Polynomial kernel. More...

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

Inheritance diagram for shark::PolynomialKernel< 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 kerneland metric features (flags) More...

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

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

typedef base_type::ConstInputReference	ConstInputReference
	Const references to InputType. More...

typedef base_type::ConstBatchInputReference	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 Types inherited from shark::AbstractMetric< InputType >
typedef InputType	InputType
	Input type of the Kernel. More...

typedef Batch< InputType >::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...

Public Member Functions
	PolynomialKernel (unsigned int degree=2, double offset=0.0, bool degree_is_parameter=true, bool unconstrained=false)

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

void	setDegree (unsigned int deg)

unsigned int	degree () const

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

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

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

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

double	eval (ConstInputReference x1, ConstInputReference x2) const
	\( k(x_1, x_2) = \left( \langle x_1, x_2 \rangle + b \right)^n \) 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	eval (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix &result, State &state) 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

void	read (InArchive &ar)
	From ISerializable, reads a metric from an archive. More...

void	write (OutArchive &ar) const
	From ISerializable, writes a metric to an archive. More...

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

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
	Computes the squared distance in the kernel induced feature space. More...

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

virtual	~AbstractMetric ()

virtual double	featureDistanceSqr (ConstInputReference x1, ConstInputReference x2) const=0
	Computes the squared distance in the kernel induced feature space. More...

virtual RealMatrix	featureDistanceSqr (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2) const=0

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 ()

Protected Attributes
int	m_degree
	exponent n More...

double	m_offset
	offset b More...

bool	m_degreeIsParam
	is the degree a model parameter? More...

bool	m_unconstrained
	is the degree internally represented as exponential of the parameter? More...

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

Detailed Description

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

Polynomial kernel.

: The polynomial kernel is defined as \( \left( \left\langle x_1, x_2 \right\rangle + b \right)^n \) with degree \( n \in \mathbb{N} \) and non-negative offset \( b \geq 0 \). For n=1 and b=0 it matches the linear kernel (standard inner product).

Definition at line 52 of file PolynomialKernel.h.

Member Typedef Documentation

§ BatchInputType

template<class InputType = RealVector>

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

Definition at line 67 of file PolynomialKernel.h.

§ ConstBatchInputReference

template<class InputType = RealVector>

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

Definition at line 69 of file PolynomialKernel.h.

§ ConstInputReference

template<class InputType = RealVector>

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

Definition at line 68 of file PolynomialKernel.h.

Constructor & Destructor Documentation

§ PolynomialKernel()

template<class InputType = RealVector>

shark::PolynomialKernel< InputType >::PolynomialKernel	(	unsigned int	degree = `2`,
		double	offset = `0.0`,
		bool	degree_is_parameter = `true`,
		bool	unconstrained = `false`
	)

inline

Constructor.

Parameters

degree	exponent of the polynomial
offset	constant added to the standard inner product
degree_is_parameter	should the degree be a regular model parameter? if yes, the kernel will not be differentiable
unconstrained	should the offset internally be represented as exponential of the externally visible parameter?

Definition at line 77 of file PolynomialKernel.h.

References shark::PolynomialKernel< InputType >::degree(), shark::AbstractKernelFunction< InputType >::HAS_FIRST_INPUT_DERIVATIVE, shark::AbstractKernelFunction< InputType >::HAS_FIRST_PARAMETER_DERIVATIVE, shark::PolynomialKernel< InputType >::m_degreeIsParam, shark::AbstractKernelFunction< InputType >::m_features, SHARK_CHECK, and shark::AbstractKernelFunction< InputType >::SUPPORTS_VARIABLE_INPUT_SIZE.

Member Function Documentation

§ createState()

template<class InputType = RealVector>

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

inlinevirtual

creates the internal state of the kernel

Reimplemented from shark::AbstractKernelFunction< InputType >.

Definition at line 153 of file PolynomialKernel.h.

§ degree()

template<class InputType = RealVector>

unsigned int shark::PolynomialKernel< InputType >::degree ( ) const

inline

Definition at line 99 of file PolynomialKernel.h.

References shark::PolynomialKernel< InputType >::m_degree.

Referenced by shark::PolynomialKernel< InputType >::PolynomialKernel().

§ eval() [1/3]

template<class InputType = RealVector>

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

inlinevirtual

\( k(x_1, x_2) = \left( \langle x_1, x_2 \rangle + b \right)^n \)

Reimplemented from shark::AbstractKernelFunction< InputType >.

Definition at line 160 of file PolynomialKernel.h.

References shark::blas::inner_prod(), shark::PolynomialKernel< InputType >::m_degree, shark::PolynomialKernel< InputType >::m_offset, and SIZE_CHECK.

§ eval() [2/3]

template<class InputType = RealVector>

void shark::PolynomialKernel< 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 166 of file PolynomialKernel.h.

References shark::PolynomialKernel< InputType >::m_degree, shark::PolynomialKernel< InputType >::m_offset, shark::blas::noalias(), shark::blas::prod(), SIZE_CHECK, and shark::blas::trans().

§ eval() [3/3]

template<class InputType = RealVector>

void shark::PolynomialKernel< InputType >::eval	(	ConstBatchInputReference	batchX1,
		ConstBatchInputReference	batchX2,
		RealMatrix &	result,
		State &	state
	)		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]); The State object is filled in with data used in subsequent derivative computations.

Implements shark::AbstractKernelFunction< InputType >.

Definition at line 180 of file PolynomialKernel.h.

References shark::PolynomialKernel< InputType >::m_degree, shark::PolynomialKernel< InputType >::m_offset, shark::blas::noalias(), shark::blas::prod(), SIZE_CHECK, shark::State::toState(), and shark::blas::trans().

§ name()

template<class InputType = RealVector>

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

inlinevirtual

From INameable: return the class name.

Reimplemented from shark::INameable.

Definition at line 90 of file PolynomialKernel.h.

§ numberOfParameters()

template<class InputType = RealVector>

std::size_t shark::PolynomialKernel< InputType >::numberOfParameters ( ) const

inlinevirtual

Return the number of parameters.

Reimplemented from shark::IParameterizable.

Definition at line 145 of file PolynomialKernel.h.

References shark::PolynomialKernel< InputType >::m_degreeIsParam.

§ parameterVector()

template<class InputType = RealVector>

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

inlinevirtual

Return the parameter vector.

Reimplemented from shark::IParameterizable.

Definition at line 103 of file PolynomialKernel.h.

References shark::PolynomialKernel< InputType >::m_degree, shark::PolynomialKernel< InputType >::m_degreeIsParam, shark::PolynomialKernel< InputType >::m_offset, and shark::PolynomialKernel< InputType >::m_unconstrained.

§ read()

template<class InputType = RealVector>

void shark::PolynomialKernel< InputType >::read ( InArchive & archive )

inlinevirtual

From ISerializable, reads a metric from an archive.

Reimplemented from shark::AbstractMetric< InputType >.

Definition at line 281 of file PolynomialKernel.h.

References shark::PolynomialKernel< InputType >::m_degree, shark::PolynomialKernel< InputType >::m_degreeIsParam, shark::PolynomialKernel< InputType >::m_offset, and shark::PolynomialKernel< InputType >::m_unconstrained.

§ setDegree()

template<class InputType = RealVector>

void shark::PolynomialKernel< InputType >::setDegree ( unsigned int deg )

inline

Definition at line 93 of file PolynomialKernel.h.

References shark::PolynomialKernel< InputType >::m_degree, shark::PolynomialKernel< InputType >::m_degreeIsParam, RANGE_CHECK, and SHARK_CHECK.

§ setParameterVector()

template<class InputType = RealVector>

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

inlinevirtual

Set the parameter vector.

Reimplemented from shark::IParameterizable.

Definition at line 122 of file PolynomialKernel.h.

References shark::PolynomialKernel< InputType >::m_degree, shark::PolynomialKernel< InputType >::m_degreeIsParam, shark::PolynomialKernel< InputType >::m_offset, shark::PolynomialKernel< InputType >::m_unconstrained, RANGE_CHECK, SHARK_ASSERT, and SIZE_CHECK.

§ weightedInputDerivative()

template<class InputType = RealVector>

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

inlinevirtual

\( k(x_1, x_2) = \left( \langle x_1, x_2 \rangle + b \right)^n \)
\( \frac{\partial k(x_1, x_2)}{\partial x_1} = \left[ n \cdot (\langle x_1, x_2 \rangle + b)^{n-1} \right] \cdot x_2 \)

Reimplemented from shark::AbstractKernelFunction< InputType >.

Definition at line 241 of file PolynomialKernel.h.

References shark::PolynomialKernel< InputType >::m_degree, shark::blas::noalias(), shark::blas::prod(), shark::blas::safe_div(), SIZE_CHECK, and shark::State::toState().

§ weightedParameterDerivative()

template<class InputType = RealVector>

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