la rejilla\n", " x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n", " x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n", " xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),\n", " np.arange(x2_min, x2_max, resolution))\n", " Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)\n", " Z = Z.reshape(xx1.shape)\n", " plt.figure(figsize=(10,8))\n", " plt.contourf(xx1, xx2, Z, alpha=0.4, cmap=cmap)\n", " plt.xlim(xx1.min(), xx1.max())\n", " plt.ylim(xx2.min(), xx2.max())\n", " # Dibujamos las clases\n", " for idx, cl in enumerate(np.unique(y)):\n", " plt.scatter(x=X[y == cl, 0], y=X[y == cl, 1],\n", " alpha=0.8, c=cmap(idx),\n", " marker=markers[idx], label=cl)\n", " \n", "from sklearn.linear_model import LogisticRegression\n", "from sklearn.decomposition import PCA\n", "pca = PCA(n_components=2) # Nos quedamos con dos componentes\n", "lr = LogisticRegression()\n", "X_train_pca = pca.fit_transform(X_train_std) #Ajustamos y calculamos nuevas coordenadas\n", "X_test_pca = pca.transform(X_test_std)\n", "lr.fit(X_train_pca, y_train)\n", "plot_decision_regions(X_train_pca, y_train, classifier=lr)\n", "plt.xlabel('PC1')\n", "plt.ylabel('PC2')\n", "plt.legend(loc='lower left')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notar que la figura mostrada más arriba es como si fuera una imagen de la que se ha obtenido anteriormente de forma manual. Esto no es debido a ningún error, si no más bien al hecho de que el signo de los valores obtenidos depende del tipo de resolución que se haya usado para calcular los valores y los vectores propios, los cuales pueden cambiar de signo al utilizar uno u otro tipo de resolución. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Otro ejemplo\n", "\n", "Para afianzar los conceptos expuestos anteriormente sobre este modelo, a continuación se muestra otro ejemplo, en este caso con un conjunto de datos ampliamente utilizado en el mundo de machine learning, me estoy refiriendo a data set denominado iris. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "url = \"https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data\"\n", "df = pd.read_csv(url, names=['sepal length','sepal width','petal length','petal width','target'])" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "from sklearn.preprocessing import StandardScaler\n", "\n", "features = ['sepal length', 'sepal width', 'petal length', 'petal width']\n", "\n", "# Nos quedamos sólo con las features\n", "x3 = df.loc[:, features].values\n", "# Ahora elegimos el valor del target\n", "y3 = df.loc[:,['target']].values\n", "# SEstandarizamos las features\n", "x3 = StandardScaler().fit_transform(x3)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "from sklearn.decomposition import PCA\n", "pca = PCA(n_components=2)\n", "# fit_transform ajustamos el modelo y calculamos los nuevos valores en los\n", "# ejes factoriales\n", "principalComponents = pca.fit_transform(x3)\n", "principalDf = pd.DataFrame(data = principalComponents\n", " , columns = ['Componente Principal 1', 'Componente Principal 2'])" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "finalDf = pd.concat([principalDf, df[['target']]], axis = 1)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pylab as plt\n", "fig = plt.figure(figsize = (8,8))\n", "ax = fig.add_subplot(1,1,1) \n", "ax.set_xlabel('Componente Principal 1', fontsize = 15)\n", "ax.set_ylabel('Componente Principal 2', fontsize = 15)\n", "ax.set_title('2 componentes PCA', fontsize = 20)\n", "targets = ['Iris-setosa', 'Iris-versicolor', 