jsat.distributions.kernels

Class GeneralRBFKernel

java.lang.Object

jsat.distributions.kernels.DistanceMetricBasedKernel

jsat.distributions.kernels.GeneralRBFKernel

All Implemented Interfaces:

Serializable, Cloneable, KernelTrick, Parameterized

public class GeneralRBFKernel
extends DistanceMetricBasedKernel

This class provides a generalization of the RBFKernel to arbitrary distance metrics, and is of the form exp(-d(x, y)²/(2 σ² )). So long as the distance metric is valid, the resulting kernel trick will be a valid kernel.

If the EuclideanDistance is used, then this becomes equivalent to the RBFKernel.

Note, that since the KernelTrick has no concept of training - the distance metric can not require training either. A pre-trained metric can be admissible thought.

Author:

Edward Raff

See Also:

Serialized Form

Field Summary

Fields inherited from class jsat.distributions.kernels.DistanceMetricBasedKernel

d

Constructor Summary

Constructors

Constructor and Description
GeneralRBFKernel(DistanceMetric d, double sigma) Creates a new Generic RBF Kernel

Method Summary

Modifier and Type	Method and Description
KernelTrick	clone()
double	eval(int a, int b, List<? extends Vec> vecs, 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.
double	getSigma()
Distribution	guessSigma(DataSet d) Guess the distribution to use for the kernel width term σ in the General RBF kernel.
static Distribution	guessSigma(DataSet d, DistanceMetric dist) Guess the distribution to use for the kernel width term σ in the General RBF kernel.
boolean	normalized() This method indicates if a kernel is a normalized kernel or not.
void	setSigma(double sigma) Sets the kernel width parameter, which must be a positive value.

Methods inherited from class jsat.distributions.kernels.DistanceMetricBasedKernel

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

Methods inherited from class java.lang.Object

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

Methods inherited from interface jsat.distributions.kernels.KernelTrick

toString

Constructor Detail

GeneralRBFKernel

public GeneralRBFKernel(DistanceMetric d,
                        double sigma)

Creates a new Generic RBF Kernel

Parameters:

d - the distance metric to use

sigma - the standard deviation to use

Method Detail

setSigma

public void setSigma(double sigma)

Sets the kernel width parameter, which must be a positive value. Larger values indicate a larger width

Parameters:

sigma - the sigma value

getSigma

public double getSigma()

Returns:

the width parameter to use for the kernel

clone

public KernelTrick clone()

Specified by:

clone in interface KernelTrick

Specified by:

clone in class DistanceMetricBasedKernel

eval

public double eval(Vec a,
                   Vec b)

Description copied from interface: KernelTrick

Evaluate this kernel function for the two given vectors.

Parameters:

a - the first vector

b - the first vector

Returns:

the evaluation

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.

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

eval

public double eval(int a,
                   int b,
                   List<? extends Vec> vecs,
                   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.

Parameters:

a - the index of the first training vector

b - the index of the second training vector

vecs - 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)

guessSigma

public Distribution guessSigma(DataSet d)

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

Parameters:

d - the data set to get the guess for

Returns:

the guess for the σ parameter in the General RBF Kernel

guessSigma

public static Distribution guessSigma(DataSet d,
                                      DistanceMetric dist)

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

Parameters:

d - the data set to get the guess for

dist - the distance metric to assume is being used in the kernel

Returns:

the guess for the σ parameter in the General 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.