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| 1 | +#!/usr/bin/python |
| 2 | +# -*- coding: utf-8 -*- |
| 3 | +""" |
| 4 | +====================== |
| 5 | +Feature discretization |
| 6 | +====================== |
| 7 | +
|
| 8 | +A demonstration of feature discretization on synthetic classification datasets. |
| 9 | +Feature discretization decomposes each feature into a set of bins, here equally |
| 10 | +distributed in width. The discrete values are then one-hot encoded, and given |
| 11 | +to a linear classifier. This preprocessing enables a non-linear behavior even |
| 12 | +though the classifier is linear. |
| 13 | +
|
| 14 | +On this example, the first two rows represent linearly non-separable datasets |
| 15 | +(moons and concentric circles) while the third is approximately linearly |
| 16 | +separable. On the two linearly non-separable datasets, feature discretization |
| 17 | +largely increases the performance of linear classifiers. On the linearly |
| 18 | +separable dataset, feature discretization decreases the performance of linear |
| 19 | +classifiers. Two non-linear classifiers are also shown for comparison. |
| 20 | +
|
| 21 | +This example should be taken with a grain of salt, as the intuition conveyed |
| 22 | +does not necessarily carry over to real datasets. Particularly in |
| 23 | +high-dimensional spaces, data can more easily be separated linearly. Moreover, |
| 24 | +using feature discretization and one-hot encoding increases the number of |
| 25 | +features, which easily lead to overfitting when the number of samples is small. |
| 26 | +
|
| 27 | +The plots show training points in solid colors and testing points |
| 28 | +semi-transparent. The lower right shows the classification accuracy on the test |
| 29 | +set. |
| 30 | +""" |
| 31 | +print(__doc__) |
| 32 | + |
| 33 | +# Code source: Tom Dupré la Tour |
| 34 | +# Adapted from plot_classifier_comparison by Gaël Varoquaux and Andreas Müller |
| 35 | +# |
| 36 | +# License: BSD 3 clause |
| 37 | + |
| 38 | +import numpy as np |
| 39 | +import matplotlib.pyplot as plt |
| 40 | +from matplotlib.colors import ListedColormap |
| 41 | +from sklearn.model_selection import train_test_split |
| 42 | +from sklearn.preprocessing import StandardScaler |
| 43 | +from sklearn.datasets import make_moons, make_circles, make_classification |
| 44 | +from sklearn.linear_model import LogisticRegression |
| 45 | +from sklearn.model_selection import GridSearchCV |
| 46 | +from sklearn.pipeline import make_pipeline |
| 47 | +from sklearn.preprocessing import KBinsDiscretizer |
| 48 | +from sklearn.svm import SVC, LinearSVC |
| 49 | +from sklearn.ensemble import GradientBoostingClassifier |
| 50 | + |
| 51 | +h = .02 # step size in the mesh |
| 52 | + |
| 53 | + |
| 54 | +def get_name(estimator): |
| 55 | + name = estimator.__class__.__name__ |
| 56 | + if name == 'Pipeline': |
| 57 | + name = [get_name(est[1]) for est in estimator.steps] |
| 58 | + name = ' + '.join(name) |
| 59 | + return name |
| 60 | + |
| 61 | + |
| 62 | +# list of (estimator, param_grid), where param_grid is used in GridSearchCV |
| 63 | +classifiers = [ |
| 64 | + (LogisticRegression(solver='lbfgs', random_state=0), { |
| 65 | + 'C': np.logspace(-2, 7, 10) |
| 66 | + }), |
| 67 | + (LinearSVC(random_state=0), { |
| 68 | + 'C': np.logspace(-2, 7, 10) |
| 69 | + }), |
| 70 | + (make_pipeline( |
| 71 | + KBinsDiscretizer(encode='onehot'), |
| 72 | + LogisticRegression(solver='lbfgs', random_state=0)), { |
| 73 | + 'kbinsdiscretizer__n_bins': np.arange(2, 10), |
| 74 | + 'logisticregression__C': np.logspace(-2, 7, 10), |
| 75 | + }), |
| 76 | + (make_pipeline( |
| 77 | + KBinsDiscretizer(encode='onehot'), LinearSVC(random_state=0)), { |
| 78 | + 'kbinsdiscretizer__n_bins': np.arange(2, 10), |
| 79 | + 'linearsvc__C': np.logspace(-2, 7, 10), |
| 80 | + }), |
| 81 | + (GradientBoostingClassifier(n_estimators=50, random_state=0), { |
| 82 | + 'learning_rate': np.logspace(-4, 0, 10) |
| 83 | + }), |
| 84 | + (SVC(random_state=0), { |
| 85 | + 'C': np.logspace(-2, 7, 10) |
| 86 | + }), |
| 87 | +] |
| 88 | + |
| 89 | +names = [get_name(e) for e, g in classifiers] |
| 90 | + |