'Iris-virginica']\n", "colors = ['r', 'g', 'b']\n", "for target, color in zip(targets,colors):\n", " indicesToKeep = finalDf['target'] == target\n", " ax.scatter(finalDf.loc[indicesToKeep, 'Componente Principal 1']\n", " , finalDf.loc[indicesToKeep, 'Componente Principal 2']\n", " , c = color\n", " , s = 50)\n", "ax.legend(targets)\n", "ax.grid()\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.72770452, 0.23030523])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pca.explained_variance_ratio_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Análisis discriminante lineal.\n", "\n", "El análisis discriminante lineal ( en inglés **Linear Discriminant Analysis**, con siglas LDA), presenta muchas similitudes con el análisis factorial descrito anteriormente, sin embargo presenta ciertas propiedades que son características de este modelo y que a continuación se pasan a exponer.\n", "\n", "LDA supone que los datos con los que se trabaja están normalmente distribuidos, así como que las clases tienen igual matriz de covarianzas así como que las features son independientes entre ellas. No obstante si una o más de las condiciones anteriores son ligeramente violadas, el modelo con este sistema puede trabajar razonablemente bien.\n", "\n", "Al igual que se ha hecho para el análisis factorial, los pasos a dar para realizar este tipo de análisis, son los siguientes:\n", "\n", "1.- Estandarizar por columnas la matriz de los datos.\n", "\n", "2.- Para cada clase calcular su media.\n", "\n", "3.- Construir la matriz de varianzas entre clases \\\\( S_B \\\\), y la matriz de varianzas dentro de las clases \\\\( S_W \\\\)\n", "\n", "4.- Calcular los valores y vectores propios de la matriz \\\\( S_W^{-1}S_B \\\\)\n", "\n", "5.- Elegir lo valores propios sociados a los k mayores valores propios para construir la matriz de transformación W, siendo esos valores propios elegidos anteriormente las columnas de esa matriz.\n", "\n", "6.- Proyectar las muestra de los datos sobre el nuevo subespacio, utilizando para ello la matriz de transformación W.\n", "\n", "Para el ejemplo que sigue se va a utilizar los datos \"wine\" utilizados anteriormente, que como ya están estandarizados, se puede decir que el punto 1 ya se ha realizado. \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Construcción manual del modelo\n", "\n", "Comenzamos pues por el segundo paso, es decir calculamos la media de cada feaure para cada una de las clases . " ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MV 1: [ 0.9259 -0.3091 0.2592 -0.7989 0.3039 0.9608 1.0515 -0.6306 0.5354\n", " 0.2209 0.4855 0.798 1.2017]\n", "\n", "MV 2: [-0.8727 -0.3854 -0.4437 0.2481 -0.2409 -0.1059 0.0187 -0.0164 0.1095\n", " -0.8796 0.4392 0.2776 -0.7016]\n", "\n", "MV 3: [ 0.1637 0.8929 0.3249 0.5658 -0.01 -0.9499 -1.228 0.7436 -0.7652\n", " 0.979 -1.1698 -1.3007 -0.3912]\n", "\n" ] } ], "source": [ "np.set_printoptions(precision=4)\n", "mean_vecs = []\n", "for label in range(1,4):\n", " mean_vecs.append(np.mean(\n", " #Lo siguiente calcula la media de cada feature por clase\n", " X_train_std[y_train==label], axis=0))\n", " print('MV %s: %s\\n' %(label, mean_vecs[label-1]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Con las medias calculadas anteriormente, se podrá calcular la matriz de varianzas dentro de la clases \\\\(( S_W \\\\)\n", "\n", "\\\\[ S_W=\\sum_{i=1}^c S_i \\\\]\n", "\n", "Donde \\\\( S_i \\\\) es la matriz de varianzas dentro de cada clase.