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SVM Tie Breaking Example#

Tie breaking is costly if decision_function_shape='ovr', and therefore it is not enabled by default. This example illustrates the effect of the break_ties parameter for a multiclass classification problem and decision_function_shape='ovr'.

The two plots differ only in the area in the middle where the classes are tied. If break_ties=False, all input in that area would be classified as one class, whereas if break_ties=True, the tie-breaking mechanism will create a non-convex decision boundary in that area.

break_ties = False, break_ties = True

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
importmatplotlib.pyplotasplt
importnumpyasnp
fromsklearn.datasetsimport make_blobs
fromsklearn.svmimport SVC
X, y = make_blobs (random_state=27)
fig, sub = plt.subplots (2, 1, figsize=(5, 8))
titles = ("break_ties = False", "break_ties = True")
for break_ties, title, ax in zip((False, True), titles, sub.flatten()):
 svm = SVC (
 kernel="linear", C=1, break_ties=break_ties, decision_function_shape="ovr"
 ).fit(X, y)
 xlim = [X[:, 0].min(), X[:, 0].max()]
 ylim = [X[:, 1].min(), X[:, 1].max()]
 xs = np.linspace (xlim[0], xlim[1], 1000)
 ys = np.linspace (ylim[0], ylim[1], 1000)
 xx, yy = np.meshgrid (xs, ys)
 pred = svm.predict(np.c_ [xx.ravel(), yy.ravel()])
 colors = [plt.cm.Accent(i) for i in [0, 4, 7]]
 points = ax.scatter(X[:, 0], X[:, 1], c=y, cmap="Accent")
 classes = [(0, 1), (0, 2), (1, 2)]
 line = np.linspace (X[:, 1].min() - 5, X[:, 1].max() + 5)
 ax.imshow(
 -pred.reshape(xx.shape),
 cmap="Accent",
 alpha=0.2,
 extent=(xlim[0], xlim[1], ylim[1], ylim[0]),
 )
 for coef, intercept, col in zip(svm.coef_, svm.intercept_, classes):
 line2 = -(line * coef[1] + intercept) / coef[0]
 ax.plot(line2, line, "-", c=colors[col[0]])
 ax.plot(line2, line, "--", c=colors[col[1]])
 ax.set_xlim(xlim)
 ax.set_ylim(ylim)
 ax.set_title(title)
 ax.set_aspect("equal")
plt.show ()