Linear model in a kernel feature space. More...

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

Inheritance diagram for shark::KernelExpansion< InputType >:

Public Types
typedef AbstractKernelFunction< InputType >	KernelType

typedef base_type::BatchInputType	BatchInputType

typedef base_type::BatchOutputType	BatchOutputType

Public Types inherited from shark::AbstractModel< InputType, RealVector >
enum	Feature

typedef InputType	InputType
	Defines the input type of the model.

typedef RealVector	OutputType
	Defines the output type of the model.

typedef AbstractModel< InputType, RealVector, RealVector >	ModelBaseType
	Defines the BaseType used by the model (this type). Useful for creating derived models.

typedef Batch< InputType >::type	BatchInputType
	defines the batch type of the input type.

typedef Batch< OutputType >::type	BatchOutputType
	defines the batch type of the output type

typedef TypedFlags< Feature >	Features

typedef TypedFeatureNotAvailableException< Feature >	FeatureNotAvailableException

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

Public Member Functions
	KernelExpansion ()

	KernelExpansion (KernelType *kernel)

	KernelExpansion (KernelType *kernel, Data< InputType > const &basis, bool offset, std::size_t outputs=1)

void	setStructure (KernelType *kernel, Data< InputType > const &basis, bool offset, std::size_t outputs=1)

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

Shape	outputShape () const
	dimensionality of the output RealVector

Shape	inputShape () const
	Returns the expected shape of the input.

KernelType const *	kernel () const

KernelType *	kernel ()

void	setKernel (KernelType *kernel)

bool	hasOffset () const

RealMatrix &	alpha ()

RealMatrix const &	alpha () const

double &	alpha (std::size_t example, std::size_t cls)

double const &	alpha (std::size_t example, std::size_t cls) const

RealVector &	offset ()

RealVector const &	offset () const

double &	offset (std::size_t cls)

double const &	offset (std::size_t cls) const

Data< InputType > const &	basis () const

Data< InputType > &	basis ()

void	sparsify ()

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 an internal state of the model.

void	eval (BatchInputType const &patterns, BatchOutputType &output) const
	Standard interface for evaluating the response of the model to a batch of patterns.

void	eval (BatchInputType const &patterns, BatchOutputType &outputs, State &state) const
	Standard interface for evaluating the response of the model to a batch of patterns.

void	read (InArchive &archive)
	From ISerializable, reads a model from an archive.

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

Public Member Functions inherited from shark::AbstractModel< InputType, RealVector >
	AbstractModel ()

virtual	~AbstractModel ()

const Features &	features () const

virtual void	updateFeatures ()

bool	hasFirstParameterDerivative () const
	Returns true when the first parameter derivative is implemented.

bool	hasFirstInputDerivative () const
	Returns true when the first input derivative is implemented.

virtual void	eval (InputType const &pattern, OutputType &output) const
	Standard interface for evaluating the response of the model to a single pattern.

Data< OutputType >	operator() (Data< InputType > const &patterns) const
	Model evaluation as an operator for a whole dataset. This is a convenience function.

OutputType	operator() (InputType const &pattern) const
	Model evaluation as an operator for a single pattern. This is a convenience function.

BatchOutputType	operator() (BatchInputType const &patterns) const
	Model evaluation as an operator for a single pattern. This is a convenience function.

virtual void	weightedParameterDerivative (BatchInputType const &pattern, BatchOutputType const &outputs, BatchOutputType const &coefficients, State const &state, RealVector &derivative) const
	calculates the weighted sum of derivatives w.r.t the parameters.

virtual void	weightedInputDerivative (BatchInputType const &pattern, BatchOutputType const &outputs, BatchOutputType const &coefficients, State const &state, BatchInputType &derivative) const
	calculates the weighted sum of derivatives w.r.t the inputs

virtual void	weightedDerivatives (BatchInputType const &patterns, BatchOutputType const &outputs, BatchOutputType const &coefficients, State const &state, RealVector &parameterDerivative, BatchInputType &inputDerivative) const
	calculates weighted input and parameter derivative at the same time

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

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

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
KernelType *	mep_kernel
	kernel function used in the expansion

Data< InputType >	m_basis
	"support" basis vectors

RealMatrix	m_alpha
	kernel coefficients

RealVector	m_b
	offset or bias term

Protected Attributes inherited from shark::AbstractModel< InputType, RealVector >
Features	m_features

Detailed Description

template<class InputType>
class shark::KernelExpansion< InputType >

Linear model in a kernel feature space.

