.. _sphx_glr_auto_examples_classification_plot_lda.py: ==================================================================== Normal and Shrinkage Linear Discriminant Analysis for classification ==================================================================== Shows how shrinkage improves classification. .. image:: /auto_examples/classification/images/sphx_glr_plot_lda_001.png :align: center .. code-block:: python from __future__ import division import numpy as np import matplotlib.pyplot as plt from sklearn.datasets import make_blobs from sklearn.discriminant_analysis import LinearDiscriminantAnalysis n_train = 20 # samples for training n_test = 200 # samples for testing n_averages = 50 # how often to repeat classification n_features_max = 75 # maximum number of features step = 4 # step size for the calculation def 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, y acc_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_train plt.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() **Total running time of the script:** (0 minutes 5.999 seconds) .. container:: sphx-glr-download **Download Python source code:** :download:`plot_lda.py ` .. container:: sphx-glr-download **Download IPython notebook:** :download:`plot_lda.ipynb `