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

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

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

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

importnumpyasnp
fromsklearnimport 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

importmatplotlib.font_manager
importmatplotlib.linesasmlines
importmatplotlib.pyplotasplt
fromsklearn.inspectionimport 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 ()