A kernel is a positive definite function k(x,y), which can be understood as a generalized scalar product. Kernel methods. like support vector machines or gaussian processes rely on the kernels.

Collaboration diagram for Kernels:

Classes
class	shark::AbstractKernelFunction< InputTypeT >
	Base class of all Kernel functions. More...

class	shark::AbstractMetric< InputTypeT >
	Base-class for metrics. More...

class	shark::ARDKernelUnconstrained< InputType >
	Automatic relevance detection kernel for unconstrained parameter optimization. More...

class	shark::DiscreteKernel
	Kernel on a finite, discrete space. More...

class	shark::GaussianRbfKernel< InputType >
	Gaussian radial basis function kernel. More...

class	shark::LinearKernel< InputType >
	Linear Kernel, parameter free. More...

class	shark::MklKernel< InputType >
	Weighted sum of kernel functions. More...

class	shark::ModelKernel< InputType >
	Kernel function that uses a Model as transformation function for another kernel. More...

class	shark::MonomialKernel< InputType >
	Monomial kernel. Calculates \( \left\langle x_1, x_2 \right\rangle^m_exponent \). More...

struct	shark::MultiTaskSample< InputTypeT >
	Aggregation of input data and task index. More...

class	shark::GaussianTaskKernel< InputTypeT >
	Special "Gaussian-like" kernel function on tasks. More...

class	shark::NormalizedKernel< InputType >
	Normalized version of a kernel function. More...

class	shark::PointSetKernel< InputType >
	Normalized version of a kernel function. More...

class	shark::PolynomialKernel< InputType >
	Polynomial kernel. More...

class	shark::ProductKernel< InputType >
	Product of kernel functions. More...

class	shark::ScaledKernel< InputType >
	Scaled version of a kernel function. More...

class	shark::WeightedSumKernel< InputType >
	Weighted sum of kernel functions. More...

Modules
	Kernel Optimization
	All kinds of objective functions to optimize kernel functions.

Functions
template<typename InputType , typename InputTypeT1 , typename InputTypeT2 >
double	shark::evalSkipMissingFeatures (const AbstractKernelFunction< InputType > &kernelFunction, const InputTypeT1 &inputA, const InputTypeT2 &inputB)

template<typename InputType , typename InputTypeT1 , typename InputTypeT2 , typename InputTypeT3 >
double	shark::evalSkipMissingFeatures (const AbstractKernelFunction< InputType > &kernelFunction, const InputTypeT1 &inputA, const InputTypeT2 &inputB, InputTypeT3 const &missingness)

template<class InputType , class M , class Device >
void	shark::calculateRegularizedKernelMatrix (AbstractKernelFunction< InputType >const &kernel, Data< InputType > const &dataset, blas::matrix_expression< M, Device > &matrix, double regularizer=0)
	Calculates the regularized kernel gram matrix of the points stored inside a dataset.

template<class InputType , class M , class Device >
void	shark::calculateMixedKernelMatrix (AbstractKernelFunction< InputType >const &kernel, Data< InputType > const &dataset1, Data< InputType > const &dataset2, blas::matrix_expression< M, Device > &matrix)
	Calculates the kernel gram matrix between two data sets.

template<class InputType >
RealMatrix	shark::calculateRegularizedKernelMatrix (AbstractKernelFunction< InputType >const &kernel, Data< InputType > const &dataset, double regularizer=0)
	Calculates the regularized kernel gram matrix of the points stored inside a dataset.

template<class InputType >
RealMatrix	shark::calculateMixedKernelMatrix (AbstractKernelFunction< InputType >const &kernel, Data< InputType > const &dataset1, Data< InputType > const &dataset2)
	Calculates the kernel gram matrix between two data sets.

template<class InputType , class WeightMatrix >
RealVector	shark::calculateKernelMatrixParameterDerivative (AbstractKernelFunction< InputType > const &kernel, Data< InputType > const &dataset, WeightMatrix const &weights)
	Efficiently calculates the weighted derivative of a Kernel Gram Matrix w.r.t the Kernel Parameters.

Function Documentation

◆ calculateKernelMatrixParameterDerivative()

template<class InputType , class WeightMatrix >

RealVector shark::calculateKernelMatrixParameterDerivative	(	AbstractKernelFunction< InputType > const &	kernel,
		Data< InputType > const &	dataset,
		WeightMatrix const &	weights
	)

Efficiently calculates the weighted derivative of a Kernel Gram Matrix w.r.t the Kernel Parameters.

The formula is \( \sum_i \sum_j w_{ij} k(x_i,x_j)\) where w_ij are the weights of the gradient and x_i x_j are the datapoints defining the gram matrix and k is the kernel. For efficiency it is assumd that w_ij = w_ji. This method is only useful when the whole Kernel Gram Matrix neds to be computed to get the weights w_ij and only computing smaller blocks is not sufficient.

Parameters

kernel	the kernel for which to calculate the kernel gram matrix
dataset	the set of points used in the gram matrix
weights	the weights of the derivative, they must be symmetric!

Returns: the weighted derivative w.r.t the parameters.

Definition at line 186 of file KernelHelpers.h.

References shark::Data< Type >::batch(), shark::batchSize(), shark::AbstractKernelFunction< InputTypeT >::createState(), shark::AbstractKernelFunction< InputTypeT >::eval(), shark::Data< Type >::numberOfBatches(), shark::IParameterizable< VectorType >::numberOfParameters(), and shark::AbstractKernelFunction< InputTypeT >::weightedParameterDerivative().

Referenced by shark::NegativeGaussianProcessEvidence< InputType, OutputType, LabelType >::evalDerivative(), and shark::RadiusMarginQuotient< InputType, CacheType >::evalDerivative().

◆ calculateMixedKernelMatrix() [1/2]

template<class InputType >

RealMatrix shark::calculateMixedKernelMatrix	(	AbstractKernelFunction< InputType >const &	kernel,
		Data< InputType > const &	dataset1,
		Data< InputType > const &	dataset2
	)

Calculates the kernel gram matrix between two data sets.

Parameters

kernel	the kernel for which to calculate the kernel gram matrix
dataset1	the set of points corresponding to rows of the Gram matrix
dataset2	the set of points corresponding to columns of the Gram matrix

Returns: matrix the target kernel matrix

Definition at line 163 of file KernelHelpers.h.

References shark::calculateMixedKernelMatrix().

◆ calculateMixedKernelMatrix() [2/2]

template<class InputType , class M , class Device >

void shark::calculateMixedKernelMatrix	(	AbstractKernelFunction< InputType >const &	kernel,
		Data< InputType > const &	dataset1,
		Data< InputType > const &	dataset2,
		blas::matrix_expression< M, Device > &	matrix
	)

Calculates the kernel gram matrix between two data sets.

Parameters

kernel	the kernel for which to calculate the kernel gram matrix
dataset1	the set of points corresponding to rows of the Gram matrix
dataset2	the set of points corresponding to columns of the Gram matrix
matrix	the target kernel matrix

Definition at line 97 of file KernelHelpers.h.

References shark::Data< Type >::batch(), shark::batchSize(), shark::Data< Type >::numberOfBatches(), shark::Data< Type >::numberOfElements(), SHARK_PARALLEL_FOR, and SIZE_CHECK.

Referenced by shark::calculateMixedKernelMatrix().

◆ calculateRegularizedKernelMatrix() [1/2]

template<class InputType , class M , class Device >

void shark::calculateRegularizedKernelMatrix	(	AbstractKernelFunction< InputType >const &	kernel,
		Data< InputType > const &	dataset,
		blas::matrix_expression< M, Device > &	matrix,
		double	regularizer = `0`
	)

Calculates the regularized kernel gram matrix of the points stored inside a dataset.

Regularization is applied by adding the regularizer on the diagonal

Parameters

kernel	the kernel for which to calculate the kernel gram matrix
dataset	the set of points used in the gram matrix
matrix	the target kernel matrix
regularizer	the regularizer of the matrix which is always >= 0. default is 0.

Definition at line 53 of file KernelHelpers.h.