\n", "\n", "\\\\[ S_i=\\sum_{x \\epsilon D_i}(x-m_i)(x-m_i)^T \\\\]\n", "\n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Within-class scatter matrix: 13x13\n" ] } ], "source": [ "d = X_train_std.shape[1] # número de features\n", "S_W = np.zeros((d, d))\n", "for label, mv in zip(range(1, 4), mean_vecs):\n", " class_scatter = np.zeros((d, d)) # scatter matrix for each class\n", " for row in X_train_std[y_train == label]:\n", " row, mv = row.reshape(d, 1), mv.reshape(d, 1) # make column vectors\n", " class_scatter += (row - mv).dot((row - mv).T)\n", " S_W += class_scatter # sum class scatter matrices\n", "\n", "print('Within-class scatter matrix: %sx%s' % (S_W.shape[0], S_W.shape[1]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Para calcular la matriz de varianzas dentro de las clases, hemos supuesto que el número de elementos dentro de cada clase es el mismo, pero podemos ver que esta suposición no es cierta." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Distribución de las clases: [40 49 35]\n" ] } ], "source": [ "print('Distribución de las clases: %s' % np.bincount(y_train)[1:])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Por lo tanto para hacer un cálculo correcto, debemos ponderar por el peso de cada clase." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scaled within-class scatter matrix: 13x13\n" ] } ], "source": [ "d = X_train_std.shape[1] # número de features\n", "S_W = np.zeros((d, d))\n", "for label, mv in zip(range(1, 4), mean_vecs):\n", " class_scatter = np.cov(X_train_std[y_train == label].T)\n", " S_W += class_scatter\n", "print('Scaled within-class scatter matrix: %sx%s' % (S_W.shape[0],\n", " S_W.shape[1]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ahora procedemos a calcular la varianza entre clases \\\\( S_B \\\\)\n", "\n", "\\\\[ S_B=\\sum_{i=1}^c (m_i-m)(m_i-m)^T \\\\]\n", "\n", "Suemdo m la la media global" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 2.8902e-15, -1.2556e-15, 1.1451e-15, 2.5625e-15, -3.2590e-16,\n", " -1.3511e-15, 2.7756e-16, -1.6394e-15, 1.0816e-15, -3.9395e-17,\n", " -1.8623e-16, 1.0690e-15, 2.2831e-17])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Calculo del vector m\n", "mean_overall = np.mean(X_train_std, axis=0)\n", "mean_overall" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Matriz varianza entre clases: 13x13\n" ] } ], "source": [ "d = X_train_std.shape[1] # número de features\n", "S_B = np.zeros((d, d))\n", "for i, mean_vec in enumerate(mean_vecs):\n", " n = X_train[y_train == i + 1, :].shape[0]\n", " mean_vec = mean_vec.reshape(d, 1) # make column vector\n", " mean_overall = mean_overall.reshape(d, 1) # make column vector\n", " S_B += n * (mean_vec - mean_overall).dot((mean_vec - mean_overall).T)\n", "\n", "print('Matriz varianza entre clases: %sx%s' % (S_B.shape[0], S_B.shape[1]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ahora damos el siguiente paso y calculamos los valores y vectores propios de la matriz \\\\( S_W^{-1}S_B \\\\)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "eigen_vals, eigen_vecs = np.linalg.eig(np.linalg.inv(S_W).dot(S_B))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Elaboramos los pares valor propio-vector propio y ordenamos en orden descendente" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Valores propios en orden decreciente:\n", "\n", "452.72158124497423\n", "156.43636121952318\n", "1.0758537055464728e-13\n", "4.4387356399897533e-14\n", "2.872660093414232e-14\n", "2.842170943040401e-14\n", "2.40168676571112e-14\n", "1.594530890236398e-14\n", "1.594530890236398e-14\n", "9.937234430308325e-15\n", "9.937234430308325e-15\n", "2.827698412874921e-15\n", "2.827698412874921e-15\n" ] } ], "source": [ "# Make a list of (eigenvalue, eigenvector) tuples\n", "eigen_pairs = [(np.abs(eigen_vals[i]), eigen_vecs[:, i])\n", " for i in range(len(eigen_vals))]\n", "\n", "# Sort the (eigenvalue, eigenvector) tuples from high to low\n", "eigen_pairs = sorted(eigen_pairs, key=lambda k: k[0], reverse=True)\n", "\n", "# Visually confirm that the list is correctly sorted by decreasing eigenvalues\n", "\n", "print('Valores propios en orden decreciente:\\n')\n", "for eigen_val in eigen_pairs:\n", " print(eigen_val[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Al igual que hemos hecho con el modelo PCA, ahora lo hacemos con LDA colocando en una gráfica los valores propios obtenidos." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tot = sum(eigen_vals.real)\n", "discr = [(i / tot) for i in sorted(eigen_vals.real, reverse=True)]\n", "cum_discr = np.cumsum(discr)\n", "plt.bar(range(1, 14), discr, alpha=0.5, align='center',\n", " label='discriminación individual')\n", "plt.step(range(1, 14), cum_discr, where='mid',\n", " label='Disriminación acumulada')\n", "plt.ylabel('ratio discriminación')\n", "plt.xlabel('Discriminantes lineales')\n", "plt.ylim([-0.1, 1.1])\n", "plt.legend(loc='best')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ahora creamos la matriz de transformación W" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Matriz W:\n", " [[-0.0662 -0.3797]\n", " [ 0.0386 -0.2206]\n", " [-0.0217 -0.3816]\n", " [ 0.184 0.3018]\n", " [-0.0034 0.0141]\n", " [ 0.2326 0.0234]\n", " [-0.7747 0.1869]\n", " [-0.0811 0.0696]\n", " [ 0.0875 0.1796]\n", " [ 0.185 -0.284 ]\n", " [-0.066 0.2349]\n", " [-0.3805 0.073 ]\n", " [-0.3285 -0.5971]]\n" ] } ], "source": [ "w = np.hstack((eigen_pairs[0][1][:, np.newaxis].real,\n", " eigen_pairs[1][1][:, np.newaxis].real))\n", "print('Matriz W:\\n', w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ahora no tenemos más que proyectar los puntos \\\\( X^{'}=XW\\\\)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,7))\n", "X_train_lda = X_train_std.dot(w)\n", "colors = ['r', 'b', 'g']\n", "markers = ['s', 'x', 'o']\n", "for l, c, m in zip(np.unique(y_train), colors, markers):\n", " plt.scatter(X_train_lda[y_train==l, 0],\n", " X_train_lda[y_train==l, 1],\n", " c=c, label=l, marker=m)\n", "plt.xlabel('LD 1')\n", "plt.ylabel('LD 2')\n", "plt.legend(loc='upper right')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La salida que se obtiene con el gráfico está invertida (efecto espejo) respecto de la salida que genera scikit learn. Ello es debido a que los vectores propios que aquí se obtienen tienen un signo contrario al que se obtienen con scikip learn. Para corregirlo, no tenemos más que multiplicarlo por -1 y se tendría la salida igual que la generada con scikip-learn. Veamos a continuación cómo conseguir esto. " ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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nictYzdw9wR6ML2uCQjtJF3klahBRdnlUM38MwK8ET6jq/wHwaQBvZmseVUFRw2vhwJIk0LTzHiIyK3aIT1V/J+b8IQBXF9Yi6hgcXiOiLIxtWNgODvG5icNr+eL9JNdZv2EhVQeH1/LDsk1UJQxQRI5g2SaqmqaljkTkcgAfB7Bx6dRxAA+r6pmiG0ZEjVi2iaqmWSWJTQCOARgG8BMAfwvgfQCOisjGuPcRUXHyKtvE7UfIBc2G+P4QQE1VP6GqM6o6rap3AfgUgKlymkdEQXmUbeI8FrmiWYDaoqpfCZ9U1UcAbC6uSUQUJY91ZZzHIpc0m4P6tzafI6IC5LGujPNY5JJmpY7mAeyPegrAmKpeWWTDonAdFNmsrPVJeXyOqle811evMzhRefJYB/W/APREPC4D8Kd5NJKoU5Q5r5N1XRm3HyFXNCt1tC/uOREZK6Y5RO4JzusA3lBZcK7