Squared Hinge-loss for large margin classification. More...

#include <shark/ObjectiveFunctions/Loss/SquaredHingeLoss.h>

Inheritance diagram for shark::SquaredHingeLoss:

Public Member Functions
	SquaredHingeLoss ()
	constructor

std::string	name () const
	Returns class name "HingeLoss".

double	eval (BatchLabelType const &labels, BatchOutputType const &predictions) const
	calculates the sum of all

double	evalDerivative (BatchLabelType const &labels, BatchOutputType const &predictions, BatchOutputType &gradient) const
	evaluate the loss and the derivative w.r.t. the prediction

Public Member Functions inherited from shark::AbstractLoss< unsigned int, RealVector >
	AbstractLoss ()

virtual double	eval (ConstLabelReference target, ConstOutputReference prediction) const
	evaluate the loss for a target and a prediction

double	eval (Data< LabelType > const &targets, Data< OutputType > const &predictions) const

virtual double	evalDerivative (ConstLabelReference target, ConstOutputReference prediction, OutputType &gradient) const
	evaluate the loss and its derivative for a target and a prediction

virtual double	evalDerivative (ConstLabelReference target, ConstOutputReference prediction, OutputType &gradient, MatrixType &hessian) const
	evaluate the loss and its first and second derivative for a target and a prediction

double	operator() (LabelType const &target, OutputType const &prediction) const
	evaluate the loss for a target and a prediction

double	operator() (BatchLabelType const &target, BatchOutputType const &prediction) const

Public Member Functions inherited from shark::AbstractCost< LabelT, OutputT >
virtual	~AbstractCost ()

const Features &	features () const

virtual void	updateFeatures ()

bool	hasFirstDerivative () const
	returns true when the first parameter derivative is implemented

bool	isLossFunction () const
	returns true when the cost function is in fact a loss function

virtual double	eval (Data< LabelType > const &targets, Data< OutputType > const &predictions) const =0

double	operator() (Data< LabelType > const &targets, Data< OutputType > const &predictions) const

Public Member Functions inherited from shark::INameable
virtual	~INameable ()

Additional Inherited Members
Public Types inherited from shark::AbstractLoss< unsigned int, RealVector >
typedef RealVector	OutputType

typedef unsigned int	LabelType

typedef RealMatrix	MatrixType

typedef Batch< OutputType >::type	BatchOutputType

typedef Batch< LabelType >::type	BatchLabelType

typedef ConstProxyReference< LabelTypeconst >::type	ConstLabelReference
	Const references to LabelType.

typedef ConstProxyReference< OutputTypeconst >::type	ConstOutputReference
	Const references to OutputType.

Public Types inherited from shark::AbstractCost< LabelT, OutputT >
enum	Feature { HAS_FIRST_DERIVATIVE = 1 , HAS_SECOND_DERIVATIVE = 2 , IS_LOSS_FUNCTION = 4 }
	list of features a cost function can have More...

typedef OutputT	OutputType

typedef LabelT	LabelType

typedef Batch< OutputType >::type	BatchOutputType

typedef Batch< LabelType >::type	BatchLabelType

typedef TypedFlags< Feature >	Features

typedef TypedFeatureNotAvailableException< Feature >	FeatureNotAvailableException

Protected Attributes inherited from shark::AbstractCost< LabelT, OutputT >
Features	m_features

Detailed Description

Squared Hinge-loss for large margin classification.

The squared hinge loss for two class problems is defined as \( L_i = 1/2\max \{ 0 , (1- y_i f(x_i))^2 \} \) where \( y_i \in \{-1,1} \) is the label and \( f(x_i) \) is the prediction of the model for the ith input. The loss introduces the concept of a margin, that is, the point should not only be correctly classified but also not too close to the decision boundary. Therefore even correctly classified points are getting punished.

for multi class problems the concept of sums of the relative margin is used: \( L_i = 1/2 \sum_{c \neq y_i} \max \{ 0 , 1- 1/2 (f_{y_i}(x_i)- f_c(x_i) \} \). This loss requires that there is a margin between the different class outputs and the functions needs as many outputs as classes. the pre-factor 1/2 ensures that in the 2 class 2 output case with a linear function the value of loss is the same as in the single output version.

The loss is implemented for class labels 0,1,...,n, even in the binary cases.

The difference to the normal hinge loss is, that the squared hinge-loss is always differentiable. However compared to the hinge loss, small margin violations are not as much punished - but big deviations are punished much stronger.

Definition at line 58 of file SquaredHingeLoss.h.

Constructor & Destructor Documentation

◆ SquaredHingeLoss()

shark::SquaredHingeLoss::SquaredHingeLoss ( )

inline

constructor

Definition at line 62 of file SquaredHingeLoss.h.

References shark::AbstractCost< LabelT, OutputT >::m_features.

Member Function Documentation

◆ eval()

double shark::SquaredHingeLoss::eval	(	BatchLabelType const &	labels,
		BatchOutputType const &	predictions
	)		const

inlinevirtual

calculates the sum of all

Implements shark::AbstractLoss< unsigned int, RealVector >.

Definition at line 72 of file SquaredHingeLoss.h.

References SIZE_CHECK, and shark::sqr().

◆ evalDerivative()

double shark::SquaredHingeLoss::evalDerivative	(	BatchLabelType const &	target,
		BatchOutputType const &	prediction,
		BatchOutputType &	gradient
	)		const

inlinevirtual

evaluate the loss and the derivative w.r.t. the prediction

: The default implementations throws an exception. If you overwrite this method, don't forget to set the flag HAS_FIRST_DERIVATIVE.

Parameters

target	target value
prediction	prediction, typically made by a model
gradient	the gradient of the loss function with respect to the prediction

Reimplemented from shark::AbstractLoss< unsigned int, RealVector >.

Definition at line 100 of file SquaredHingeLoss.h.

References SIZE_CHECK, and shark::sqr().

◆ name()

std::string shark::SquaredHingeLoss::name ( ) const

inlinevirtual

Returns class name "HingeLoss".

Reimplemented from shark::INameable.

Definition at line 67 of file SquaredHingeLoss.h.

The documentation for this class was generated from the following file:

include/shark/ObjectiveFunctions/Loss/SquaredHingeLoss.h

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ SquaredHingeLoss()

Member Function Documentation

◆ eval()

◆ evalDerivative()

◆ name()