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Hinge loss
Loss function in machine learning / From Wikipedia, the free encyclopedia
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In machine learning, the hinge loss is a loss function used for training classifiers. The hinge loss is used for "maximum-margin" classification, most notably for support vector machines (SVMs).[1]
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For an intended output t = ±1 and a classifier score y, the hinge loss of the prediction y is defined as
Note that should be the "raw" output of the classifier's decision function, not the predicted class label. For instance, in linear SVMs,
, where
are the parameters of the hyperplane and
is the input variable(s).
When t and y have the same sign (meaning y predicts the right class) and , the hinge loss
. When they have opposite signs,
increases linearly with y, and similarly if
, even if it has the same sign (correct prediction, but not by enough margin).