The vertical axis represents the value of the Hinge loss (in blue) and zero-one loss (in green) for fixed t = 1, while the horizontal axis represents the value of the prediction y. The plot shows that the Hinge loss penalizes predictions y < 1, corresponding to the notion of a margin in a support vector machine.
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]
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).
^Rosasco, L.; De Vito, E. D.; Caponnetto, A.; Piana, M.; Verri, A. (2004). "Are Loss Functions All the Same?" (PDF). Neural Computation. 16 (5): 1063–1076. CiteSeerX 10.1.1.109.6786. doi:10.1162/089976604773135104. PMID 15070510.
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