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LaplacianKernel Class Reference

The standard Laplacian kernel. More...

Public Member Functions

 LaplacianKernel ()
 Default constructor; sets bandwidth to 1.0. More...

 
 LaplacianKernel (double bandwidth)
 Construct the Laplacian kernel with a custom bandwidth. More...

 
double Bandwidth () const
 Get the bandwidth. More...

 
double & Bandwidth ()
 Modify the bandwidth. More...

 
template
<
typename
VecTypeA
,
typename
VecTypeB
>
double Evaluate (const VecTypeA &a, const VecTypeB &b) const
 Evaluation of the Laplacian kernel. More...

 
double Evaluate (const double t) const
 Evaluation of the Laplacian kernel given the distance between two points. More...

 
double Gradient (const double t) const
 Evaluation of the gradient of the Laplacian kernel given the distance between two points. More...

 
template
<
typename
Archive
>
void serialize (Archive &ar, const unsigned int)
 Serialize the kernel. More...

 

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 30 of file laplacian_kernel.hpp.

Constructor & Destructor Documentation

◆ LaplacianKernel() [1/2]

LaplacianKernel ( )
inline

Default constructor; sets bandwidth to 1.0.

Definition at line 36 of file laplacian_kernel.hpp.

◆ LaplacianKernel() [2/2]

LaplacianKernel ( double  bandwidth)
inline

Construct the Laplacian kernel with a custom bandwidth.

Parameters
bandwidthThe bandwidth of the kernel ( $\mu$).

Definition at line 44 of file laplacian_kernel.hpp.

Member Function Documentation

◆ Bandwidth() [1/2]

double Bandwidth ( ) const
inline

Get the bandwidth.

Definition at line 95 of file laplacian_kernel.hpp.

◆ Bandwidth() [2/2]

double& Bandwidth ( )
inline

Modify the bandwidth.

Definition at line 97 of file laplacian_kernel.hpp.

◆ Evaluate() [1/2]

double Evaluate ( const VecTypeA &  a,
const VecTypeB &  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
VecTypeAType of first vector (likely arma::vec or arma::sp_vec).
VecTypeBType of second vector (arma::vec / arma::sp_vec).
Parameters
aFirst vector.
bSecond vector.
Returns
K(a, b) using the bandwidth ( $\mu$) specified in the constructor.

Definition at line 61 of file laplacian_kernel.hpp.

References LMetric< TPower, TTakeRoot >::Evaluate().

◆ Evaluate() [2/2]

double Evaluate ( const double  t) const
inline

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

Parameters
tThe 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 75 of file laplacian_kernel.hpp.

◆ Gradient()

double Gradient ( const double  t) const
inline

Evaluation of the gradient of the Laplacian kernel given the distance between two points.

Parameters
tThe 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 90 of file laplacian_kernel.hpp.

◆ serialize()

void serialize ( Archive &  ar,
const unsigned  int 
)
inline

Serialize the kernel.

Definition at line 101 of file laplacian_kernel.hpp.


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