Normal, Ledoit-Wolf and OAS Linear Discriminant Analysis for classification

This example illustrates how the Ledoit-Wolf and Oracle Shrinkage Approximating (OAS) estimators of covariance can improve classification.

Linear Discriminant Analysis vs.  Shrinkage Linear Discriminant Analysis vs.  OAS Linear Discriminant Analysis (1 discriminative feature)
import numpy as np
import matplotlib.pyplot as plt

from sklearn.datasets import make_blobs
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
from sklearn.covariance import OAS

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, acc_clf3 = [], [], []
n_features_range = range(1, n_features_max + 1, step)
for n_features in n_features_range:
    score_clf1, score_clf2, score_clf3 = 0, 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)
        oa = OAS(store_precision=False, assume_centered=False)
        clf3 = LinearDiscriminantAnalysis(solver='lsqr',
                                          covariance_estimator=oa).fit(X, y)

        X, y = generate_data(n_test, n_features)
        score_clf1 += clf1.score(X, y)
        score_clf2 += clf2.score(X, y)
        score_clf3 += clf3.score(X, y)

    acc_clf1.append(score_clf1 / n_averages)
    acc_clf2.append(score_clf2 / n_averages)
    acc_clf3.append(score_clf3 / 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 Ledoit Wolf", color='navy')
plt.plot(features_samples_ratio, acc_clf2, linewidth=2,
         label="Linear Discriminant Analysis", color='gold')
plt.plot(features_samples_ratio, acc_clf3, linewidth=2,
         label="Linear Discriminant Analysis with OAS", color='red')

plt.xlabel('n_features / n_samples')
plt.ylabel('Classification accuracy')

plt.legend(loc=3, prop={'size': 12})
plt.suptitle('Linear Discriminant Analysis vs. ' + '\n'
             + 'Shrinkage Linear Discriminant Analysis vs. ' + '\n'
             + 'OAS Linear Discriminant Analysis (1 discriminative feature)')

Total running time of the script: ( 0 minutes 6.732 seconds)

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