Normalized version of a kernel function. More...

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

Inheritance diagram for shark::NormalizedKernel< InputType >:

Public Types
typedef base_type::BatchInputType	BatchInputType

typedef base_type::ConstBatchInputReference	ConstBatchInputReference

typedef base_type::ConstInputReference	ConstInputReference

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 Types inherited from shark::IParameterizable<>
typedef RealVector	ParameterVectorType

Public Member Functions
	NormalizedKernel (AbstractKernelFunction< InputType > *base)

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...

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

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

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

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

void	weightedInputDerivative (ConstBatchInputReference const &batchX1, ConstBatchInputReference const &batchX2, RealMatrix const &coefficientsX2, State const &state, BatchInputType &gradient) const

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

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). More...

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). More...

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 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...

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

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

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
AbstractKernelFunction< InputType > *	m_base
	kernel to normalize More...

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

Detailed Description

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

Normalized version of a kernel function.

For a positive definite kernel k, the normalized kernel

\[ \tilde k(x, y) := \frac{k(x, y)}{\sqrt{k(x, x) \cdot k(y, y)}} \]

is again a positive definite kernel function.

Definition at line 50 of file NormalizedKernel.h.

Member Typedef Documentation

◆ BatchInputType

template<class InputType = RealVector>

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

Definition at line 80 of file NormalizedKernel.h.

◆ ConstBatchInputReference

template<class InputType = RealVector>

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

Definition at line 81 of file NormalizedKernel.h.

◆ ConstInputReference

template<class InputType = RealVector>

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

Definition at line 82 of file NormalizedKernel.h.

Constructor & Destructor Documentation

◆ NormalizedKernel()

template<class InputType = RealVector>

shark::NormalizedKernel< InputType >::NormalizedKernel ( AbstractKernelFunction< InputType > * base )

inline

Definition at line 84 of file NormalizedKernel.h.

References shark::AbstractKernelFunction< InputType >::HAS_FIRST_INPUT_DERIVATIVE, shark::AbstractKernelFunction< InputType >::HAS_FIRST_PARAMETER_DERIVATIVE, shark::AbstractKernelFunction< InputTypeT >::hasFirstInputDerivative(), shark::AbstractKernelFunction< InputTypeT >::hasFirstParameterDerivative(), shark::AbstractKernelFunction< InputType >::IS_NORMALIZED, shark::NormalizedKernel< InputType >::m_base, shark::AbstractKernelFunction< InputType >::m_features, and SHARK_ASSERT.

Member Function Documentation

◆ createState()

template<class InputType = RealVector>

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

inlinevirtual

creates the internal state of the kernel

Reimplemented from shark::AbstractKernelFunction< InputType >.

Definition at line 110 of file NormalizedKernel.h.

◆ eval() [1/3]

template<class InputType = RealVector>

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

inlinevirtual

evaluates \( k(x,y) \)

calculates

\[ \tilde k(x, y) := \frac{k(x, y)}{\sqrt{k(x, x) \cdot k(y, y)}} \]

Reimplemented from shark::AbstractKernelFunction< InputType >.

Definition at line 119 of file NormalizedKernel.h.

References shark::AbstractKernelFunction< InputTypeT >::eval(), and shark::NormalizedKernel< InputType >::m_base.

◆ eval() [2/3]

template<class InputType = RealVector>

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

inline

evaluates \( k(x_i,y_j) \) for a batch of inputs x=(x...x_n) and x=(y_1...y_m)

calculates

\[ \tilde k(x_i,y_j) := \frac{k(x_i,y_j)}{\sqrt{k(x_i,x_i) \cdot k(y_j, y_j)}} \]

Definition at line 131 of file NormalizedKernel.h.

References shark::batchSize(), shark::createBatch(), shark::AbstractKernelFunction< InputTypeT >::eval(), shark::getBatchElement(), shark::NormalizedKernel< InputType >::m_base, and shark::State::toState().

◆ eval() [3/3]

template<class InputType = RealVector>

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

inline

evaluates \( k(x,y) \) for a batch of inputs

calculates

\[ \tilde k(x, y) := \frac{k(x, y)}{\sqrt{k(x, x) \cdot k(y, y)}} \]

Definition at line 171 of file NormalizedKernel.h.

