Gaussian radial basis function kernel. More...

#include <shark/Models/Kernels/GaussianRbfKernel.h>

Inheritance diagram for shark::GaussianRbfKernel< InputType >:

Collaboration diagram for shark::GaussianRbfKernel< InputType >:

Public Types
typedef base_type::BatchInputType	BatchInputType

typedef base_type::ConstInputReference	ConstInputReference

typedef base_type::ConstBatchInputReference	ConstBatchInputReference

Public Types inherited from shark::AbstractKernelFunction< InputType >
enum	Feature
	enumerations of kernel features (flags) More...

typedef InputType	InputType
	Input type of the Kernel. More...

typedef Traits::type	BatchInputType
	batch input type of the kernel More...

typedef ConstProxyReference < InputType const >::type	ConstInputReference
	Const references to InputType. More...

typedef ConstProxyReference < BatchInputType const > ::type	ConstBatchInputReference
	Const references to BatchInputType. More...

typedef TypedFlags< Feature >	Features
	This statement declares the member m_features. See Core/Flags.h for details. More...

typedef TypedFeatureNotAvailableException < Feature >	FeatureNotAvailableException

Public Member Functions
	GaussianRbfKernel (double gamma=1.0, bool unconstrained=false)

std::string	name () const
	From INameable: return the class name. More...

RealVector	parameterVector () const
	Return the parameter vector. More...

void	setParameterVector (RealVector const &newParameters)
	Set the parameter vector. More...

size_t	numberOfParameters () const
	Return the number of parameters. More...

double	gamma () const
	Get the bandwidth parameter value. More...

double	sigma () const
	Return ``standard deviation'' of Gaussian. More...

void	setGamma (double gamma)

double	setSigma (double sigma) const
	Set ``standard deviation'' of Gaussian. More...

void	read (InArchive &ar)
	From ISerializable. More...

void	write (OutArchive &ar) const
	From ISerializable. More...

boost::shared_ptr< State >	createState () const
	creates the internal state of the kernel More...

double	eval (ConstInputReference x1, ConstInputReference x2) const
	evaluates \( k(x_1,x_2)\) More...

void	eval (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix &result, State &state) const
	evaluates \( k(x_1,x_2)\) and computes the intermediate value More...

void	eval (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix &result) const
	Evaluates the subset of the KernelGram matrix which is defined by X1(rows) and X2 (columns). More...

void	weightedParameterDerivative (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix const &coefficients, State const &state, RealVector &gradient) const
	Computes the gradient of the parameters as a weighted sum over the gradient of all elements of the batch. More...

void	weightedInputDerivative (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix const &coefficientsX2, State const &state, BatchInputType &gradient) const
	Calculates the derivative of the inputs X1 (only x1!). More...

Public Member Functions inherited from shark::AbstractKernelFunction< InputType >
	AbstractKernelFunction ()

virtual	~AbstractKernelFunction ()

void	configure (PropertyTree const &node)
	configure the kernel More...

const Features &	features () const

virtual void	updateFeatures ()

bool	hasFirstParameterDerivative () const

bool	hasFirstInputDerivative () const

bool	isNormalized () const

bool	supportsVariableInputSize () const

double	operator() (ConstInputReference x1, ConstInputReference x2) const
	Convenience operator which evaluates the kernel function. More...

RealMatrix	operator() (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2) const
	Evaluates the subset of the KernelGram matrix which is defined by X1(rows) and X2 (columns). More...

virtual double	featureDistanceSqr (ConstInputReference x1, ConstInputReference x2) const
	Computes the squared distance in the kernel induced feature space. More...

virtual RealMatrix	featureDistanceSqr (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2) const

double	featureDistance (ConstInputReference x1, ConstInputReference x2) const
	Computes the distance in the kernel induced feature space. More...

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

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

Public Member Functions inherited from shark::ISerializable
virtual	~ISerializable ()
	Virtual d'tor. More...

void	load (InArchive &archive, unsigned int version)
	Versioned loading of components, calls read(...). More...

void	save (OutArchive &archive, unsigned int version) const
	Versioned storing of components, calls write(...). More...

	BOOST_SERIALIZATION_SPLIT_MEMBER ()

Public Member Functions inherited from shark::IConfigurable
virtual	~IConfigurable ()
	Virtual d'tor. More...

Protected Attributes
double	m_gamma
	kernel bandwidth parameter More...

bool	m_unconstrained
	use log storage More...

Protected Attributes inherited from shark::AbstractKernelFunction< InputType >
Features	m_features

Detailed Description

template<class InputType = RealVector>
class shark::GaussianRbfKernel< InputType >

Gaussian radial basis function kernel.

Gaussian radial basis function kernel \( k(x_1, x_2) = \exp(-\gamma \cdot \| x_1 - x_2 \|^2) \) with single bandwidth parameter \( \gamma \). Optionally, the parameter can be encoded as \( \exp(\eta) \), which allows for unconstrained optimization.

Definition at line 43 of file GaussianRbfKernel.h.

Member Typedef Documentation

template<class InputType = RealVector>

typedef base_type::BatchInputType shark::GaussianRbfKernel< InputType >::BatchInputType

Definition at line 58 of file GaussianRbfKernel.h.

template<class InputType = RealVector>

typedef base_type::ConstBatchInputReference shark::GaussianRbfKernel< InputType >::ConstBatchInputReference

Definition at line 60 of file GaussianRbfKernel.h.

template<class InputType = RealVector>

typedef base_type::ConstInputReference shark::GaussianRbfKernel< InputType >::ConstInputReference

Definition at line 59 of file GaussianRbfKernel.h.

Constructor & Destructor Documentation

template<class InputType = RealVector>

shark::GaussianRbfKernel< InputType >::GaussianRbfKernel	(	double	gamma = `1.0`,
		bool	unconstrained = `false`
	)

inline

Definition at line 62 of file GaussianRbfKernel.h.

References shark::GaussianRbfKernel< InputType >::gamma(), shark::AbstractKernelFunction< InputType >::HAS_FIRST_INPUT_DERIVATIVE, shark::AbstractKernelFunction< InputType >::HAS_FIRST_PARAMETER_DERIVATIVE, shark::AbstractKernelFunction< InputType >::IS_NORMALIZED, shark::AbstractKernelFunction< InputType >::m_features, shark::GaussianRbfKernel< InputType >::m_gamma, and shark::GaussianRbfKernel< InputType >::m_unconstrained.

Member Function Documentation

template<class InputType = RealVector>

boost::shared_ptr<State> shark::GaussianRbfKernel< InputType >::createState ( ) const

inlinevirtual

creates the internal state of the kernel

Reimplemented from shark::AbstractKernelFunction< InputType >.

Definition at line 134 of file GaussianRbfKernel.h.

template<class InputType = RealVector>

double shark::GaussianRbfKernel< InputType >::eval	(	ConstInputReference	x1,
		ConstInputReference	x2
	)		const

inlinevirtual

evaluates \( k(x_1,x_2)\)

Gaussian radial basis function kernel

\[ k(x_1, x_2) = \exp(-\gamma \cdot \| x_1 - x_2 \|^2) \]

Reimplemented from shark::AbstractKernelFunction< InputType >.

Definition at line 142 of file GaussianRbfKernel.h.

References shark::blas::distanceSqr(), shark::GaussianRbfKernel< InputType >::m_gamma, and SIZE_CHECK.

template<class InputType = RealVector>

void shark::GaussianRbfKernel< InputType >::eval	(	ConstBatchInputReference	batchX1,
		ConstBatchInputReference	batchX2,
		RealMatrix &	result,
		State &	state
	)		const

inlinevirtual

evaluates \( k(x_1,x_2)\) and computes the intermediate value

Gaussian radial basis function kernel

\[ k(x_1, x_2) = \exp(-\gamma \cdot \| x_1 - x_2 \|^2) \]

Implements shark::AbstractKernelFunction< InputType >.

Definition at line 153 of file GaussianRbfKernel.h.

References shark::blas::distanceSqr(), shark::GaussianRbfKernel< InputType >::m_gamma, shark::blas::noalias(), SIZE_CHECK, and shark::State::toState().

template<class InputType = RealVector>

void shark::GaussianRbfKernel< InputType >::eval	(	ConstBatchInputReference	batchX1,
		ConstBatchInputReference	batchX2,
		RealMatrix &	result
	)		const

inlinevirtual

Evaluates the subset of the KernelGram matrix which is defined by X1(rows) and X2 (columns).

The result matrix is filled in with the values result(i,j) = kernel(x1[i], x2[j]);

Reimplemented from shark::AbstractKernelFunction< InputType >.

Definition at line 168 of file GaussianRbfKernel.h.

References shark::blas::distanceSqr(), shark::GaussianRbfKernel< InputType >::m_gamma, shark::blas::noalias(), and SIZE_CHECK.

template<class InputType = RealVector>

double shark::GaussianRbfKernel< InputType >::gamma ( ) const

inline

Get the bandwidth parameter value.

Definition at line 100 of file GaussianRbfKernel.h.

References shark::GaussianRbfKernel< InputType >::m_gamma.

Referenced by shark::GaussianRbfKernel< InputType >::GaussianRbfKernel(), main(), and shark::GaussianRbfKernel< InputType >::setGamma().

template<class InputType = RealVector>

std::string shark::GaussianRbfKernel< InputType >::name ( ) const

inlinevirtual

From INameable: return the class name.

Reimplemented from shark::INameable.

Definition at line 71 of file GaussianRbfKernel.h.

template<class InputType = RealVector>

size_t shark::GaussianRbfKernel< InputType >::numberOfParameters ( ) const

inlinevirtual

Return the number of parameters.

Reimplemented from shark::IParameterizable.

Definition at line 95 of file GaussianRbfKernel.h.

template<class InputType = RealVector>

RealVector shark::GaussianRbfKernel< InputType >::parameterVector ( ) const

inlinevirtual

Return the parameter vector.

Reimplemented from shark::IParameterizable.

Definition at line 74 of file GaussianRbfKernel.h.

References shark::GaussianRbfKernel< InputType >::m_gamma, and shark::GaussianRbfKernel< InputType >::m_unconstrained.

template<class InputType = RealVector>

void shark::GaussianRbfKernel< InputType >::read ( InArchive & ar )

inlinevirtual

From ISerializable.

Reimplemented from shark::AbstractKernelFunction< InputType >.

Definition at line 122 of file GaussianRbfKernel.h.

References shark::GaussianRbfKernel< InputType >::m_gamma, and shark::GaussianRbfKernel< InputType >::m_unconstrained.

template<class InputType = RealVector>

void shark::GaussianRbfKernel< InputType >::setGamma ( double gamma )

inline

Set the bandwidth parameter value.

Exceptions

shark::Exception if gamma <= 0.

Definition at line 111 of file GaussianRbfKernel.h.

References shark::GaussianRbfKernel< InputType >::gamma(), shark::GaussianRbfKernel< InputType >::m_gamma, and SHARK_CHECK.

template<class InputType = RealVector>

void shark::GaussianRbfKernel< InputType >::setParameterVector ( RealVector const & newParameters )

inlinevirtual

Set the parameter vector.

Reimplemented from shark::IParameterizable.

Definition at line 84 of file GaussianRbfKernel.h.

References shark::GaussianRbfKernel< InputType >::m_gamma, shark::GaussianRbfKernel< InputType >::m_unconstrained, and SHARK_CHECK.

template<class InputType = RealVector>

double shark::GaussianRbfKernel< InputType >::setSigma ( double sigma ) const

inline

Set ``standard deviation'' of Gaussian.

Definition at line 117 of file GaussianRbfKernel.h.

References shark::GaussianRbfKernel< InputType >::m_gamma, and shark::GaussianRbfKernel< InputType >::sigma().

template<class InputType = RealVector>

double shark::GaussianRbfKernel< InputType >::sigma ( ) const

inline

Return ``standard deviation'' of Gaussian.

Definition at line 105 of file GaussianRbfKernel.h.

References shark::GaussianRbfKernel< InputType >::m_gamma.

Referenced by shark::GaussianRbfKernel< InputType >::setSigma().

template<class InputType = RealVector>

void shark::GaussianRbfKernel< InputType >::weightedInputDerivative	(	ConstBatchInputReference	batchX1,
		ConstBatchInputReference	batchX2,
		RealMatrix const &	coefficientsX2,
		State const &	state,
		BatchInputType &	gradient
	)		const

inlinevirtual

Calculates the derivative of the inputs X1 (only x1!).

The i-th row of the resulting matrix is a weighted sum of the form: c[i,0] * k'(x1[i], x2[0]) + c[i,1] * k'(x1[i], x2[1]) + ... + c[i,n] * k'(x1[i], x2[n]).

The default implementation throws a "not implemented" exception.

Reimplemented from shark::AbstractKernelFunction< InputType >.

Definition at line 203 of file GaussianRbfKernel.h.

References shark::GaussianRbfKernel< InputType >::m_gamma, shark::blas::noalias(), shark::blas::row(), SIZE_CHECK, and shark::State::toState().

template<class InputType = RealVector>

void shark::GaussianRbfKernel< InputType >::weightedParameterDerivative	(	ConstBatchInputReference	batchX1,
		ConstBatchInputReference	batchX2,
		RealMatrix const &	coefficients,
		State const &	state,
		RealVector &	gradient
	)		const