105 lines
3.0 KiB
Python
105 lines
3.0 KiB
Python
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"""
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===========================================================================
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Normal, Ledoit-Wolf and OAS Linear Discriminant Analysis for classification
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===========================================================================
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This example illustrates how the Ledoit-Wolf and Oracle Approximating
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Shrinkage (OAS) estimators of covariance can improve classification.
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"""
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import matplotlib.pyplot as plt
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import numpy as np
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from sklearn.covariance import OAS
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from sklearn.datasets import make_blobs
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from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
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n_train = 20 # samples for training
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n_test = 200 # samples for testing
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n_averages = 50 # how often to repeat classification
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n_features_max = 75 # maximum number of features
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step = 4 # step size for the calculation
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def generate_data(n_samples, n_features):
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"""Generate random blob-ish data with noisy features.
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This returns an array of input data with shape `(n_samples, n_features)`
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and an array of `n_samples` target labels.
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Only one feature contains discriminative information, the other features
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contain only noise.
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"""
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X, y = make_blobs(n_samples=n_samples, n_features=1, centers=[[-2], [2]])
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# add non-discriminative features
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if n_features > 1:
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X = np.hstack([X, np.random.randn(n_samples, n_features - 1)])
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return X, y
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acc_clf1, acc_clf2, acc_clf3 = [], [], []
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n_features_range = range(1, n_features_max + 1, step)
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for n_features in n_features_range:
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score_clf1, score_clf2, score_clf3 = 0, 0, 0
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for _ in range(n_averages):
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X, y = generate_data(n_train, n_features)
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clf1 = LinearDiscriminantAnalysis(solver="lsqr", shrinkage=None).fit(X, y)
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clf2 = LinearDiscriminantAnalysis(solver="lsqr", shrinkage="auto").fit(X, y)
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oa = OAS(store_precision=False, assume_centered=False)
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clf3 = LinearDiscriminantAnalysis(solver="lsqr", covariance_estimator=oa).fit(
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X, y
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)
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X, y = generate_data(n_test, n_features)
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score_clf1 += clf1.score(X, y)
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score_clf2 += clf2.score(X, y)
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score_clf3 += clf3.score(X, y)
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acc_clf1.append(score_clf1 / n_averages)
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acc_clf2.append(score_clf2 / n_averages)
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acc_clf3.append(score_clf3 / n_averages)
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features_samples_ratio = np.array(n_features_range) / n_train
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plt.plot(
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features_samples_ratio,
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acc_clf1,
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linewidth=2,
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label="LDA",
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color="gold",
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linestyle="solid",
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)
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plt.plot(
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features_samples_ratio,
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acc_clf2,
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linewidth=2,
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label="LDA with Ledoit Wolf",
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color="navy",
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linestyle="dashed",
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)
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plt.plot(
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features_samples_ratio,
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acc_clf3,
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linewidth=2,
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label="LDA with OAS",
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color="red",
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linestyle="dotted",
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)
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plt.xlabel("n_features / n_samples")
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plt.ylabel("Classification accuracy")
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plt.legend(loc="lower left")
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plt.ylim((0.65, 1.0))
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plt.suptitle(
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"LDA (Linear Discriminant Analysis) vs. "
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+ "\n"
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+ "LDA with Ledoit Wolf vs. "
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+ "\n"
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+ "LDA with OAS (1 discriminative feature)"
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)
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plt.show()
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