IpkoP4XmsYFsBM8N8rIxBcdrd8n0cwHSeDSGyVatfoC7N69hWH3Fy0gvuflv8ANrXx6xCarMWn4i8zDkoqoI0v0CLntfJs6dhQ6+lWW/OxuBO+Sm6Fl+m0WoR+XUReUFE6iLSspFEJqRJyS56XifvOS4b6iPmueMydShVjXwAOAfgtYjHOQBvxb0vyQPAJgDvBvD/AGxL+r7h4WElKlO9rlqrqXohwXvUat75qNf4z4WP82pDEdc3rV5vvL+ufx9qDcBhTfA7v1mSRE+BQfE4AAj/iUSWS7JlfdHzOi7NcaUV1/N0/XtRTpJEsaIeSNCDAjAK4DCAw/39/blHcqJmkvSggq9tdpzks1odd1JPo9N7hhQPCXtQhW23ISJPisixiMcdaa6jqgdVdZuqblu/fn1RzSVaITyJ36q0UJZ5nVZzTM3muMLtyGveq11J2xPX86zVuOMyedpNM29JVT9c1LWJytDO0F072XHBZAxgZTZbvQ6Mj0dnuz3zDLB9OzA9bUeadtq08cnJxnvk32MGJwJg/xBf8MEkCTIh6dDd3r3e0NTi4vLrajXV++9P9hnNhhL9a/vH9brqnj2q27fbM0TGITtKCgmH+EwFpo8CmAfw7wD+EcA3k7yPAYpsFfxlPDTkBangcdIg1WyOKeo4zRxZGWxrD9kpaYBqa6GuKVyoSzar14HhYWBubvnc0JB33Crjzh8KC2YLJs3SU8sKv9rWHrJP0Qt1iSikqws4cqTxXNrglHafJ/+9QXHvCZ/L49+m4WvU6yxES/lhgCLKiaqXzBC2f3/zHkS72WxpAlsR1dbD1/R7kFk2VCQKKiyLjyiKWlADrgjBYOEP6/mGh72eVVeTfw42y2aLu2dJsww1IktwbAx44IHlauv+Z6b5vuFrjo9733toaDkoF5H1SBWSZKLKlgeTJNwWlYlWq3nnO8H993sJEX5iwOJi43E7iQJJ7lmSLMOo5IU9exoTLdL+PcQlRPhZjM3ak/S7UWeC6YW6REHBf3G3Krzqqn37gNtvX+7R+HNS7S48TXrPkiwQDvZmwtr9e4i6pv+9W7WnCj8PlIMkUcyWB3tQbqtKCnLWkkfh9+Zxz6KuU8Q101ynKj8PtBJsXgfV7oMByn2dVk+uDFnvWdSC2T178r9mO4ty+fNQTUkDFIf4qDSaIiWaPHncs3AyRZSs12ynjh5/HqilJFHMlgd7UO6yoQxOnkNvZUh7z9JWnvCTJLL8PbR7T234eSBzkHU/KKI8Fb1nUitpi5iaoBEp1knvWZLv578+z7+Hdiu4m/55IEckiWK2PNiDcp+JXowL/1pvlnKdpGeU5PuFdwEOH5vgWq+W8gH2oMhGWfZMyvKZZexIG+4BRfWI4t7XbLuNsOACXH/B7oED3nHc9wv3sIDGHpapHouJnwdyB5MkqBLi1uzk9QsxquxPeMPBVm3zywJ1dTXu/RTVxvDnRQkO93HNEbmIAYoqQQvMGAsHgL17l2vSnT27MlhFSRNAowKOX7ooyH+uVQD0r0lknSTjgLY8OAdF7ShjDipq0Wl4X6hmn5V20WrcwttmmXnhNUeLi40bH7LEEJUFnIMi8pSRMeZfM7if09wc0N3t/Tk8XBecnwr2gMJbugPRPamoz9uzZ+X36+1dHuYbG2u8xnXXAR/84HLPa/t2Fmslu3DDQqqMdpMYkl47vOFgUHDTvqiU8Btv9J77wQ8aA8rP/3z00GDU511/PXDDDcD0tHeNet2rMN7bCywseK/ds8d7bXg4cM+e5fcRFY0bFhKFFJUxFgwWtRqwuOhtORHkzwfFJSw8+yzwxhvJ5oLCn1evewHmuee8wDM25r1mfNx7zcKCF6RqNS8ITU+vvCaDE1kpyTigLQ/OQVEZotYItZqn8tcxBeechoa8LTjC80Fx81Vp5sii1k35c0lx81j+Z4fr8AXnruLuR7NjorTAYrFE6e3d6/2SD+6VlDSJwP/FHQxW/vmoPZzCCQtpK3vHlTKKK74aDk579qw8Dl+TezZREZIGKCZJEC1RBf71X73htmefXT6fNIkgOMcUfF1wd1z/c8Ip7+Pj3i60wTmlVuu0op6LSqX3ryPizWlt3+49gkN9zz7rPReeo2u2gLjZvSDKRZIoZsuDPSgqWjtDYGmvH5fy7g/zJe1BJb1u+DpRQ5hxu+ByzyYqAhL2oJjFRxSiunJX2GAWXlbhLL563VvYOze3Ms08TTmmdgvitnpf+H7keS+ompJm8XGIjyhAI9YLAd65vDLd9u71/hscArz9dm9NUpZ1Wq2GFqO0GsbzU9WDgsOGRIVK0s2y5cEhPipSO0kEaa6t2jyBwlS2XNwwXlQVDNuqwJObwCQJonTSJhEk5Q+h7d+/3Fv5zne8XpO/gLZZ1fKiRVWl8HtI3LOJTDIyByUinwNwG4A3AfwdgLtV9Wyr93EOisrg/y8RzLoLHqe9VnDIbP/+5fkmX97bfiRpU/Cz/GG8YIAKtin8+vAxUVq2V5L4NoDNqroVwE8A/L6hdhCt4Kdkxx2nvVawknh3d2NwAsoNTlHbgviV1/05J7+twWroQQxOVBYjAUpVv6Wqby0dPgNgg4l2EJUhaiuNoLy2/WglmBDhf+b4uBcwh4a83l0woHIYj0yzYQ7qHgBfNt0IoqL4w3xBQ0PAkSONQ2tF96Sa7Sy8f/9yKnmS7D+iMhQWoETkSQC/EPHUhKp+fek1EwDeAjDb5DqjAEYBoL+/v4CWEhUnPAfV2ws8+qjXa/GrR6g29laKnONplhARfh2RacYW6orIXQB+C8AOVT2f5D1MkiAXRS3MHR/3ghLglVfy11glXVzbrmDA9JWdpEFkdZKEiNwM4HcB3J40OBG5anKyMQB0dXnHe/d6geuBBxq33vC3is/7347h3lxUQgSRTUzNQf0xgEsAfFu8/2ufUdXfMtQWcpRL6c9RQ2iq8XNCcSneWdvAdU3kEtbiIye1W3fOFsH2A4217hYXveOivpNLgZ06k9VDfERZRKVLFzk0lrdg+8fGVtb+Gx72ht+K+k5MiCBX2JBmTpRKs3RpFyb7/farLu81BQCf+hTwve95GX7d3d45V74TURE4xEfOymMbCJPDXVHtV10OTv45BifqNBzio44Wtfg1bSZauOyPf8085nvC7Yg6Drd/bCz7dypDq+9GlBcGKHJOHunSRc5jtQp8Ue3fs8cb7nvgAe/PtqaAFxnUicI4B0XOySNduqh5rFYbAPpDiOH2T097W3oAy4t2bUsBT/rdiPLCOShyVh7zR3nMY0VdM0m1hqj2A3angLMSBeUh6RwUAxRVVpG/bIsIfLbo5O9G5WCSBFETRZb9ySOBw1ad/N3IPpyDokoqquxPOPAF52kAt4fCOvm7uejChQuYn5/HG2+8YbopsdasWYMNGzZg9erVbb2fAYoqa3KycY4nj32QOrneXSd/NxfNz8+jp6cHg4ODEAtvvqrizJkzmJ+fx1VXXdXWNTgHRVSATq5318nfzSXHjx/Hxo0brQxOPlXFiy++iE2bNjWc5xwUkUGdXO+uk7+ba2wOTkD29jFAERGRlRigiIioLffccw+uuOIKbN68uZDrM0AREXW6deu8sdjwY926TJf9xCc+gUOHDuXUyJUYoIiIOt25c+nOJ/SBD3wAb3/72zNdoxkGKCIishIDFBERWYkBioiIrMQARUREVmKAIiLqdD096c4ndOedd+LGG2/ESy+9hA0bNuDBBx/MdL0w1uIjIup0r71WyGUffvjhQq7rYw+KiIisxABFRERWYoAiIiIrMUAREZGVjAQoEflDEfmxiMyJyLdE5BdNtIOIiOxlqgf1OVXdqqpDAP4SwP2G2kFERJYyEqBUNZjz+HMA3NnWl4jIQeHN07Nupv7yyy/jpptuwqZNm3DttddiZmYm2wUjGFsHJSJTAP4rgAUANzV53SiAUQDo7+8vp3FERB1kchI4exY4cMDbZUMVuO8+oK/Pe64dq1atwuc//3lcd911OHfuHIaHh7Fz505cc801ubW7sB6UiDwpIsciHncAgKpOqOqVAGYBfDLuOqp6UFW3qeq29evXF9VcIqKOpOoFp5kZLyj5wWlmxjvfbk/qne98J6677joAQE9PDzZt2oRXXnklx5YX2INS1Q8nfOn/BfA4gL1FtYWIqKpEvJ4T4AUlfySuVlvuUWV14sQJPP/889i+fXv2iwWYyuK7OnB4O4AXTbSDiKgKgkHKl1dw+tnPfoZdu3Zhenoa6zLu0BtmKovvfywN9/0YwK8CqBlqBxFRx/OH9YL84b4sLly4gF27dmFkZAQf+9jHsl0sgqksvl2qunkp1fw2Vc134JKIiAA0zjnVakC97v03OCfV3nUV9957LzZt2oTx8fF8G72E1cyJiDqYiJetF5xz8of7+vraH+b7/ve/jy996UvYsmULhoaGAACf/exnceutt+bUcgYoIqKONznp9ZT8YOQHqSxzUO9///uhWccIW2AtPiKiCggHozwSJIrGAEVERFZigCIiIisxQBERkZUYoIiIyEoMUEREZCUGKCIiSu2NN97A9ddfj/e85z249tprsXdv/uVUGaCIiCpg9ugsBqcH0bWvC4PTg5g9Opvpepdccgmefvpp/OhHP8Lc3BwOHTqEZ555JqfWerhQl8gRwYWWUcdEcWaPzmL0sVGcv3AeAHBy4SRGHxsFAIxsGWnrmiKCyy67DIBXk+/ChQuQnH8g2YMicsDkZGPdNL++WrubzVG1TDw1cTE4+c5fOI+JpyYyXXdxcRFDQ0O44oorsHPnzs7YboOIkitqwzmqjlMLp1KdT6q7uxtzc3OYn5/Hc889h2PHjmW6XhiH+IgsV8aGc9TZ+nv7cXLhZOT5PPT19eFDH/oQDh06hM2bN+dyTYA9KCInFLnhHHW+qR1TWLt6bcO5tavXYmrHVNvXPH36NM6ePQsAeP311/Hkk09i48aNmdoZxgBF5ICiNpyjahjZMoKDtx3EQO8ABIKB3gEcvO1g2wkSAPDqq6/ipptuwtatW/G+970PO3fuxEc+8pEcW80hPiLrhTecO3Bg+RhgT4qSGdkykikghW3duhXPP/98bteLwgBFZLmiNpwjsh0DFJEDithwjsh2nIMicoSLG85RsYre0TarrO1jgCIictCaNWtw5swZa4OUquLMmTNYs2ZN29fgEB8RkYM2bNiA+fl5nD592nRTYq1ZswYbNmxo+/0MUEREDlq9ejWuuuoq080oFIf4iIjISgxQRERkJQYoIiKyktiaARJFRE4DWFnxsDjvAPDPJX5eJ+G9aw/vW/t479pX9r0bUNX1rV7kVIAqm4gcVtVtptvhIt679vC+tY/3rn223jsO8RERkZUYoIiIyEoMUM0dNN0Ah/HetYf3rX28d+2z8t5xDoqIiKzEHhQREVmJAYqIiKzEANWCiHxORF4UkR+LyF+ISJ/pNrlCRH5dRF4QkbqIWJfCahsRuVlEXhKRn4rI75lujytE5CER+ScROWa6LS4RkStF5K9E5PjS/6c1020KY4Bq7dsANqvqVgA/AfD7htvjkmMAPgbgu6YbYjsR6QbwJwBuAXANgDtF5BqzrXLGnwG42XQjHPQWgE+r6iYANwD4bdt+5higWlDVb6nqW0uHzwBov3Z8xajqcVV9yXQ7HHHNoCZtAAACSElEQVQ9gJ+q6t+r6psA/hzAHYbb5ARV/S6AfzHdDteo6quq+sOlP58DcBzAu8y2qhEDVDr3AHjCdCOoI70LwMuB43lY9suCOpeIDAJ4L4BnzbakEfeDAiAiTwL4hYinJlT160uvmYDXJZ4ts222S3LvKJGoDdy5BoQKJyKXAXgEwJiqvma6PUEMUABU9cPNnheRuwB8BMAO5cKxBq3uHSU2D+DKwPEGAP9gqC1UESKyGl5wmlXVr5puTxiH+FoQkZsB/C6A21X1vOn2UMf6awBXi8hVIvI2AL8B4FHDbaIOJiIC4EEAx1V1v+n2RGGAau2PAfQA+LaIzInI/zTdIFeIyEdFZB7AjQAeF5Fvmm6TrZYScT4J4JvwJqu/oqovmG2VG0TkYQA/APBuEZkXkXtNt8kRvwzgvwD4laXfbXMicqvpRgWx1BEREVmJPSgiIrISAxQREVmJAYqIiKzEAEVERFZigCIiIisxQBGVQER+FnFuUkReWUrv/VsR+WpcsU5WhqcqYoAiMuuAqg6p6tUAvgzgaRFZH/E6VoanymGAIrKEqn4ZwLcAfDziOVaGp8phgCKyyw8BbDTdCCIbMEAR2SWqqjlRJTFAEdnlvfBq8RFVHgMUkSVEZBeAXwXwsOm2ENmAxWKJSiAidTTu77QfwDoA/w3AaQA/By9Tb0JV/ybi/R8F8EcA1gM4C2BOVX+t6HYTmcQARUREVuIQHxERWYkBioiIrMQARUREVmKAIiIiKzFAERGRlRigiIjISgxQRERkpf8AKHCdRn7Tq/gAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X_train_lda = X_train_std.dot(w)\n", "colors = ['r', 'b', 'g']\n", "markers = ['s', 'x', 'o']\n", "\n", "for l, c, m in zip(np.unique(y_train), colors, markers):\n", " plt.scatter(X_train_lda[y_train == l, 0] * (-1),\n", " X_train_lda[y_train == l, 1] * (-1),\n", " c=c, label=l, marker=m)\n", "\n", "plt.xlabel('LD 1')\n", "plt.ylabel('LD 2')\n", "plt.legend(loc='lower right')\n", "plt.tight_layout()\n", "# plt.savefig('./figures/lda2.