An affine linear kernel expansion is a model of the type

\[ x : \mathbb{R}^d \to \mathbb{R}^d \enspace , \enspace x \mapsto \sum_{n=1}^{\ell} \alpha_n k(x_n, x) + b \enspace ,\]

with parameters \( \alpha_n \in \mathbb{R}^{d} \) for all \( n \in \{1, \dots, \ell\} \) and \( b \in \mathbb{R}^d \).

One way in which the possibility for vector-valued input and output of dimension \( d \) may be interpreted is as allowing for a KernelExpansion model for \( d \) different classes/outputs in multi-class problems. Then, the i-th column of the matrix m_alpha is the KernelExpansion for class/output i.

For a choice of kernel, see Kernels.

Template Parameters

InputType Type of basis elements supplied to the kernel

Definition at line 69 of file KernelExpansion.h.

Member Typedef Documentation

◆ BatchInputType

template<class InputType >

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

Definition at line 74 of file KernelExpansion.h.

◆ BatchOutputType

template<class InputType >

typedef base_type::BatchOutputType shark::KernelExpansion< InputType >::BatchOutputType

Definition at line 75 of file KernelExpansion.h.

◆ KernelType

template<class InputType >

typedef AbstractKernelFunction<InputType> shark::KernelExpansion< InputType >::KernelType

Definition at line 72 of file KernelExpansion.h.

Constructor & Destructor Documentation

◆ KernelExpansion() [1/3]

template<class InputType >

shark::KernelExpansion< InputType >::KernelExpansion ( )

inline

Definition at line 81 of file KernelExpansion.h.

◆ KernelExpansion() [2/3]

template<class InputType >

shark::KernelExpansion< InputType >::KernelExpansion ( KernelType * kernel )

inline

Definition at line 83 of file KernelExpansion.h.

References shark::KernelExpansion< InputType >::kernel(), and SHARK_ASSERT.

◆ KernelExpansion() [3/3]

template<class InputType >

shark::KernelExpansion< InputType >::KernelExpansion	(	KernelType *	kernel,
		Data< InputType > const &	basis,
		bool	offset,
		std::size_t	outputs = `1`
	)

inline

Definition at line 87 of file KernelExpansion.h.

References shark::KernelExpansion< InputType >::basis(), shark::KernelExpansion< InputType >::kernel(), shark::KernelExpansion< InputType >::offset(), shark::KernelExpansion< InputType >::setStructure(), and SHARK_ASSERT.

Member Function Documentation

◆ alpha() [1/4]

template<class InputType >

RealMatrix & shark::KernelExpansion< InputType >::alpha ( )

inline

Definition at line 136 of file KernelExpansion.h.

References shark::KernelExpansion< InputType >::m_alpha.

Referenced by shark::MergeBudgetMaintenanceStrategy< RealVector >::addToModel(), shark::ProjectBudgetMaintenanceStrategy< RealVector >::addToModel(), shark::RemoveBudgetMaintenanceStrategy< InputType >::addToModel(), shark::MissingFeaturesKernelExpansion< InputType >::computeNorm(), shark::MissingFeaturesKernelExpansion< InputType >::computeNorm(), shark::LooErrorCSvm< InputType, CacheType >::eval(), shark::AbstractBudgetMaintenanceStrategy< InputType >::findSmallestVector(), shark::kMeans(), shark::MergeBudgetMaintenanceStrategy< RealVector >::reduceBudget(), shark::KernelBudgetedSGDTrainer< InputType, CacheType >::train(), shark::KernelSGDTrainer< InputType, CacheType >::train(), shark::Perceptron< InputType >::train(), shark::RegularizationNetworkTrainer< InputType >::train(), and shark::OneClassSvmTrainer< InputType, CacheType >::trainSVM().

◆ alpha() [2/4]

template<class InputType >

RealMatrix const & shark::KernelExpansion< InputType >::alpha ( ) const

inline

Definition at line 139 of file KernelExpansion.h.

References shark::KernelExpansion< InputType >::m_alpha.

◆ alpha() [3/4]

template<class InputType >

double & shark::KernelExpansion< InputType >::alpha	(	std::size_t	example,
		std::size_t	cls
	)

inline

Definition at line 142 of file KernelExpansion.h.

References shark::KernelExpansion< InputType >::m_alpha.

◆ alpha() [4/4]

template<class InputType >

double const & shark::KernelExpansion< InputType >::alpha	(	std::size_t	example,
		std::size_t	cls
	)		const

inline

Definition at line 145 of file KernelExpansion.h.

References shark::KernelExpansion< InputType >::m_alpha.

◆ basis() [1/2]

template<class InputType >

Data< InputType > & shark::KernelExpansion< InputType >::basis ( )

inline

Definition at line 174 of file KernelExpansion.h.

References shark::KernelExpansion< InputType >::m_basis.

◆ basis() [2/2]

template<class InputType >

Data< InputType > const & shark::KernelExpansion< InputType >::basis ( ) const

inline

Definition at line 170 of file KernelExpansion.h.

References shark::KernelExpansion< InputType >::m_basis.

Referenced by shark::MergeBudgetMaintenanceStrategy< RealVector >::addToModel(), shark::ProjectBudgetMaintenanceStrategy< RealVector >::addToModel(), shark::RemoveBudgetMaintenanceStrategy< InputType >::addToModel(), shark::KernelExpansion< InputType >::KernelExpansion(), shark::MergeBudgetMaintenanceStrategy< RealVector >::reduceBudget(), and shark::KernelExpansion< InputType >::setStructure().

◆ createState()

template<class InputType >

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

inlinevirtual

Creates an internal state of the model.

The state is needed when the derivatives are to be calculated. Eval can store a state which is then reused to speed up the calculations of the derivatives. This also allows eval to be evaluated in parallel!

Reimplemented from shark::AbstractModel< InputType, RealVector >.

Reimplemented in shark::MissingFeaturesKernelExpansion< InputType >.

Definition at line 231 of file KernelExpansion.h.

◆ eval() [1/2]

template<class InputType >

void shark::KernelExpansion< InputType >::eval	(	BatchInputType const &	patterns,
		BatchOutputType &	outputs
	)		const

inlinevirtual

Standard interface for evaluating the response of the model to a batch of patterns.

Parameters

patterns	the inputs of the model
outputs	the predictions or response of the model to every pattern

Reimplemented from shark::AbstractModel< InputType, RealVector >.

Reimplemented in shark::MissingFeaturesKernelExpansion< InputType >.

Definition at line 236 of file KernelExpansion.h.

References shark::Data< Type >::batch(), shark::batchEnd(), shark::batchSize(), shark::KernelExpansion< InputType >::hasOffset(), shark::KernelExpansion< InputType >::m_alpha, shark::KernelExpansion< InputType >::m_b, shark::KernelExpansion< InputType >::m_basis, shark::KernelExpansion< InputType >::mep_kernel, shark::Data< Type >::numberOfBatches(), and SHARK_ASSERT.

Referenced by shark::KernelExpansion< InputType >::eval(), and shark::KernelBudgetedSGDTrainer< InputType, CacheType >::train().

◆ eval() [2/2]

template<class InputType >

void shark::KernelExpansion< InputType >::eval	(	BatchInputType const &	patterns,
		BatchOutputType &	outputs,
		State &	state
	)		const

inlinevirtual

Standard interface for evaluating the response of the model to a batch of patterns.

Parameters

patterns	the inputs of the model
outputs	the predictions or response of the model to every pattern
state	intermediate results stored by eval which can be reused for derivative computation.

Implements shark::AbstractModel< InputType, RealVector >.

Reimplemented in shark::MissingFeaturesKernelExpansion< InputType >.

Definition at line 261 of file KernelExpansion.h.

References shark::KernelExpansion< InputType >::eval().