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Plot Sgdocsvm Vs Ocsvm

==================================================================== 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.

Imports for One-Class SVM vs. SGD One-Class SVM

One-Class SVM is an unsupervised anomaly detection algorithm that learns a decision boundary enclosing the “normal” training data. New samples falling outside this boundary are flagged as anomalies. The kernel version (OneClassSVM with RBF kernel) produces flexible non-linear boundaries but has O(n^2) to O(n^3) training complexity, making it impractical for large datasets.

The SGD approximation: SGDOneClassSVM provides a scalable alternative by combining the Nystroem kernel approximation (which maps data to a finite-dimensional feature space that approximates the RBF kernel) with a linear One-Class SVM trained via Stochastic Gradient Descent. This reduces training complexity to O(n), enabling anomaly detection on datasets with millions of samples. The nu parameter controls the fraction of training points allowed to be outside the boundary, serving as an upper bound on the expected proportion of outliers. This approach is widely used in fraud detection, network intrusion detection, and manufacturing quality control.

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause

# %%
import matplotlib
import matplotlib.lines as mlines
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))

# 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

# 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


# %%
from sklearn.inspection import DecisionBoundaryDisplay

_, ax = plt.subplots(figsize=(9, 6))

xx, yy = np.meshgrid(np.linspace(-4.5, 4.5, 50), np.linspace(-4.5, 4.5, 50))
X = np.concatenate([xx.ravel().reshape(-1, 1), yy.ravel().reshape(-1, 1)], axis=1)
DecisionBoundaryDisplay.from_estimator(
    clf,
    X,
    response_method="decision_function",
    plot_method="contourf",
    ax=ax,
    cmap="PuBu",
)
DecisionBoundaryDisplay.from_estimator(
    clf,
    X,
    response_method="decision_function",
    plot_method="contour",
    ax=ax,
    linewidths=2,
    colors="darkred",
    levels=[0],
)
DecisionBoundaryDisplay.from_estimator(
    clf,
    X,
    response_method="decision_function",
    plot_method="contourf",
    ax=ax,
    colors="palevioletred",
    levels=[0, clf.decision_function(X).max()],
)

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")

ax.set(
    title="One-Class SVM",
    xlim=(-4.5, 4.5),
    ylim=(-4.5, 4.5),
    xlabel=(
        f"error train: {n_error_train}/{X_train.shape[0]}; "
        f"errors novel regular: {n_error_test}/{X_test.shape[0]}; "
        f"errors novel abnormal: {n_error_outliers}/{X_outliers.shape[0]}"
    ),
)
_ = ax.legend(
    [mlines.Line2D([], [], color="darkred", label="learned frontier"), b1, b2, c],
    [
        "learned frontier",
        "training observations",
        "new regular observations",
        "new abnormal observations",
    ],
    loc="upper left",
)

# %%
_, ax = plt.subplots(figsize=(9, 6))

xx, yy = np.meshgrid(np.linspace(-4.5, 4.5, 50), np.linspace(-4.5, 4.5, 50))
X = np.concatenate([xx.ravel().reshape(-1, 1), yy.ravel().reshape(-1, 1)], axis=1)
DecisionBoundaryDisplay.from_estimator(
    pipe_sgd,
    X,
    response_method="decision_function",
    plot_method="contourf",
    ax=ax,
    cmap="PuBu",
)
DecisionBoundaryDisplay.from_estimator(
    pipe_sgd,
    X,
    response_method="decision_function",
    plot_method="contour",
    ax=ax,
    linewidths=2,
    colors="darkred",
    levels=[0],
)
DecisionBoundaryDisplay.from_estimator(
    pipe_sgd,
    X,
    response_method="decision_function",
    plot_method="contourf",
    ax=ax,
    colors="palevioletred",
    levels=[0, pipe_sgd.decision_function(X).max()],
)

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")

ax.set(
    title="Online One-Class SVM",
    xlim=(-4.5, 4.5),
    ylim=(-4.5, 4.5),
    xlabel=(
        f"error train: {n_error_train_sgd}/{X_train.shape[0]}; "
        f"errors novel regular: {n_error_test_sgd}/{X_test.shape[0]}; "
        f"errors novel abnormal: {n_error_outliers_sgd}/{X_outliers.shape[0]}"
    ),
)
ax.legend(
    [mlines.Line2D([], [], color="darkred", label="learned frontier"), b1, b2, c],
    [
        "learned frontier",
        "training observations",
        "new regular observations",
        "new abnormal observations",
    ],
    loc="upper left",
)
plt.show()