sklearn.metrics.hinge_loss

sklearn.metrics.hinge_loss(y_true, pred_decision, labels=None, sample_weight=None)

Average hinge loss (non-regularized)

In binary class case, assuming labels in y_true are encoded with +1 and -1, when a prediction mistake is made, margin = y_true * pred_decision is always negative (since the signs disagree), implying 1 - margin is always greater than 1. The cumulated hinge loss is therefore an upper bound of the number of mistakes made by the classifier.

In multiclass case, the function expects that either all the labels are included in y_true or an optional labels argument is provided which contains all the labels. The multilabel margin is calculated according to Crammer-Singer’s method. As in the binary case, the cumulated hinge loss is an upper bound of the number of mistakes made by the classifier.

Read more in the User Guide.

Parameters:

y_true : array, shape = [n_samples]

True target, consisting of integers of two values. The positive label must be greater than the negative label.

pred_decision : array, shape = [n_samples] or [n_samples, n_classes]

Predicted decisions, as output by decision_function (floats).

labels : array, optional, default None

Contains all the labels for the problem. Used in multiclass hinge loss.

sample_weight : array-like of shape = [n_samples], optional

Sample weights.

Returns:

loss : float

References

[R167]

Wikipedia entry on the Hinge loss

[R168]

Koby Crammer, Yoram Singer. On the Algorithmic Implementation of Multiclass Kernel-based Vector Machines. Journal of Machine Learning Research 2, (2001), 265-292

[R169]

L1 AND L2 Regularization for Multiclass Hinge Loss Models by Robert C. Moore, John DeNero.

Examples

>>> from sklearn import svm
>>> from sklearn.metrics import hinge_loss
>>> X = [[0], [1]]
>>> y = [-1, 1]
>>> est = svm.LinearSVC(random_state=0)
>>> est.fit(X, y)
LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,
     intercept_scaling=1, loss='squared_hinge', max_iter=1000,
     multi_class='ovr', penalty='l2', random_state=0, tol=0.0001,
     verbose=0)
>>> pred_decision = est.decision_function([[-2], [3], [0.5]])
>>> pred_decision  
array([-2.18...,  2.36...,  0.09...])
>>> hinge_loss([-1, 1, 1], pred_decision)  
0.30...

In the multiclass case:

>>> X = np.array([[0], [1], [2], [3]])
>>> Y = np.array([0, 1, 2, 3])
>>> labels = np.array([0, 1, 2, 3])
>>> est = svm.LinearSVC()
>>> est.fit(X, Y)
LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,
     intercept_scaling=1, loss='squared_hinge', max_iter=1000,
     multi_class='ovr', penalty='l2', random_state=None, tol=0.0001,
     verbose=0)
>>> pred_decision = est.decision_function([[-1], [2], [3]])
>>> y_true = [0, 2, 3]
>>> hinge_loss(y_true, pred_decision, labels)  
0.56...