Shows how shrinkage improves classification.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 | from __future__ import divisionimport numpy as npimport matplotlib.pyplot as pltfrom sklearn.datasets import make_blobsfrom sklearn.discriminant_analysis import LinearDiscriminantAnalysisn_train = 20 # samples for trainingn_test = 200 # samples for testingn_averages = 50 # how often to repeat classificationn_features_max = 75 # maximum number of featuresstep = 4 # step size for the calculationdef generate_data(n_samples, n_features): """Generate random blob-ish data with noisy features. This returns an array of input data with shape `(n_samples, n_features)` and an array of `n_samples` target labels. Only one feature contains discriminative information, the other features contain only noise. """ X, y = make_blobs(n_samples=n_samples, n_features=1, centers=[[-2], [2]]) # add non-discriminative features if n_features > 1: X = np.hstack([X, np.random.randn(n_samples, n_features - 1)]) return X, yacc_clf1, acc_clf2 = [], []n_features_range = range(1, n_features_max + 1, step)for n_features in n_features_range: score_clf1, score_clf2 = 0, 0 for _ in range(n_averages): X, y = generate_data(n_train, n_features) clf1 = LinearDiscriminantAnalysis(solver='lsqr', shrinkage='auto').fit(X, y) clf2 = LinearDiscriminantAnalysis(solver='lsqr', shrinkage=None).fit(X, y) X, y = generate_data(n_test, n_features) score_clf1 += clf1.score(X, y) score_clf2 += clf2.score(X, y) acc_clf1.append(score_clf1 / n_averages) acc_clf2.append(score_clf2 / n_averages)features_samples_ratio = np.array(n_features_range) / n_trainplt.plot(features_samples_ratio, acc_clf1, linewidth=2, label="Linear Discriminant Analysis with shrinkage", color='navy')plt.plot(features_samples_ratio, acc_clf2, linewidth=2, label="Linear Discriminant Analysis", color='gold')plt.xlabel('n_features / n_samples')plt.ylabel('Classification accuracy')plt.legend(loc=1, prop={'size': 12})plt.suptitle('Linear Discriminant Analysis vs. \shrinkage Linear Discriminant Analysis (1 discriminative feature)')plt.show() |
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Download Python source code:
plot_lda.py
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