SYNOPSIS

Public Member Functions

EpanechnikovKernel (const double bandwidth=1.0)
Instantiate the Epanechnikov kernel with the given bandwidth (default 1.0).
template<typename VecType > double ConvolutionIntegral (const VecType &a, const VecType &b)
Obtains the convolution integral [integral of K(||x-a||) K(||b-x||) dx] for the two vectors.
template<typename Vec1Type , typename Vec2Type > double Evaluate (const Vec1Type &a, const Vec2Type &b) const
Evaluate the Epanechnikov kernel on the given two inputs.
double Evaluate (const double distance) const
Evaluate the Epanechnikov kernel given that the distance between the two input points is known.
double Normalizer (const size_t dimension)
Compute the normalizer of this Epanechnikov kernel for the given dimension.
std::string ToString () const

Private Attributes

double bandwidth
Bandwidth of the kernel.
double inverseBandwidthSquared
Cached value of the inverse bandwidth squared (to speed up computation).

Detailed Description

The Epanechnikov kernel, defined as.

\

where $ b $ is the bandwidth the of the kernel (defaults to 1.0).

Definition at line 39 of file epanechnikov_kernel.hpp.

Constructor & Destructor Documentation

mlpack::kernel::EpanechnikovKernel::EpanechnikovKernel (const doublebandwidth = 1.0) [inline]

Instantiate the Epanechnikov kernel with the given bandwidth (default 1.0).

Parameters:

bandwidth Bandwidth of the kernel.

Definition at line 47 of file epanechnikov_kernel.hpp.

Member Function Documentation

template<typename VecType > double mlpack::kernel::EpanechnikovKernel::ConvolutionIntegral (const VecType &a, const VecType &b)

Obtains the convolution integral [integral of K(||x-a||) K(||b-x||) dx] for the two vectors.

Template Parameters:

VecType Type of vector (arma::vec, arma::spvec should be expected).

Parameters:

a First vector.
b Second vector.

Returns:

the convolution integral value.

template<typename Vec1Type , typename Vec2Type > double mlpack::kernel::EpanechnikovKernel::Evaluate (const Vec1Type &a, const Vec2Type &b) const

Evaluate the Epanechnikov kernel on the given two inputs.

Parameters:

a One input vector.
b The other input vector.

double mlpack::kernel::EpanechnikovKernel::Evaluate (const doubledistance) const

Evaluate the Epanechnikov kernel given that the distance between the two input points is known.

double mlpack::kernel::EpanechnikovKernel::Normalizer (const size_tdimension)

Compute the normalizer of this Epanechnikov kernel for the given dimension.

Parameters:

dimension Dimension to calculate the normalizer for.

std::string mlpack::kernel::EpanechnikovKernel::ToString () const

Member Data Documentation

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

Bandwidth of the kernel.

Definition at line 92 of file epanechnikov_kernel.hpp.

double mlpack::kernel::EpanechnikovKernel::inverseBandwidthSquared [private]

Cached value of the inverse bandwidth squared (to speed up computation).

Definition at line 94 of file epanechnikov_kernel.hpp.

Author

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