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# LDA con scikit-Learn\n", "\n", "El ejemplo de antes lo repetimos, pero en esta ocasión utilizando las clases que nos ofrece scikit-learn" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA\n", "lda = LDA(n_components=2)\n", "X_train_lda = lda.fit_transform(X_train_std, y_train)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ahora hacemos una regresión logit sobre los datos transformados" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.linear_model import LogisticRegression\n", "lr = LogisticRegression()\n", "lr = lr.fit(X_train_lda, y_train)\n", "plot_decision_regions(X_train_lda, y_train, classifier=lr)\n", "plt.xlabel('LD 1')\n", "plt.ylabel('LD 2')\n", "plt.legend(loc='lower left')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ahoro lo hacemos para el conjunto de datos test" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X_test_lda = lda.transform(X_test_std)\n", "plot_decision_regions(X_test_lda, y_test, classifier=lr)\n", "plt.xlabel('LD 1')\n", "plt.ylabel('LD 2')\n", "plt.legend(loc='lower left')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Lineal y cuadrática Análisis discriminante\n", "\n", "Dentro de los modelos de reducción de la dimensionalidad se encuentra también el análisis discriminante cuadrático, que no me voy a extender en él en este post, simplemente indicar que se puede localizar [en este enlace](http://scikit-learn.org/stable/auto_examples/classification/plot_lda_qda.html){:target=\"_blank\"} , del que se entresaca el siguiente código a efectos ilustrativos. " ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Automatically created module for IPython interactive environment\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print(__doc__)\n", "\n", "from scipy import linalg\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib as mpl\n", "from matplotlib import colors\n", "\n", "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n", "from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis\n", "plt.figure(figsize=(15,10))\n", "# #############################################################################\n", "# Colormap\n", "cmap = colors.LinearSegmentedColormap(\n", " 'red_blue_classes',\n", " {'red': [(0, 1, 1), (1, 0.7, 0.7)],\n", " 'green': [(0, 0.7, 0.7), (1, 0.7, 0.7)],\n", " 'blue': [(0, 0.7, 0.7), (1, 1, 1)]})\n", "plt.cm.register_cmap(cmap=cmap)\n", "\n", "\n", "# #############################################################################\n", "# Generate datasets\n", "def dataset_fixed_cov():\n", " '''Generate 2 Gaussians samples with the same covariance matrix'''\n", " n, dim = 300, 2\n", " np.random.seed(0)\n", " C = np.array([[0., -0.23], [0.83, .23]])\n", " X = np.r_[np.dot(np.random.randn(n, dim), C),\n", " np.dot(np.random.randn(n, dim), C) + np.array([1, 1])]\n", " y = np.hstack((np.zeros(n), np.ones(n)))\n", " return X, y\n", "\n", "\n", "def dataset_cov():\n", " '''Generate 2 Gaussians samples with different covariance matrices'''\n", " n, dim = 300, 2\n", " np.random.seed(0)\n", " C = np.array([[0., -1.], [2.5, .7]]) * 2.\n", " X = np.r_[np.dot(np.random.randn(n, dim), C),\n", " np.dot(np.random.randn(n, dim), C.T) + np.array([1, 4])]\n", " y = np.hstack((np.zeros(n), np.ones(n)))\n", " return X, y\n", "\n", "\n", "# #############################################################################\n", "# Plot functions\n", "def plot_data(lda, X, y, y_pred, fig_index):\n", " splot = plt.subplot(2, 2, fig_index)\n", " if fig_index == 1:\n", " plt.title('Análisis con Discriminante lineal')\n", " plt.ylabel('Datos con\\n covarianza fija')\n", " elif fig_index == 2:\n", " plt.title('Análisis discriminante cuadático')\n", " elif fig_index == 3:\n", " plt.ylabel('Datos con \\n covarianzas variable')\n", "\n", " tp = (y == y_pred) # True Positive\n", " tp0, tp1 = tp[y == 0], tp[y == 1]\n", " X0, X1 = X[y == 0], X[y == 1]\n", " X0_tp, X0_fp = X0[tp0], X0[~tp0]\n", " X1_tp, X1_fp = X1[tp1], X1[~tp1]\n", "\n", " alpha = 0.5\n", "\n", " # class 0: dots\n", " plt.plot(X0_tp[:, 0], X0_tp[:, 1], 'o', alpha=alpha,\n", " color='red', markeredgecolor='k')\n", " plt.plot(X0_fp[:, 0], X0_fp[:, 1], '*', alpha=alpha,\n", " color='#990000', markeredgecolor='k') # dark red\n", "\n", " # class 1: dots\n", " plt.plot(X1_tp[:, 0], X1_tp[:, 1], 'o', alpha=alpha,\n", " color='blue', markeredgecolor='k')\n", " plt.plot(X1_fp[:, 0], X1_fp[:, 1], '*', alpha=alpha,\n", " color='#000099', markeredgecolor='k') # dark blue\n", "\n", " # class 0 and 1 : areas\n", " nx, ny = 200, 100\n", " x_min, x_max = plt.xlim()\n", " y_min, y_max = plt.ylim()\n", " xx, yy = np.meshgrid(np.linspace(x_min, x_max, nx),\n", " np.linspace(y_min, y_max, ny))\n", " Z = lda.predict_proba(np.c_[xx.ravel(), yy.ravel()])\n", " Z = Z[:, 1].reshape(xx.shape)\n", " plt.pcolormesh(xx, yy, Z, cmap='red_blue_classes',\n", " norm=colors.Normalize(0., 1.))\n", " plt.contour(xx, yy, Z, [0.5], linewidths=2., colors='k')\n", "\n", " # means\n", " plt.plot(lda.means_[0][0], lda.means_[0][1],\n", " 'o', color='black', markersize=10, markeredgecolor='k')\n", " plt.plot(lda.means_[1][0], lda.means_[1][1],\n", " 'o', color='black', markersize=10, markeredgecolor='k')\n", "\n", " return splot\n", "\n", "\n", "def plot_ellipse(splot, mean, cov, color):\n", " v, w = linalg.eigh(cov)\n", " u = w[0] / linalg.norm(w[0])\n", " angle = np.arctan(u[1] / u[0])\n", " angle = 180 * angle / np.pi # convert to degrees\n", " # filled Gaussian at 2 standard deviation\n", " ell = mpl.patches.Ellipse(mean, 2 * v[0] ** 0.5, 2 * v[1] ** 0.5,\n", " 180 + angle, facecolor=color,\n", " edgecolor='yellow',\n", " linewidth=2, zorder=2)\n", " ell.set_clip_box(splot.bbox)\n", " ell.set_alpha(0.5)\n", " splot.add_artist(ell)\n", " splot.set_xticks(())\n", " splot.set_yticks(())\n", "\n", "\n", "def plot_lda_cov(lda, splot):\n", " plot_ellipse(splot, lda.means_[0], lda.covariance_, 'red')\n", " plot_ellipse(splot, lda.means_[1], lda.covariance_, 'blue')\n", "\n", "\n", "def plot_qda_cov(qda, splot):\n", " plot_ellipse(splot, qda.means_[0], qda.covariance_[0], 'red')\n", " plot_ellipse(splot, qda.means_[1], qda.covariance_[1], 'blue')\n", "\n", "for i, (X, y) in enumerate([dataset_fixed_cov(), dataset_cov()]):\n", " # Linear Discriminant Analysis\n", " lda = LinearDiscriminantAnalysis(solver=\"svd\", store_covariance=True)\n", " y_pred = lda.fit(X, y).predict(X)\n", " splot = plot_data(lda, X, y, y_pred, fig_index=2 * i + 1)\n", " plot_lda_cov(lda, splot)\n", " plt.axis('tight')\n", "\n", " # Quadratic Discriminant Analysis\n", " qda = QuadraticDiscriminantAnalysis(store_covariance=True)\n", " y_pred = qda.fit(X, y).predict(X)\n", " splot = plot_data(qda, X, y, y_pred, fig_index=2 * i + 2)\n", " plot_qda_cov(qda, splot)\n", " plt.axis('tight')\n", "plt.suptitle('Análisis discriminante Lineal vs Anáisis Discriminate cuadrático')\n", "plt.show()" ] } ], "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": "3.6.5" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Tabla de contenidos", "title_sidebar": "Contenidos", "toc_cell": true, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }