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< InputTypeT >
enum	Feature { HAS_FIRST_PARAMETER_DERIVATIVE = 1 , HAS_FIRST_INPUT_DERIVATIVE = 2 , IS_NORMALIZED = 4 , SUPPORTS_VARIABLE_INPUT_SIZE = 8 }
	enumerations of kerneland metric features (flags) More...

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

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

typedef base_type::ConstInputReference	ConstInputReference
	Const references to InputType.

typedef base_type::ConstBatchInputReference	ConstBatchInputReference
	Const references to BatchInputType.

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

typedef TypedFeatureNotAvailableException< Feature >	FeatureNotAvailableException

Public Types inherited from shark::AbstractMetric< InputTypeT >
typedef InputTypeT	InputType
	Input type of the Kernel.

typedef Batch< InputTypeT >::type	BatchInputType
	batch input type of the kernel

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

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

Public Types inherited from shark::IParameterizable< VectorType >
typedef VectorType	ParameterVectorType

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.

void	setDegree (unsigned int deg)

unsigned int	degree () const

RealVector	parameterVector () const
	Return the parameter vector.

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

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

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

double	eval (ConstInputReference x1, ConstInputReference x2) const
	\( k(x_1, x_2) = \left( \langle x_1, x_2 \rangle + b \right)^n \)

void	eval (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix &result) const

void	eval (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix &result, State &state) const

void	weightedParameterDerivative (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix const &coefficients, State const &state, RealVector &gradient) const

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.

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

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

const Features &	features () const

virtual void	updateFeatures ()

bool	hasFirstParameterDerivative () const

bool	hasFirstInputDerivative () const

bool	isNormalized () const

bool	supportsVariableInputSize () const

virtual double	eval (ConstInputReference x1, ConstInputReference x2) const
	Evaluates the kernel function.

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

virtual void	eval (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix &result, State &state) const =0
	Evaluates the subset of the KernelGram matrix which is defined by X1(rows) and X2 (columns).

virtual 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).

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

virtual 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.

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

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

virtual RealMatrix	featureDistanceSqr (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2) const
	Computes the squared distance in the kernel induced feature space.

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

virtual	~AbstractMetric ()

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

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

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

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

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

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

	BOOST_SERIALIZATION_SPLIT_MEMBER ()

Protected Attributes
int	m_degree
	exponent n

double	m_offset
	offset b

bool	m_degreeIsParam
	is the degree a model parameter?

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

Protected Attributes inherited from shark::AbstractKernelFunction< InputTypeT >
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 53 of file PolynomialKernel.h.

Member Typedef Documentation

◆ BatchInputType

template<class InputType = RealVector>

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

Definition at line 68 of file PolynomialKernel.h.

◆ ConstBatchInputReference

template<class InputType = RealVector>

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

Definition at line 70 of file PolynomialKernel.h.

◆ ConstInputReference

template<class InputType = RealVector>

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

Definition at line 69 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 78 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< InputTypeT >::m_features, SHARK_RUNTIME_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< InputTypeT >.

Definition at line 154 of file PolynomialKernel.h.

◆ degree()

template<class InputType = RealVector>

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

inline

Definition at line 100 of file PolynomialKernel.h.

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

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

◆ eval() [1/3]

template<class InputType = RealVector>

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

inline

Definition at line 167 of file PolynomialKernel.h.

References 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,
		State &	state
	)		const

inline

Definition at line 181 of file PolynomialKernel.h.

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

◆ eval() [3/3]

template<class InputType = RealVector>

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

inline

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

Definition at line 161 of file PolynomialKernel.h.

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

◆ 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 91 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< VectorType >.

Definition at line 146 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< VectorType >.

Definition at line 104 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< InputTypeT >.

Definition at line 282 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 94 of file PolynomialKernel.h.

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

◆ setParameterVector()

template<class InputType = RealVector>

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

inlinevirtual

Set the parameter vector.

Reimplemented from shark::IParameterizable< VectorType >.

Definition at line 123 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

inline

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

Definition at line 242 of file PolynomialKernel.h.

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

inline

Definition at line 205 of file PolynomialKernel.h.

References shark::PolynomialKernel< InputType >::m_degree, shark::PolynomialKernel< InputType >::m_offset, shark::PolynomialKernel< InputType >::m_unconstrained, SIZE_CHECK, and shark::State::toState().

◆ write()

template<class InputType = RealVector>

void shark::PolynomialKernel< InputType >::write ( OutArchive & archive ) const

inlinevirtual

From ISerializable, writes a metric to an archive.

The default implementation just saves the parameters.

Reimplemented from shark::AbstractMetric< InputTypeT >.

Definition at line 289 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.

Member Data Documentation

◆ m_degree

template<class InputType = RealVector>

int shark::PolynomialKernel< InputType >::m_degree

protected

exponent n

Definition at line 297 of file PolynomialKernel.h.

◆ m_degreeIsParam

template<class InputType = RealVector>

bool shark::PolynomialKernel< InputType >::m_degreeIsParam

protected

is the degree a model parameter?

Definition at line 299 of file PolynomialKernel.h.

Referenced by shark::PolynomialKernel< InputType >::numberOfParameters(), shark::PolynomialKernel< InputType >::parameterVector(), shark::PolynomialKernel< InputType >::PolynomialKernel(), shark::PolynomialKernel< InputType >::read(), shark::PolynomialKernel< InputType >::setDegree(), shark::PolynomialKernel< InputType >::setParameterVector(), and shark::PolynomialKernel< InputType >::write().

◆ m_offset

template<class InputType = RealVector>

double shark::PolynomialKernel< InputType >::m_offset

protected

offset b

Definition at line 298 of file PolynomialKernel.h.

Referenced by shark::PolynomialKernel< InputType >::eval(), shark::PolynomialKernel< InputType >::eval(), shark::PolynomialKernel< InputType >::eval(), shark::PolynomialKernel< InputType >::parameterVector(), shark::PolynomialKernel< InputType >::read(), shark::PolynomialKernel< InputType >::setParameterVector(), shark::PolynomialKernel< InputType >::weightedParameterDerivative(), and shark::PolynomialKernel< InputType >::write().

◆ m_unconstrained

template<class InputType = RealVector>

bool shark::PolynomialKernel< InputType >::m_unconstrained

protected

is the degree internally represented as exponential of the parameter?

Definition at line 300 of file PolynomialKernel.h.

Referenced by shark::PolynomialKernel< InputType >::parameterVector(), shark::PolynomialKernel< InputType >::read(), shark::PolynomialKernel< InputType >::setParameterVector(), shark::PolynomialKernel< InputType >::weightedParameterDerivative(), and shark::PolynomialKernel< InputType >::write().

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

include/shark/Models/Kernels/PolynomialKernel.h

Public Types

Public Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ BatchInputType

◆ ConstBatchInputReference

◆ ConstInputReference

Constructor & Destructor Documentation

◆ PolynomialKernel()

Member Function Documentation

◆ createState()

◆ degree()

◆ eval() [1/3]

◆ eval() [2/3]

◆ eval() [3/3]

◆ name()

◆ numberOfParameters()

◆ parameterVector()

◆ read()

◆ setDegree()

◆ setParameterVector()

◆ weightedInputDerivative()

◆ weightedParameterDerivative()

◆ write()

Member Data Documentation

◆ m_degree

◆ m_degreeIsParam

◆ m_offset

◆ m_unconstrained