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SVM: Weighted samples#

Plot decision function of a weighted dataset, where the size of points is proportional to its weight.

The sample weighting rescales the C parameter, which means that the classifier puts more emphasis on getting these points right. The effect might often be subtle. To emphasize the effect here, we particularly increase the weight of the positive class, making the deformation of the decision boundary more visible.

Constant weights, Modified weights

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
importmatplotlib.pyplotasplt
importnumpyasnp
fromsklearn.datasetsimport make_classification
fromsklearn.inspectionimport DecisionBoundaryDisplay
fromsklearn.svmimport SVC
X, y = make_classification (
 n_samples=1_000,
 n_features=2,
 n_informative=2,
 n_redundant=0,
 n_clusters_per_class=1,
 class_sep=1.1,
 weights=[0.9, 0.1],
 random_state=0,
)
# down-sample for plotting
rng = np.random.RandomState (0)
plot_indices = rng.choice(np.arange (X.shape[0]), size=100, replace=True)
X_plot, y_plot = X[plot_indices], y[plot_indices]
defplot_decision_function(classifier, sample_weight, axis, title):
"""Plot the synthetic data and the classifier decision function. Points with
 larger sample_weight are mapped to larger circles in the scatter plot."""
 axis.scatter(
 X_plot[:, 0],
 X_plot[:, 1],
 c=y_plot,
 s=100 * sample_weight[plot_indices],
 alpha=0.9,
 cmap=plt.cm.bone,
 edgecolors="black",
 )
 DecisionBoundaryDisplay.from_estimator (
 classifier,
 X_plot,
 response_method="decision_function",
 alpha=0.75,
 ax=axis,
 cmap=plt.cm.bone,
 )
 axis.axis("off")
 axis.set_title(title)
# we define constant weights as expected by the plotting function
sample_weight_constant = np.ones (len(X))
# assign random weights to all points
sample_weight_modified = abs(rng.randn(len(X)))
# assign bigger weights to the positive class
positive_class_indices = np.asarray (y == 1).nonzero()[0]
sample_weight_modified[positive_class_indices] *= 15
# This model does not include sample weights.
clf_no_weights = SVC (gamma=1)
clf_no_weights.fit(X, y)
# This other model includes sample weights.
clf_weights = SVC (gamma=1)
clf_weights.fit(X, y, sample_weight=sample_weight_modified)
fig, axes = plt.subplots (1, 2, figsize=(14, 6))
plot_decision_function(
 clf_no_weights, sample_weight_constant, axes[0], "Constant weights"
)
plot_decision_function(clf_weights, sample_weight_modified, axes[1], "Modified weights")
plt.show ()