References shark::Data< Type >::batch(), shark::batchSize(), shark::Data< Type >::numberOfBatches(), shark::Data< Type >::numberOfElements(), SHARK_PARALLEL_FOR, SHARK_RUNTIME_CHECK, and SIZE_CHECK.

Referenced by shark::calculateRegularizedKernelMatrix(), shark::NegativeGaussianProcessEvidence< InputType, OutputType, LabelType >::eval(), shark::NegativeGaussianProcessEvidence< InputType, OutputType, LabelType >::evalDerivative(), shark::kMeans(), shark::KernelMatrix< InputType, CacheType >::matrix(), and shark::RegularizationNetworkTrainer< InputType >::train().

◆ calculateRegularizedKernelMatrix() [2/2]

template<class InputType >

RealMatrix shark::calculateRegularizedKernelMatrix	(	AbstractKernelFunction< InputType >const &	kernel,
		Data< InputType > const &	dataset,
		double	regularizer = `0`
	)

Calculates the regularized kernel gram matrix of the points stored inside a dataset.

Regularization is applied by adding the regularizer on the diagonal

Parameters

kernel	the kernel for which to calculate the kernel gram matrix
dataset	the set of points used in the gram matrix
regularizer	the regularizer of the matrix which is always >= 0. default is 0.

Returns: the kernel gram matrix

Definition at line 144 of file KernelHelpers.h.

References shark::calculateRegularizedKernelMatrix(), and SHARK_RUNTIME_CHECK.

◆ evalSkipMissingFeatures() [1/2]

template<typename InputType , typename InputTypeT1 , typename InputTypeT2 >

double shark::evalSkipMissingFeatures	(	const AbstractKernelFunction< InputType > &	kernelFunction,
		const InputTypeT1 &	inputA,
		const InputTypeT2 &	inputB
	)

Does a kernel function evaluation with Missing features in the inputs

Parameters

kernelFunction	The kernel function used to do evaluation
inputA	a input
inputB	another input

The kernel k(x,y) is evaluated taking missing features into account. For this it is checked whether a feature of x or y is nan and in this case the corresponding features in inputA and inputB won't be considered.

Definition at line 59 of file EvalSkipMissingFeatures.h.

References shark::AbstractKernelFunction< InputTypeT >::eval(), SHARK_RUNTIME_CHECK, SIZE_CHECK, and shark::AbstractKernelFunction< InputTypeT >::supportsVariableInputSize().

Referenced by shark::MissingFeaturesKernelExpansion< InputType >::computeNorm(), shark::MissingFeaturesKernelExpansion< InputType >::computeNorm(), shark::ExampleModifiedKernelMatrix< InputType, CacheType >::entry(), and shark::MissingFeaturesKernelExpansion< InputType >::eval().

◆ evalSkipMissingFeatures() [2/2]

template<typename InputType , typename InputTypeT1 , typename InputTypeT2 , typename InputTypeT3 >

double shark::evalSkipMissingFeatures	(	const AbstractKernelFunction< InputType > &	kernelFunction,
		const InputTypeT1 &	inputA,
		const InputTypeT2 &	inputB,
		InputTypeT3 const &	missingness
	)

Do kernel function evaluation while Missing features in the inputs

Parameters

kernelFunction	The kernel function used to do evaluation
inputA	a input
inputB	another input
missingness	used to decide which features in the inputs to take into consideration for the purpose of evaluation. If a feature is NaN, then the corresponding features in inputA and inputB won't be considered.

Definition at line 106 of file EvalSkipMissingFeatures.h.

References shark::AbstractKernelFunction< InputTypeT >::eval(), SHARK_RUNTIME_CHECK, SIZE_CHECK, and shark::AbstractKernelFunction< InputTypeT >::supportsVariableInputSize().

Classes

Modules

Functions

Function Documentation

◆ calculateKernelMatrixParameterDerivative()

◆ calculateMixedKernelMatrix() [1/2]

◆ calculateMixedKernelMatrix() [2/2]

◆ calculateRegularizedKernelMatrix() [1/2]

◆ calculateRegularizedKernelMatrix() [2/2]

◆ evalSkipMissingFeatures() [1/2]

◆ evalSkipMissingFeatures() [2/2]