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Plot Oneclass

========================================== One-class SVM with non-linear kernel (RBF)

An example using a one-class SVM for novelty detection.

ref:

One-class SVM <svm_outlier_detection> is an unsupervised algorithm that learns a decision function for novelty detection: classifying new data as similar or different to the training set.

Imports for One-Class SVM Novelty Detection

One-Class SVM learns a boundary that encloses the “normal” training data in feature space. Unlike standard SVM which requires labeled positive and negative examples, One-Class SVM is trained on a single class and detects novelties (anomalies) as points falling outside the learned boundary. The RBF kernel allows the boundary to take complex non-linear shapes that adapt to the data distribution.

Key parameters: The nu parameter is an upper bound on the fraction of training errors (points outside the boundary) and a lower bound on the fraction of support vectors – it controls how tightly the boundary wraps around the data. gamma controls the RBF kernel bandwidth, affecting boundary smoothness. Novelty detection is used in manufacturing quality control, fraud detection, and health monitoring where “abnormal” examples are rare or undefined during training.

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

# %%
import numpy as np

from sklearn import svm

# Generate train data
X = 0.3 * np.random.randn(100, 2)
X_train = np.r_[X + 2, X - 2]
# Generate some regular novel observations
X = 0.3 * np.random.randn(20, 2)
X_test = np.r_[X + 2, X - 2]
# Generate some abnormal novel observations
X_outliers = np.random.uniform(low=-4, high=4, size=(20, 2))

# fit the model
clf = svm.OneClassSVM(nu=0.1, kernel="rbf", gamma=0.1)
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

# %%
import matplotlib.font_manager
import matplotlib.lines as mlines
import matplotlib.pyplot as plt

from sklearn.inspection import DecisionBoundaryDisplay

_, ax = plt.subplots()

# generate grid for the boundary display
xx, yy = np.meshgrid(np.linspace(-5, 5, 10), np.linspace(-5, 5, 10))
X = np.concatenate([xx.reshape(-1, 1), yy.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="contourf",
    ax=ax,
    levels=[0, 10000],
    colors="palevioletred",
)
DecisionBoundaryDisplay.from_estimator(
    clf,
    X,
    response_method="decision_function",
    plot_method="contour",
    ax=ax,
    levels=[0],
    colors="darkred",
    linewidths=2,
)

s = 40
b1 = ax.scatter(X_train[:, 0], X_train[:, 1], c="white", s=s, edgecolors="k")
b2 = ax.scatter(X_test[:, 0], X_test[:, 1], c="blueviolet", s=s, edgecolors="k")
c = ax.scatter(X_outliers[:, 0], X_outliers[:, 1], c="gold", s=s, edgecolors="k")
plt.legend(
    [mlines.Line2D([], [], color="darkred"), b1, b2, c],
    [
        "learned frontier",
        "training observations",
        "new regular observations",
        "new abnormal observations",
    ],
    loc="upper left",
    prop=matplotlib.font_manager.FontProperties(size=11),
)
ax.set(
    xlabel=(
        f"error train: {n_error_train}/200 ; errors novel regular: {n_error_test}/40 ;"
        f" errors novel abnormal: {n_error_outliers}/40"
    ),
    title="Novelty Detection",
    xlim=(-5, 5),
    ylim=(-5, 5),
)
plt.show()