mlpack::kernel::LaplacianKernel Class Reference

The standard Laplacian kernel. More...

Public Member Functions
	LaplacianKernel (double bandwidth)
	Construct the Laplacian kernel with a custom bandwidth.
	LaplacianKernel ()
	Default constructor; sets bandwidth to 1.0.
double &	Bandwidth ()
	Modify the bandwidth.
double	Bandwidth () const
	Get the bandwidth.
double	Evaluate (const double t) const
	Evaluation of the Laplacian kernel given the distance between two points.
template<typename VecType >
double	Evaluate (const VecType &a, const VecType &b) const
	Evaluation of the Laplacian kernel.
Private Attributes
double	bandwidth
	Kernel bandwidth.

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 ( ) [inline]

Modify the bandwidth.

Definition at line 93 of file laplacian_kernel.hpp.

References bandwidth.

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::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.

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().

Member Data Documentation

double mlpack::kernel::LaplacianKernel::bandwidth [private]

Kernel bandwidth.

Definition at line 97 of file laplacian_kernel.hpp.

Referenced by Bandwidth(), and Evaluate().

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

src/mlpack/core/kernels/laplacian_kernel.hpp

mlpack::kernel::LaplacianKernel Class Reference

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation