Toggle Menu
Prev Up Next

scikit-learn 1.3.2
Other versions

Please cite us if you use the software.

Note

Go to the end to download the full example code or to run this example in your browser via Binder

# One-Class SVM versus One-Class SVM using Stochastic Gradient Descent

This example shows how to approximate the solution of `sklearn.svm.OneClassSVM` in the case of an RBF kernel with `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 `sklearn.linear_model.SGDOneClassSVM` which implements a linear One-Class SVM using SGD.

Note that `sklearn.linear_model.SGDOneClassSVM` scales linearly with the number of samples whereas the complexity of a kernelized `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.

    /root/scikit-learn-1.3.2/examples/linear_model/plot_sgdocsvm_vs_ocsvm.py:99: MatplotlibDeprecationWarning:

    The collections attribute was deprecated in Matplotlib 3.8 and will be removed two minor releases later.

    /root/scikit-learn-1.3.2/examples/linear_model/plot_sgdocsvm_vs_ocsvm.py:135: MatplotlibDeprecationWarning:

    The collections attribute was deprecated in Matplotlib 3.8 and will be removed two minor releases later.

    import matplotlib
    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.kernel_approximation import Nystroem
    from sklearn.linear_model import SGDOneClassSVM
    from sklearn.pipeline import make_pipeline
    from sklearn.svm import OneClassSVM

    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()

Total running time of the script: (0 minutes 0.262 seconds)

Gallery generated by Sphinx-Gallery