| 91 | +n_samples = 100 |
| 92 | +datasets = [ |
| 93 | + make_moons(n_samples=n_samples, noise=0.2, random_state=0), |
| 94 | + make_circles(n_samples=n_samples, noise=0.2, factor=0.5, random_state=1), |
| 95 | + make_classification(n_samples=n_samples, n_features=2, n_redundant=0, |
| 96 | + n_informative=2, random_state=2, |
| 97 | + n_clusters_per_class=1) |
| 98 | +] |
| 99 | + |
| 100 | +figure = plt.figure(figsize=(21, 9)) |
| 101 | +cm = plt.cm.PiYG |
| 102 | +cm_bright = ListedColormap(['#b30065', '#178000']) |
| 103 | +i = 1 |
| 104 | +# iterate over datasets |
| 105 | +for ds_cnt, (X, y) in enumerate(datasets): |
| 106 | + print('\ndataset %d\n---------' % ds_cnt) |
| 107 | + |
| 108 | + # preprocess dataset, split into training and test part |
| 109 | + X = StandardScaler().fit_transform(X) |
| 110 | + X_train, X_test, y_train, y_test = train_test_split( |
| 111 | + X, y, test_size=.5, random_state=42) |
| 112 | + |
| 113 | + # create the grid for background colors |
| 114 | + x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5 |
| 115 | + y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5 |
| 116 | + xx, yy = np.meshgrid( |
| 117 | + np.arange(x_min, x_max, h), np.arange(y_min, y_max, h)) |
| 118 | + |
| 119 | + # plot the dataset first |
| 120 | + ax = plt.subplot(len(datasets), len(classifiers) + 1, i) |
| 121 | + if ds_cnt == 0: |
| 122 | + ax.set_title("Input data") |
| 123 | + # plot the training points |
| 124 | + ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright, |
| 125 | + edgecolors='k') |
| 126 | + # and testing points |
| 127 | + ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, alpha=0.6, |
| 128 | + edgecolors='k') |
| 129 | + ax.set_xlim(xx.min(), xx.max()) |
| 130 | + ax.set_ylim(yy.min(), yy.max()) |
| 131 | + ax.set_xticks(()) |
| 132 | + ax.set_yticks(()) |
| 133 | + i += 1 |
| 134 | + |
| 135 | + # iterate over classifiers |
| 136 | + for name, (estimator, param_grid) in zip(names, classifiers): |
| 137 | + ax = plt.subplot(len(datasets), len(classifiers) + 1, i) |
| 138 | + |
| 139 | + clf = GridSearchCV(estimator=estimator, param_grid=param_grid, cv=5) |
| 140 | + clf.fit(X_train, y_train) |
| 141 | + score = clf.score(X_test, y_test) |
| 142 | + print('%s: %.2f' % (name, score)) |
| 143 | + |
| 144 | + # plot the decision boundary. For that, we will assign a color to each |
| 145 | + # point in the mesh [x_min, x_max]*[y_min, y_max]. |
| 146 | + if hasattr(clf, "decision_function"): |
| 147 | + Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()]) |
| 148 | + else: |
| 149 | + Z = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1] |
| 150 | + |
| 151 | + # put the result into a color plot |
| 152 | + Z = Z.reshape(xx.shape) |
| 153 | + ax.contourf(xx, yy, Z, cmap=cm, alpha=.8) |
| 154 | + |
| 155 | + # plot the training points |
| 156 | + ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright, |
| 157 | + edgecolors='k') |
| 158 | + # and testing points |
| 159 | + ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, |
| 160 | + edgecolors='k', alpha=0.6) |
| 161 | + ax.set_xlim(xx.min(), xx.max()) |
| 162 | + ax.set_ylim(yy.min(), yy.max()) |
| 163 | + ax.set_xticks(()) |
| 164 | + ax.set_yticks(()) |
| 165 | + |
| 166 | + if ds_cnt == 0: |
| 167 | + ax.set_title(name.replace(' + ', '\n')) |
| 168 | + ax.text(0.95, 0.06, ('%.2f' % score).lstrip('0'), size=15, |
| 169 | + bbox=dict(boxstyle='round', alpha=0.8, facecolor='white'), |
| 170 | + transform=ax.transAxes, horizontalalignment='right') |
| 171 | + |
| 172 | + i += 1 |
| 173 | + |
| 174 | +plt.tight_layout() |
| 175 | + |
| 176 | +# Add suptitles above the figure |
| 177 | +plt.subplots_adjust(top=0.90) |
| 178 | +suptitles = [ |
| 179 | + 'Linear classifiers', |
| 180 | + 'Feature discretization and linear classifiers', |
| 181 | + 'Non-linear classifiers', |
| 182 | +] |
| 183 | +for i, suptitle in zip([2, 4, 6], suptitles): |
| 184 | + ax = plt.subplot(len(datasets), len(classifiers) + 1, i) |
| 185 | + ax.text(1.05, 1.25, suptitle, transform=ax.transAxes, |
| 186 | + horizontalalignment='center', size='x-large') |
| 187 | +plt.show() |
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