jsat.distributions.kernels

Class RBFKernel

java.lang.Object

jsat.distributions.kernels.BaseL2Kernel

jsat.distributions.kernels.RBFKernel

All Implemented Interfaces:

Serializable, Cloneable, KernelTrick, Parameterized

public class RBFKernel
extends BaseL2Kernel

Provides a kernel for the Radial Basis Function, which is of the form
k(x, y) = exp(-||x-y||²/(2*σ²))

Author:

Edward Raff

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
RBFKernel() Creates a new RBF kernel with σ = 1
RBFKernel(double sigma) Creates a new RBF kernel

Method Summary

Modifier and Type	Method and Description
RBFKernel	clone()
double	eval(int a, int b, List<? extends Vec> trainingSet, List<Double> cache) Produces the correct kernel evaluation given the training set and the cache generated by KernelTrick.getAccelerationCache(List).
double	eval(int a, Vec b, List<Double> qi, List<? extends Vec> vecs, List<Double> cache) Computes the kernel product between one vector in the original list of vectors with that of another vector not from the original list, but had information generated by KernelTrick.getQueryInfo(jsat.linear.Vec).
double	eval(Vec a, Vec b) Evaluate this kernel function for the two given vectors.
static double	gammToSigma(double gamma) Another common (equivalent) form of the RBF kernel is k(x, y) = exp(-γ||x-y||2).
double	getSigma()
static Distribution	guessSigma(DataSet d) Guess the distribution to use for the kernel width term σ in the RBF kernel.
boolean	normalized() This method indicates if a kernel is a normalized kernel or not.
void	setSigma(double sigma) Sets the sigma parameter, which must be a positive value
static double	sigmaToGamma(double sigma) Another common (equivalent) form of the RBF kernel is k(x, y) = exp(-γ||x-y||2).
String	toString() A descriptive name for the type of KernelFunction

Methods inherited from class jsat.distributions.kernels.BaseL2Kernel

addToCache, evalSum, evalSum, getAccelerationCache, getParameter, getParameters, getQueryInfo, getSqrdNorm, getSqrdNorm, getSqrdNorm, supportsAcceleration

Methods inherited from class java.lang.Object

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

Constructor Detail

RBFKernel

public RBFKernel()

Creates a new RBF kernel with σ = 1

RBFKernel

public RBFKernel(double sigma)

Creates a new RBF kernel

Parameters:

sigma - the sigma parameter

Method Detail

eval

public double eval(Vec a,
                   Vec b)

Description copied from interface: KernelTrick

Evaluate this kernel function for the two given vectors.

Specified by:

eval in interface KernelTrick

Specified by:

eval in class BaseL2Kernel

Parameters:

a - the first vector

b - the first vector

Returns:

the evaluation

eval

public double eval(int a,
                   int b,
                   List<? extends Vec> trainingSet,
                   List<Double> cache)

Description copied from interface: KernelTrick

Produces the correct kernel evaluation given the training set and the cache generated by KernelTrick.getAccelerationCache(List). The training vectors should be in the same order.

Specified by:

eval in interface KernelTrick

Specified by:

eval in class BaseL2Kernel

Parameters:

a - the index of the first training vector

b - the index of the second training vector

trainingSet - the list of training set vectors

cache - the double list of cache values generated by this kernel for the given training set

Returns:

the same kernel evaluation result as KernelTrick.eval(jsat.linear.Vec, jsat.linear.Vec)

eval

public double eval(int a,
                   Vec b,
                   List<Double> qi,
                   List<? extends Vec> vecs,
                   List<Double> cache)

Description copied from interface: KernelTrick

Computes the kernel product between one vector in the original list of vectors with that of another vector not from the original list, but had information generated by KernelTrick.getQueryInfo(jsat.linear.Vec).
If the cache input is null, then KernelTrick.eval(jsat.linear.Vec, jsat.linear.Vec) will be called directly.

Specified by:

eval in interface KernelTrick

Specified by:

eval in class BaseL2Kernel

Parameters:

a - the index of the vector in the cache

b - the other vector

qi - the query information about b

vecs - the list of vectors used to build the cache

cache - the cache associated with the given list of vectors

Returns:

the kernel product of the two vectors

setSigma

public void setSigma(double sigma)

Sets the sigma parameter, which must be a positive value

Parameters:

sigma - the sigma value

getSigma

public double getSigma()

toString

public String toString()

Description copied from interface: KernelTrick

A descriptive name for the type of KernelFunction

Specified by:

toString in interface KernelTrick

Overrides:

toString in class Object

Returns:

a descriptive name for the type of KernelFunction

clone

public RBFKernel clone()

Specified by:

clone in interface KernelTrick

Specified by:

clone in class BaseL2Kernel

sigmaToGamma

public static double sigmaToGamma(double sigma)

Another common (equivalent) form of the RBF kernel is k(x, y) = exp(-γ||x-y||²). This method converts the σ value used by this class to the equivalent γ value.

Parameters:

sigma - the value of σ

Returns:

the equivalent γ value.

gammToSigma

public static double gammToSigma(double gamma)

Another common (equivalent) form of the RBF kernel is k(x, y) = exp(-γ||x-y||²). This method converts the γ value equivalent σ value used by this class.

Parameters:

gamma - the value of γ

Returns:

the equivalent σ value

guessSigma

public static Distribution guessSigma(DataSet d)

Guess the distribution to use for the kernel width term σ in the RBF kernel.

Parameters:

d - the data set to get the guess for

Returns:

the guess for the σ parameter in the RBF Kernel

normalized

public boolean normalized()

Description copied from interface: KernelTrick

This method indicates if a kernel is a normalized kernel or not. A normalized kernel is one in which k(x,x) = 1 for the same object, and no value greater than 1 can be returned.

Returns:

true if this is a normalized kernel. false otherwise.