com.aliasi.matrix
Class GaussianRadialBasisKernel

java.lang.Object
  com.aliasi.matrix.GaussianRadialBasisKernel

All Implemented Interfaces:

KernelFunction, Proximity<Vector>, Serializable

public class GaussianRadialBasisKernel
extends Object
implements KernelFunction, Serializable

A GaussianRadialBasisKernel provides a kernel based on a Gaussian radial basis function with a fixed variance parameter. As a kernel function, it unfolds into an infinite-dimension Hilbert space.

The radial basis kernel function of radius r is defined between vectors v1 and v2 as follows:

 rbf(v1,v2) = exp(- r * distance(v1,v2)2)
 

where distance(v1,v2) is the Euclidean distance, as defined in the class documentation for EuclideanDistance. In this formulation, the radius r is related to the variance σ2 by:

 r = 1/(2 * σ2)

For more information on the Gaussian radial basis kernel and applications, see:

• Wikipedia: Radial Basis Function

Since:

LingPipe3.1

Version:

3.8

Author:

Bob Carpenter

See Also:

Serialized Form

Constructor Summary

GaussianRadialBasisKernel(double radius)
Construct a Gaussian radial basis kernel with the specified radius of influence.

Method Summary

double	proximity(Vector v1, Vector v2) Returns the result of applying this Guassian radial basis kernel to the specified vectors.
String	toString() Returns a string-based representation of this kernel function, including the kernel type and radius.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

GaussianRadialBasisKernel

public GaussianRadialBasisKernel(double radius)

Construct a Gaussian radial basis kernel with the specified radius of influence.

Parameters:

radius - The radius of influence for the kernel.

Method Detail

proximity

public double proximity(Vector v1,
                        Vector v2)

Returns the result of applying this Guassian radial basis kernel to the specified vectors. See the class documentation above for a full definition.

Specified by:

proximity in interface KernelFunction

Specified by:

proximity in interface Proximity<Vector>

Parameters:

v1 - First vector.

v2 - Second vector.

Returns:

Kernel function applied to the two vectors.

Throws:

IllegalArgumentException - If the vectors are not of the same dimensionality.

toString

public String toString()

Returns a string-based representation of this kernel function, including the kernel type and radius.

Overrides:

toString in class Object

Returns:

A string representing this kernel.