155 lines
5.1 KiB
Python
155 lines
5.1 KiB
Python
"""
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====================================================================
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One-Class SVM versus One-Class SVM using Stochastic Gradient Descent
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====================================================================
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This example shows how to approximate the solution of
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:class:`sklearn.svm.OneClassSVM` in the case of an RBF kernel with
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:class:`sklearn.linear_model.SGDOneClassSVM`, a Stochastic Gradient Descent
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(SGD) version of the One-Class SVM. A kernel approximation is first used in
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order to apply :class:`sklearn.linear_model.SGDOneClassSVM` which implements a
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linear One-Class SVM using SGD.
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Note that :class:`sklearn.linear_model.SGDOneClassSVM` scales linearly with
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the number of samples whereas the complexity of a kernelized
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:class:`sklearn.svm.OneClassSVM` is at best quadratic with respect to the
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number of samples. It is not the purpose of this example to illustrate the
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benefits of such an approximation in terms of computation time but rather to
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show that we obtain similar results on a toy dataset.
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""" # noqa: E501
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import numpy as np
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import matplotlib.pyplot as plt
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import matplotlib
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from sklearn.svm import OneClassSVM
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from sklearn.linear_model import SGDOneClassSVM
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from sklearn.kernel_approximation import Nystroem
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from sklearn.pipeline import make_pipeline
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font = {"weight": "normal", "size": 15}
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matplotlib.rc("font", **font)
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random_state = 42
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rng = np.random.RandomState(random_state)
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# Generate train data
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X = 0.3 * rng.randn(500, 2)
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X_train = np.r_[X + 2, X - 2]
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# Generate some regular novel observations
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X = 0.3 * rng.randn(20, 2)
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X_test = np.r_[X + 2, X - 2]
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# Generate some abnormal novel observations
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X_outliers = rng.uniform(low=-4, high=4, size=(20, 2))
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xx, yy = np.meshgrid(np.linspace(-4.5, 4.5, 50), np.linspace(-4.5, 4.5, 50))
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# OCSVM hyperparameters
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nu = 0.05
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gamma = 2.0
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# Fit the One-Class SVM
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clf = OneClassSVM(gamma=gamma, kernel="rbf", nu=nu)
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clf.fit(X_train)
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y_pred_train = clf.predict(X_train)
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y_pred_test = clf.predict(X_test)
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y_pred_outliers = clf.predict(X_outliers)
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n_error_train = y_pred_train[y_pred_train == -1].size
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n_error_test = y_pred_test[y_pred_test == -1].size
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n_error_outliers = y_pred_outliers[y_pred_outliers == 1].size
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Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
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Z = Z.reshape(xx.shape)
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# Fit the One-Class SVM using a kernel approximation and SGD
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transform = Nystroem(gamma=gamma, random_state=random_state)
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clf_sgd = SGDOneClassSVM(
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nu=nu, shuffle=True, fit_intercept=True, random_state=random_state, tol=1e-4
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)
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pipe_sgd = make_pipeline(transform, clf_sgd)
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pipe_sgd.fit(X_train)
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y_pred_train_sgd = pipe_sgd.predict(X_train)
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y_pred_test_sgd = pipe_sgd.predict(X_test)
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y_pred_outliers_sgd = pipe_sgd.predict(X_outliers)
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n_error_train_sgd = y_pred_train_sgd[y_pred_train_sgd == -1].size
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n_error_test_sgd = y_pred_test_sgd[y_pred_test_sgd == -1].size
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n_error_outliers_sgd = y_pred_outliers_sgd[y_pred_outliers_sgd == 1].size
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Z_sgd = pipe_sgd.decision_function(np.c_[xx.ravel(), yy.ravel()])
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Z_sgd = Z_sgd.reshape(xx.shape)
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# plot the level sets of the decision function
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plt.figure(figsize=(9, 6))
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plt.title("One Class SVM")
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plt.contourf(xx, yy, Z, levels=np.linspace(Z.min(), 0, 7), cmap=plt.cm.PuBu)
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a = plt.contour(xx, yy, Z, levels=[0], linewidths=2, colors="darkred")
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plt.contourf(xx, yy, Z, levels=[0, Z.max()], colors="palevioletred")
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s = 20
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b1 = plt.scatter(X_train[:, 0], X_train[:, 1], c="white", s=s, edgecolors="k")
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b2 = plt.scatter(X_test[:, 0], X_test[:, 1], c="blueviolet", s=s, edgecolors="k")
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c = plt.scatter(X_outliers[:, 0], X_outliers[:, 1], c="gold", s=s, edgecolors="k")
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plt.axis("tight")
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plt.xlim((-4.5, 4.5))
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plt.ylim((-4.5, 4.5))
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plt.legend(
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[a.collections[0], b1, b2, c],
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[
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"learned frontier",
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"training observations",
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"new regular observations",
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"new abnormal observations",
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],
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loc="upper left",
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)
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plt.xlabel(
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"error train: %d/%d; errors novel regular: %d/%d; errors novel abnormal: %d/%d"
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% (
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n_error_train,
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X_train.shape[0],
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n_error_test,
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X_test.shape[0],
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n_error_outliers,
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X_outliers.shape[0],
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)
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)
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plt.show()
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plt.figure(figsize=(9, 6))
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plt.title("Online One-Class SVM")
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plt.contourf(xx, yy, Z_sgd, levels=np.linspace(Z_sgd.min(), 0, 7), cmap=plt.cm.PuBu)
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a = plt.contour(xx, yy, Z_sgd, levels=[0], linewidths=2, colors="darkred")
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plt.contourf(xx, yy, Z_sgd, levels=[0, Z_sgd.max()], colors="palevioletred")
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s = 20
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b1 = plt.scatter(X_train[:, 0], X_train[:, 1], c="white", s=s, edgecolors="k")
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b2 = plt.scatter(X_test[:, 0], X_test[:, 1], c="blueviolet", s=s, edgecolors="k")
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c = plt.scatter(X_outliers[:, 0], X_outliers[:, 1], c="gold", s=s, edgecolors="k")
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plt.axis("tight")
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plt.xlim((-4.5, 4.5))
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plt.ylim((-4.5, 4.5))
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plt.legend(
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[a.collections[0], b1, b2, c],
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[
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"learned frontier",
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"training observations",
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"new regular observations",
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"new abnormal observations",
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],
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loc="upper left",
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)
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plt.xlabel(
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"error train: %d/%d; errors novel regular: %d/%d; errors novel abnormal: %d/%d"
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% (
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n_error_train_sgd,
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X_train.shape[0],
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n_error_test_sgd,
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X_test.shape[0],
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n_error_outliers_sgd,
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X_outliers.shape[0],
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)
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)
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plt.show()
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