SYNOPSIS

Public Member Functions

LaplacianKernel ()
Default constructor; sets bandwidth to 1.0.
LaplacianKernel (double bandwidth)
Construct the Laplacian kernel with a custom bandwidth.
double Bandwidth () const
Get the bandwidth.
double & Bandwidth ()
Modify the bandwidth.
template<typename VecType > double Evaluate (const VecType &a, const VecType &b) const
Evaluation of the Laplacian kernel.
double Evaluate (const double t) const
Evaluation of the Laplacian kernel given the distance between two points.
std::string ToString () const
Return a string representation of the 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),

\.PP 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 (doublebandwidth) [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 () const [inline]

Get the bandwidth.

Definition at line 91 of file laplacian_kernel.hpp.

References bandwidth.

double& mlpack::kernel::LaplacianKernel::Bandwidth () [inline]

Modify the bandwidth.

Definition at line 93 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().

double mlpack::kernel::LaplacianKernel::Evaluate (const doublet) 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.

std::string mlpack::kernel::LaplacianKernel::ToString () const [inline]

Return a string representation of the kernel.

Definition at line 96 of file laplacian_kernel.hpp.

References bandwidth.

Member Data Documentation

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

Kernel bandwidth.

Definition at line 106 of file laplacian_kernel.hpp.

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

Author

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