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Plot Linearsvc Support Vectors

===================================== Plot the support vectors in LinearSVC

Unlike SVC (based on LIBSVM), LinearSVC (based on LIBLINEAR) does not provide the support vectors. This example demonstrates how to obtain the support vectors in LinearSVC.

Imports for Extracting Support Vectors from LinearSVC

LinearSVC (based on LIBLINEAR) does not directly expose support_vectors_ like SVC (based on LIBSVM), but support vectors can be recovered by computing the decision function and identifying samples within the margin (where |decision_function| <= 1). These are the samples that would be support vectors in an equivalent SVC(kernel='linear') model.

Why this matters: Support vectors are the critical training points that define the decision boundary. Knowing which samples are support vectors helps with model interpretation, data debugging (are outliers becoming support vectors?), and understanding model sensitivity. By comparing results at different C values, we see that smaller C produces wider margins with more support vectors, while larger C produces narrower margins with fewer support vectors – directly illustrating the regularization-margin tradeoff.

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

import matplotlib.pyplot as plt
import numpy as np

from sklearn.datasets import make_blobs
from sklearn.inspection import DecisionBoundaryDisplay
from sklearn.svm import LinearSVC

X, y = make_blobs(n_samples=40, centers=2, random_state=0)

plt.figure(figsize=(10, 5))
for i, C in enumerate([1, 100]):
    # "hinge" is the standard SVM loss
    clf = LinearSVC(C=C, loss="hinge", random_state=42).fit(X, y)
    # obtain the support vectors through the decision function
    decision_function = clf.decision_function(X)
    # we can also calculate the decision function manually
    # decision_function = np.dot(X, clf.coef_[0]) + clf.intercept_[0]
    # The support vectors are the samples that lie within the margin
    # boundaries, whose size is conventionally constrained to 1
    support_vector_indices = (np.abs(decision_function) <= 1 + 1e-15).nonzero()[0]
    support_vectors = X[support_vector_indices]

    plt.subplot(1, 2, i + 1)
    plt.scatter(X[:, 0], X[:, 1], c=y, s=30, cmap=plt.cm.Paired)
    ax = plt.gca()
    DecisionBoundaryDisplay.from_estimator(
        clf,
        X,
        ax=ax,
        grid_resolution=50,
        plot_method="contour",
        colors="k",
        levels=[-1, 0, 1],
        alpha=0.5,
        linestyles=["--", "-", "--"],
    )
    plt.scatter(
        support_vectors[:, 0],
        support_vectors[:, 1],
        s=100,
        linewidth=1,
        facecolors="none",
        edgecolors="k",
    )
    plt.title("C=" + str(C))
plt.tight_layout()
plt.show()