.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/linear_model/plot_sgdocsvm_vs_ocsvm.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_linear_model_plot_sgdocsvm_vs_ocsvm.py: ==================================================================== One-Class SVM versus One-Class SVM using Stochastic Gradient Descent ==================================================================== This example shows how to approximate the solution of :class:`sklearn.svm.OneClassSVM` in the case of an RBF kernel with :class:`sklearn.linear_model.SGDOneClassSVM`, a Stochastic Gradient Descent (SGD) version of the One-Class SVM. A kernel approximation is first used in order to apply :class:`sklearn.linear_model.SGDOneClassSVM` which implements a linear One-Class SVM using SGD. Note that :class:`sklearn.linear_model.SGDOneClassSVM` scales linearly with the number of samples whereas the complexity of a kernelized :class:`sklearn.svm.OneClassSVM` is at best quadratic with respect to the number of samples. It is not the purpose of this example to illustrate the benefits of such an approximation in terms of computation time but rather to show that we obtain similar results on a toy dataset. .. GENERATED FROM PYTHON SOURCE LINES 21-155 .. rst-class:: sphx-glr-horizontal * .. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_sgdocsvm_vs_ocsvm_001.png :alt: One Class SVM :srcset: /auto_examples/linear_model/images/sphx_glr_plot_sgdocsvm_vs_ocsvm_001.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/linear_model/images/sphx_glr_plot_sgdocsvm_vs_ocsvm_002.png :alt: Online One-Class SVM :srcset: /auto_examples/linear_model/images/sphx_glr_plot_sgdocsvm_vs_ocsvm_002.png :class: sphx-glr-multi-img .. code-block:: default import numpy as np import matplotlib.pyplot as plt import matplotlib from sklearn.svm import OneClassSVM from sklearn.linear_model import SGDOneClassSVM from sklearn.kernel_approximation import Nystroem from sklearn.pipeline import make_pipeline font = {"weight": "normal", "size": 15} matplotlib.rc("font", **font) random_state = 42 rng = np.random.RandomState(random_state) # Generate train data X = 0.3 * rng.randn(500, 2) X_train = np.r_[X + 2, X - 2] # Generate some regular novel observations X = 0.3 * rng.randn(20, 2) X_test = np.r_[X + 2, X - 2] # Generate some abnormal novel observations X_outliers = rng.uniform(low=-4, high=4, size=(20, 2)) xx, yy = np.meshgrid(np.linspace(-4.5, 4.5, 50), np.linspace(-4.5, 4.5, 50)) # OCSVM hyperparameters nu = 0.05 gamma = 2.0 # Fit the One-Class SVM clf = OneClassSVM(gamma=gamma, kernel="rbf", nu=nu) clf.fit(X_train) y_pred_train = clf.predict(X_train) y_pred_test = clf.predict(X_test) y_pred_outliers = clf.predict(X_outliers) n_error_train = y_pred_train[y_pred_train == -1].size n_error_test = y_pred_test[y_pred_test == -1].size n_error_outliers = y_pred_outliers[y_pred_outliers == 1].size Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()]) Z = Z.reshape(xx.shape) # Fit the One-Class SVM using a kernel approximation and SGD transform = Nystroem(gamma=gamma, random_state=random_state) clf_sgd = SGDOneClassSVM( nu=nu, shuffle=True, fit_intercept=True, random_state=random_state, tol=1e-4 ) pipe_sgd = make_pipeline(transform, clf_sgd) pipe_sgd.fit(X_train) y_pred_train_sgd = pipe_sgd.predict(X_train) y_pred_test_sgd = pipe_sgd.predict(X_test) y_pred_outliers_sgd = pipe_sgd.predict(X_outliers) n_error_train_sgd = y_pred_train_sgd[y_pred_train_sgd == -1].size n_error_test_sgd = y_pred_test_sgd[y_pred_test_sgd == -1].size n_error_outliers_sgd = y_pred_outliers_sgd[y_pred_outliers_sgd == 1].size Z_sgd = pipe_sgd.decision_function(np.c_[xx.ravel(), yy.ravel()]) Z_sgd = Z_sgd.reshape(xx.shape) # plot the level sets of the decision function plt.figure(figsize=(9, 6)) plt.title("One Class SVM") plt.contourf(xx, yy, Z, levels=np.linspace(Z.min(), 0, 7), cmap=plt.cm.PuBu) a = plt.contour(xx, yy, Z, levels=[0], linewidths=2, colors="darkred") plt.contourf(xx, yy, Z, levels=[0, Z.max()], colors="palevioletred") s = 20 b1 = plt.scatter(X_train[:, 0], X_train[:, 1], c="white", s=s, edgecolors="k") b2 = plt.scatter(X_test[:, 0], X_test[:, 1], c="blueviolet", s=s, edgecolors="k") c = plt.scatter(X_outliers[:, 0], X_outliers[:, 1], c="gold", s=s, edgecolors="k") plt.axis("tight") plt.xlim((-4.5, 4.5)) plt.ylim((-4.5, 4.5)) plt.legend( [a.collections[0], b1, b2, c], [ "learned frontier", "training observations", "new regular observations", "new abnormal observations", ], loc="upper left", ) plt.xlabel( "error train: %d/%d; errors novel regular: %d/%d; errors novel abnormal: %d/%d" % ( n_error_train, X_train.shape[0], n_error_test, X_test.shape[0], n_error_outliers, X_outliers.shape[0], ) ) plt.show() plt.figure(figsize=(9, 6)) plt.title("Online One-Class SVM") plt.contourf(xx, yy, Z_sgd, levels=np.linspace(Z_sgd.min(), 0, 7), cmap=plt.cm.PuBu) a = plt.contour(xx, yy, Z_sgd, levels=[0], linewidths=2, colors="darkred") plt.contourf(xx, yy, Z_sgd, levels=[0, Z_sgd.max()], colors="palevioletred") s = 20 b1 = plt.scatter(X_train[:, 0], X_train[:, 1], c="white", s=s, edgecolors="k") b2 = plt.scatter(X_test[:, 0], X_test[:, 1], c="blueviolet", s=s, edgecolors="k") c = plt.scatter(X_outliers[:, 0], X_outliers[:, 1], c="gold", s=s, edgecolors="k") plt.axis("tight") plt.xlim((-4.5, 4.5)) plt.ylim((-4.5, 4.5)) plt.legend( [a.collections[0], b1, b2, c], [ "learned frontier", "training observations", "new regular observations", "new abnormal observations", ], loc="upper left", ) plt.xlabel( "error train: %d/%d; errors novel regular: %d/%d; errors novel abnormal: %d/%d" % ( n_error_train_sgd, X_train.shape[0], n_error_test_sgd, X_test.shape[0], n_error_outliers_sgd, X_outliers.shape[0], ) ) plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.270 seconds) .. _sphx_glr_download_auto_examples_linear_model_plot_sgdocsvm_vs_ocsvm.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/1.0.X?urlpath=lab/tree/notebooks/auto_examples/linear_model/plot_sgdocsvm_vs_ocsvm.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_sgdocsvm_vs_ocsvm.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_sgdocsvm_vs_ocsvm.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_