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 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...

template < typename Archive >
void	serialize (Archive &ar, const uint32_t)
	Serialize the kernel. 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 30 of file laplacian_kernel.hpp.

Constructor & Destructor Documentation

◆ LaplacianKernel() [1/2]

LaplacianKernel ( )

inline

Default constructor; sets bandwidth to 1.0.

Definition at line 36 of file laplacian_kernel.hpp.

◆ LaplacianKernel() [2/2]

LaplacianKernel ( double bandwidth )

inline

Construct the Laplacian kernel with a custom bandwidth.

Parameters

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

Definition at line 44 of file laplacian_kernel.hpp.

Member Function Documentation

◆ Bandwidth() [1/2]

double Bandwidth ( ) const

inline

Get the bandwidth.

Definition at line 95 of file laplacian_kernel.hpp.

◆ Bandwidth() [2/2]

double& Bandwidth ( )

inline

Modify the bandwidth.

Definition at line 97 of file laplacian_kernel.hpp.

◆ Evaluate() [1/2]

double 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.

Definition at line 61 of file laplacian_kernel.hpp.

References LMetric< TPower, TTakeRoot >::Evaluate().

◆ Evaluate() [2/2]

double 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 75 of file laplacian_kernel.hpp.

◆ Gradient()

double 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.

Definition at line 90 of file laplacian_kernel.hpp.

◆ serialize()

void serialize	(	Archive &	ar,
		const uint32_t
	)

inline

Serialize the kernel.

Definition at line 101 of file laplacian_kernel.hpp.

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

/home/ryan/src/mlpack.org/_src/mlpack-git/src/mlpack/core/kernels/laplacian_kernel.hpp

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ LaplacianKernel() [1/2]

◆ LaplacianKernel() [2/2]

Member Function Documentation

◆ Bandwidth() [1/2]

◆ Bandwidth() [2/2]

◆ Evaluate() [1/2]

◆ Evaluate() [2/2]

◆ Gradient()

◆ serialize()