mlpack::kernel::LaplacianKernel Class Reference

The standard Laplacian kernel. More...

#include <laplacian_kernel.hpp>

Public Member Functions
	LaplacianKernel ()
	Default constructor; sets bandwidth to 1.0.
	LaplacianKernel (double bandwidth)
	Construct the Laplacian kernel with a custom bandwidth. More...
template<typename VecTypeA , typename VecTypeB >
double	Evaluate (const VecTypeA &a, const VecTypeB &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...
double	Gradient (const double t) const
	Evaluation of the gradient of the Laplacian kernel given the distance between two points. More...
double	Bandwidth () const
	Get the bandwidth.
double &	Bandwidth ()
	Modify the bandwidth.
template<typename Archive >
void	serialize (Archive &ar, const uint32_t)
	Serialize the kernel.

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.

Constructor & Destructor Documentation

LaplacianKernel()

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

inline

Construct the Laplacian kernel with a custom bandwidth.

Parameters

bandwidth

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

Member Function Documentation

Evaluate() [1/2]

template<typename VecTypeA , typename VecTypeB >

double mlpack::kernel::LaplacianKernel::Evaluate ( const VecTypeA &  a, const VecTypeB &  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

VecTypeA	Type of first vector (likely arma::vec or arma::sp_vec).
VecTypeB	Type of second vector (arma::vec / arma::sp_vec).

Parameters

a	First vector.
b	Second vector.

Returns

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

Evaluate() [2/2]

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.

Gradient()

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

inline

Evaluation of the gradient 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.

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

• src/mlpack/core/kernels/laplacian_kernel.hpp