mlpack::kernel::GaussianKernel Class Reference

The standard Gaussian kernel. More...

#include <gaussian_kernel.hpp>

Public Member Functions
	GaussianKernel ()
	Default constructor; sets bandwidth to 1.0.
	GaussianKernel (const double bandwidth)
	Construct the Gaussian kernel with a custom bandwidth. More...
template<typename VecTypeA , typename VecTypeB >
double	Evaluate (const VecTypeA &a, const VecTypeB &b) const
	Evaluation of the Gaussian kernel. More...
double	Evaluate (const double t) const
	Evaluation of the Gaussian kernel given the distance between two points. More...
double	Gradient (const double t) const
	Evaluation of the gradient of Gaussian kernel given the distance between two points. More...
double	GradientForSquaredDistance (const double t) const
	Evaluation of the gradient of Gaussian kernel given the squared distance between two points. More...
double	Normalizer (const size_t dimension)
	Obtain the normalization constant of the Gaussian kernel. More...
template<typename VecTypeA , typename VecTypeB >
double	ConvolutionIntegral (const VecTypeA &a, const VecTypeB &b)
	Obtain a convolution integral of the Gaussian kernel. More...
double	Bandwidth () const
	Get the bandwidth.
void	Bandwidth (const double bandwidth)
	Modify the bandwidth. More...
double	Gamma () const
	Get the precalculated constant.
template<typename Archive >
void	serialize (Archive &ar, const uint32_t)
	Serialize the kernel.

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.

Constructor & Destructor Documentation

GaussianKernel()

mlpack::kernel::GaussianKernel::GaussianKernel ( const double  bandwidth )

inline

Construct the Gaussian kernel with a custom bandwidth.

Parameters

bandwidth

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

Member Function Documentation

Bandwidth()

void mlpack::kernel::GaussianKernel::Bandwidth ( const double  bandwidth )

inline

Modify the bandwidth.

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

ConvolutionIntegral()

template<typename VecTypeA , typename VecTypeB >

double mlpack::kernel::GaussianKernel::ConvolutionIntegral ( const VecTypeA &  a, const VecTypeB &  b  )

inline

Obtain a convolution integral of the Gaussian kernel.

Parameters

a	First vector.
b	Second vector.

Returns

The convolution integral.

Evaluate() [1/2]

template<typename VecTypeA , typename VecTypeB >

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

Evaluate() [2/2]

double mlpack::kernel::GaussianKernel::Evaluate ( const 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.

Gradient()

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

inline

Evaluation of the gradient of 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.

GradientForSquaredDistance()

double mlpack::kernel::GaussianKernel::GradientForSquaredDistance ( const double  t ) const

inline

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

Parameters

t	The squared distance between the two points

Returns

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

Normalizer()

double mlpack::kernel::GaussianKernel::Normalizer ( const size_t  dimension )

inline

Obtain the normalization constant of the Gaussian kernel.

Parameters

dimension

Returns

the normalization constant

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

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