it.uniroma2.sag.kelp.kernel.standard

Class RbfKernel

java.lang.Object

it.uniroma2.sag.kelp.kernel.Kernel

it.uniroma2.sag.kelp.kernel.KernelComposition

it.uniroma2.sag.kelp.kernel.standard.RbfKernel

public class RbfKernel
extends KernelComposition

Radial Basis Function Kernel.
Given a kernel K, the RBF formula Kr is:
\(Kr(x,y) = e^{-\gamma * \left \lVert x-y \right \rVert ^2}\) where:
\(\left\lVert a \right\rVert\) is the norm of a in the kernel space K, thus \(\left\lVert x-y \right\rVert ^2\) can be computed as:
\(\left\lVert x-y \right\rVert ^2 = \left\lVert x \right\rVert ^2 + \left\lVert y \right\rVert ^2 - 2K(x,y) = K(x,x) + K(y,y) - 2K(x,y)\)

Author:

Simone Filice

Field Summary

Fields inherited from class it.uniroma2.sag.kelp.kernel.KernelComposition

baseKernel

Constructor Summary

Constructors

Constructor and Description
RbfKernel()
RbfKernel(float gamma, Kernel inputSpace)

Method Summary

Methods

Modifier and Type	Method and Description
float	getGamma()
protected float	kernelComputation(Example exA, Example exB) Returns the kernel similarity between the given examples.
void	setGamma(float gamma)

Methods inherited from class it.uniroma2.sag.kelp.kernel.KernelComposition

getBaseKernel, setBaseKernel

Methods inherited from class it.uniroma2.sag.kelp.kernel.Kernel

disableCache, getKernelCache, getKernelComputations, getNumberOfHits, getNumberOfMisses, getSquaredNormCache, innerProduct, load, reset, save, setKernelCache, setSquaredNormCache, squaredNorm, squaredNormOfTheDifference

Methods inherited from class java.lang.Object

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

Constructor Detail

RbfKernel

public RbfKernel(float gamma,
         Kernel inputSpace)

RbfKernel

public RbfKernel()

Method Detail

getGamma

public float getGamma()

Returns:

the gamma

setGamma

public void setGamma(float gamma)

Parameters:

gamma - the gamma to set

kernelComputation

protected float kernelComputation(Example exA,
                      Example exB)

Description copied from class: Kernel

Returns the kernel similarity between the given examples. This corresponds to the inner product in the implicit Reproducing Kernel Hilbert Space (RKHS)

Specified by:

kernelComputation in class Kernel

Parameters:

exA - the first example

exB - the second example

Returns:

the kernel operation between exA and exB