References shark::batchSize(), shark::AbstractKernelFunction< InputTypeT >::eval(), shark::getBatchElement(), and shark::NormalizedKernel< InputType >::m_base.

◆ name()

template<class InputType = RealVector>

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

inlinevirtual

From INameable: return the class name.

Reimplemented from shark::INameable.

Definition at line 94 of file NormalizedKernel.h.

References shark::NormalizedKernel< InputType >::m_base, and shark::INameable::name().

◆ numberOfParameters()

template<class InputType = RealVector>

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

inlinevirtual

Return the number of parameters.

Reimplemented from shark::IParameterizable<>.

Definition at line 105 of file NormalizedKernel.h.

References shark::NormalizedKernel< InputType >::m_base, and shark::IParameterizable< VectorType >::numberOfParameters().

Referenced by shark::NormalizedKernel< InputType >::weightedParameterDerivative().

◆ parameterVector()

template<class InputType = RealVector>

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

inlinevirtual

Return the parameter vector.

Reimplemented from shark::IParameterizable<>.

Definition at line 97 of file NormalizedKernel.h.

References shark::NormalizedKernel< InputType >::m_base, and shark::IParameterizable< VectorType >::parameterVector().

◆ setParameterVector()

template<class InputType = RealVector>

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

inlinevirtual

Set the parameter vector.

Reimplemented from shark::IParameterizable<>.

Definition at line 101 of file NormalizedKernel.h.

References shark::NormalizedKernel< InputType >::m_base, and shark::IParameterizable< VectorType >::setParameterVector().

◆ weightedInputDerivative()

template<class InputType = RealVector>

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

inline

Input derivative, calculated according to the equation:
\( \frac{\partial k(x, y)}{\partial x} \frac{\sum_i \exp(w_i) \frac{\partial k_i(x, y)}{\partial x}} {\sum_i exp(w_i)} \) and summed up over all elements of the second batch

Definition at line 240 of file NormalizedKernel.h.

References shark::batchSize(), and shark::State::toState().

◆ weightedParameterDerivative()

template<class InputType = RealVector>

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

inline

calculates the weighted derivate w.r.t. the parameters \( w \)

The derivative for a single element is calculated as follows:

\[ \frac{\partial \tilde k_w(x, y)}{\partial w} = \frac{k_w'(x,y)}{\sqrt{k_w(x,x) k_w(y,y)}} - \frac{k_w(x,y) \left(k_w(y,y) k_w'(x,x)+k_w(x,x) k_w'(y,y)\right)}{2 (k_w(x,x) k_w(y,y))^{3/2}} \]

where \( k_w'(x, y) = \partial k_w(x, y) / \partial w \).

Definition at line 193 of file NormalizedKernel.h.

References shark::batchSize(), shark::NormalizedKernel< InputType >::numberOfParameters(), and shark::State::toState().

Member Data Documentation

◆ m_base

template<class InputType = RealVector>

AbstractKernelFunction<InputType>* shark::NormalizedKernel< InputType >::m_base

protected

kernel to normalize

Definition at line 273 of file NormalizedKernel.h.

Referenced by shark::NormalizedKernel< InputType >::eval(), shark::NormalizedKernel< InputType >::name(), shark::NormalizedKernel< InputType >::NormalizedKernel(), shark::NormalizedKernel< InputType >::numberOfParameters(), shark::NormalizedKernel< InputType >::parameterVector(), and shark::NormalizedKernel< InputType >::setParameterVector().

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

include/shark/Models/Kernels/NormalizedKernel.h

Public Types

Public Member Functions

Protected Attributes

Detailed Description

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

Member Typedef Documentation

◆ BatchInputType

◆ ConstBatchInputReference

◆ ConstInputReference

Constructor & Destructor Documentation

◆ NormalizedKernel()

Member Function Documentation

◆ createState()

◆ eval() [1/3]

◆ eval() [2/3]

◆ eval() [3/3]

◆ name()

◆ numberOfParameters()

◆ parameterVector()

◆ setParameterVector()

◆ weightedInputDerivative()

◆ weightedParameterDerivative()

Member Data Documentation

◆ m_base

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