mlpack::kernel::GaussianKernel Class Reference

The standard Gaussian kernel. More...

List of all members.

Public Member Functions
	GaussianKernel (double bandwidth)
	Construct the Gaussian kernel with a custom bandwidth.
	GaussianKernel ()
	Default constructor; sets bandwidth to 1.0.
void	Bandwidth (const double bandwidth)
	Modify the bandwidth.
double	Bandwidth () const
	Get the bandwidth.
template<typename VecType >
double	ConvolutionIntegral (const VecType &a, const VecType &b)
	Obtain a convolution integral of the Gaussian kernel.
double	Evaluate (double t) const
	Evaluation of the Gaussian kernel given the distance between two points.
template<typename VecType >
double	Evaluate (const VecType &a, const VecType &b) const
	Evaluation of the Gaussian kernel.
double	Gamma () const
	Get the precalculated constant.
double	Normalizer (size_t dimension)
	Obtain the normalization constant of the Gaussian kernel.
Private Attributes
double	bandwidth
	Kernel bandwidth.
double	gamma
	Precalculated constant depending on the bandwidth; $\gamma = -\frac{1}{2 \mu^2}$ .

Detailed Description

The standard Gaussian kernel.

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

$K(x, y) = \exp(-\frac{|| x - y ||^2}{2 \mu^2}).$

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

Definition at line 43 of file gaussian_kernel.hpp.

Constructor & Destructor Documentation

mlpack::kernel::GaussianKernel::GaussianKernel ( ) [inline]

Default constructor; sets bandwidth to 1.0.

Definition at line 49 of file gaussian_kernel.hpp.

mlpack::kernel::GaussianKernel::GaussianKernel ( double bandwidth ) [inline]

Construct the Gaussian kernel with a custom bandwidth.

Parameters:

bandwidth

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

Definition at line 57 of file gaussian_kernel.hpp.

Member Function Documentation

void mlpack::kernel::GaussianKernel::Bandwidth ( const double bandwidth ) [inline]

Modify the bandwidth.

This takes an argument because we must update the precalculated constant (gamma).

Definition at line 124 of file gaussian_kernel.hpp.

References gamma.

double mlpack::kernel::GaussianKernel::Bandwidth ( ) const [inline]

Get the bandwidth.

Definition at line 120 of file gaussian_kernel.hpp.

References bandwidth.

template<typename VecType >

double mlpack::kernel::GaussianKernel::ConvolutionIntegral	(	const VecType &	a,
		const VecType &	b
	)			`[inline]`

Obtain a convolution integral of the Gaussian kernel.

Parameters:

	a,first	vector
	b,second	vector

Returns:: the convolution integral

Definition at line 112 of file gaussian_kernel.hpp.

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

double mlpack::kernel::GaussianKernel::Evaluate ( double t ) const [inline]

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

Parameters:

t

The distance between the two points the kernel is evaluated on.

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

Definition at line 87 of file gaussian_kernel.hpp.

References gamma.

template<typename VecType >

double mlpack::kernel::GaussianKernel::Evaluate	(	const VecType &	a,
		const VecType &	b
	)			const `[inline]`

Evaluation of the Gaussian 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 74 of file gaussian_kernel.hpp.

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

Referenced by ConvolutionIntegral().

double mlpack::kernel::GaussianKernel::Gamma ( ) const [inline]

Get the precalculated constant.

Definition at line 131 of file gaussian_kernel.hpp.

References gamma.

double mlpack::kernel::GaussianKernel::Normalizer ( size_t dimension ) [inline]

Obtain the normalization constant of the Gaussian kernel.

Parameters:

dimension

Returns:: the normalization constant

Definition at line 99 of file gaussian_kernel.hpp.

References bandwidth, and M_PI.

Referenced by ConvolutionIntegral().

Member Data Documentation

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

Kernel bandwidth.

Definition at line 135 of file gaussian_kernel.hpp.

Referenced by Bandwidth(), and Normalizer().

double mlpack::kernel::GaussianKernel::gamma [private]

Precalculated constant depending on the bandwidth; $\gamma = -\frac{1}{2 \mu^2}$ .

Definition at line 139 of file gaussian_kernel.hpp.

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

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

src/mlpack/core/kernels/gaussian_kernel.hpp

Generated on 13 Aug 2014 for MLPACK by 1.6.1