The standard Laplacian kernel. More...

Public Member Functions
	LaplacianKernel ()
	Default constructor; sets bandwidth to 1.0. More...

	LaplacianKernel (double bandwidth)
	Construct the Laplacian kernel with a custom bandwidth. More...

double	Bandwidth () const
	Get the bandwidth. More...

double &	Bandwidth ()
	Modify the bandwidth. More...

template<typename VecType >
double	Evaluate (const VecType &a, const VecType &b) const
	Evaluation of the Laplacian kernel. More...

double	Evaluate (const double t) const
	Evaluation of the Laplacian kernel given the distance between two points. More...

std::string	ToString () const
	Return a string representation of the kernel. More...

Private Attributes
double	bandwidth
	Kernel bandwidth. More...

Detailed Description

The standard Laplacian kernel.

Given two vectors $ x $ , $ y $ , and a bandwidth $\mu$ (set in the constructor),

$K(x, y) = \exp(-\frac{|| x - y ||}{\mu}).$

The implementation is all in the header file because it is so simple.

Definition at line 40 of file laplacian_kernel.hpp.

Constructor & Destructor Documentation

mlpack::kernel::LaplacianKernel::LaplacianKernel ( )

inline

Default constructor; sets bandwidth to 1.0.

Definition at line 46 of file laplacian_kernel.hpp.

mlpack::kernel::LaplacianKernel::LaplacianKernel ( double bandwidth )

inline

Construct the Laplacian kernel with a custom bandwidth.

Parameters

bandwidth The bandwidth of the kernel ( $\mu$ ).

Definition at line 54 of file laplacian_kernel.hpp.

Member Function Documentation

double mlpack::kernel::LaplacianKernel::Bandwidth ( ) const

inline

Get the bandwidth.

Definition at line 91 of file laplacian_kernel.hpp.

References bandwidth.

double& mlpack::kernel::LaplacianKernel::Bandwidth ( )

inline

Modify the bandwidth.

Definition at line 93 of file laplacian_kernel.hpp.

References bandwidth.

template<typename VecType >

double mlpack::kernel::LaplacianKernel::Evaluate	(	const VecType &	a,
		const VecType &	b
	)		const

inline

Evaluation of the Laplacian kernel.

This could be generalized to use any distance metric, not the Euclidean distance, but for now, the Euclidean distance is used.

Template Parameters

VecType Type of vector (likely arma::vec or arma::spvec).

Parameters

a	First vector.
b	Second vector.

Returns: K(a, b) using the bandwidth ( $\mu$ ) specified in the constructor.

Definition at line 70 of file laplacian_kernel.hpp.

References bandwidth, and mlpack::metric::LMetric< Power, TakeRoot >::Evaluate().

double mlpack::kernel::LaplacianKernel::Evaluate ( const double t ) const

inline

Evaluation of the Laplacian kernel given the distance between two points.

Parameters

t	The distance between the two points the kernel should be evaluated on.

Returns: K(t) using the bandwidth ( $\mu$ ) specified in the constructor.

Definition at line 84 of file laplacian_kernel.hpp.

References bandwidth.

std::string mlpack::kernel::LaplacianKernel::ToString ( ) const

inline

Return a string representation of the kernel.

Definition at line 96 of file laplacian_kernel.hpp.

References bandwidth.

Member Data Documentation

double mlpack::kernel::LaplacianKernel::bandwidth

private

Kernel bandwidth.

Definition at line 106 of file laplacian_kernel.hpp.

Referenced by Bandwidth(), Evaluate(), and ToString().

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

src/mlpack/core/kernels/laplacian_kernel.hpp

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation