# HingeLoss Class

## Definition

Hinge Loss, commonly used in classification tasks.

public sealed class HingeLoss : Microsoft.ML.Trainers.ILossFunction<float,float>, Microsoft.ML.Trainers.ISupportSdcaClassificationLoss
type HingeLoss = class
interface ISupportSdcaClassificationLoss
interface ISupportSdcaLoss
interface IScalarLoss
interface ILossFunction<single, single>
interface IClassificationLoss
Public NotInheritable Class HingeLoss
Implements ILossFunction(Of Single, Single), ISupportSdcaClassificationLoss
Inheritance
HingeLoss
Implements

## Remarks

The Hinge Loss function is defined as:

$L(\hat{y}, y) = max(0, m - y\hat{y})$

where $\hat{y}$ is the predicted score, $y \in \{-1, 1\}$ is the true label, and $m$ is the margin parameter set to 1 by default.

Note that the labels used in this calculation are -1 and 1, unlike Log Loss, where the labels used are 0 and 1. Also unlike Log Loss, $\hat{y}$ is the raw predicted score, not the predicted probability (which is calculated by applying a sigmoid function to the predicted score).

While the hinge loss function is both convex and continuous, it is not smooth (that is not differentiable) at $y\hat{y} = m$. Consequently, it cannot be used with gradient descent methods or stochastic gradient descent methods, which rely on differentiability over the entire domain.

For more, see Hinge Loss for classification.