jsat.distributions.kernels

Interface KernelTrick

All Superinterfaces:

Cloneable, Parameterized, Serializable

All Known Implementing Classes:

BaseKernelTrick, BaseL2Kernel, DistanceMetricBasedKernel, GeneralRBFKernel, LinearKernel, NormalizedKernel, PolynomialKernel, PukKernel, RationalQuadraticKernel, RBFKernel, SigmoidKernel

public interface KernelTrick
extends Parameterized, Cloneable, Serializable

The KernelTrick is a method can can be used to alter an algorithm to do its calculations in a projected feature space, without explicitly forming the features. If an algorithm uses only dot products, the Kernel trick can be used in place of these dot products, and computes the inner product in a different feature space.

All KerenlTrick objects are parameterized so that the values of the kernel can be exposed by the algorithm that makes use of these parameters. To avoid conflicts in parameter names, the parameters of a KernelTrick should be of the form:
< SimpleClassName >_< Variable Name >

Author:

Edward Raff

Method Summary

Modifier and Type	Method and Description
void	addToCache(Vec newVec, List<Double> cache) Appends the new cache values for the given vector to the list of cache values.
KernelTrick	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 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 getQueryInfo(jsat.linear.Vec).
double	eval(Vec a, Vec b) Evaluate this kernel function for the two given vectors.
double	evalSum(List<? extends Vec> finalSet, List<Double> cache, double[] alpha, Vec y, int start, int end) Performs an efficient summation of kernel products of the form ∑ αi k(xi, y) where x are the final set of vectors, and α the associated scalar multipliers
double	evalSum(List<? extends Vec> finalSet, List<Double> cache, double[] alpha, Vec y, List<Double> qi, int start, int end) Performs an efficient summation of kernel products of the form ∑ αi k(xi, y) where x are the final set of vectors, and α the associated scalar multipliers
List<Double>	getAccelerationCache(List<? extends Vec> trainingSet) Creates a new list cache values from a given list of training set vectors.
List<Double>	getQueryInfo(Vec q) Pre computes query information that would have be generated if the query was a member of the original list of vectors when calling getAccelerationCache(java.util.List) .
boolean	normalized() This method indicates if a kernel is a normalized kernel or not.
boolean	supportsAcceleration() Indicates if this kernel supports building an acceleration cache using the getAccelerationCache(List) and associated cache accelerated methods.
String	toString() A descriptive name for the type of KernelFunction

Methods inherited from interface jsat.parameters.Parameterized

getParameter, getParameters

Method Detail

eval

double eval(Vec a,
            Vec b)

Evaluate this kernel function for the two given vectors.

Parameters:

a - the first vector

b - the first vector

Returns:

the evaluation

toString

String toString()

A descriptive name for the type of KernelFunction

Overrides:

toString in class Object

Returns:

a descriptive name for the type of KernelFunction

clone

KernelTrick clone()

supportsAcceleration

boolean supportsAcceleration()

Indicates if this kernel supports building an acceleration cache using the getAccelerationCache(List) and associated cache accelerated methods. By default this method will return false. If true, then a cache can be obtained from this matrix and used in conjunction with eval(int, Vec, List, List, List) and eval(int, int, List, List) to perform kernel products.

Returns:

true if cache acceleration is supported for this kernel, false otherwise.

getAccelerationCache

List<Double> getAccelerationCache(List<? extends Vec> trainingSet)

Creates a new list cache values from a given list of training set vectors. If this kernel does not support acceleration, null will be returned.

Parameters:

trainingSet - the list of training set vectors

Returns:

a list of cache values that may be used by this kernel

getQueryInfo

List<Double> getQueryInfo(Vec q)

Pre computes query information that would have be generated if the query was a member of the original list of vectors when calling getAccelerationCache(java.util.List) . This can then be used if a large number of kernel computations are going to be done against points in the original set for a point that is outside the original space.

If this kernel does not support acceleration, null will be returned.

Parameters:

q - the query point to generate cache information for

Returns:

the cache information for the query point

addToCache

void addToCache(Vec newVec,
                List<Double> cache)

Appends the new cache values for the given vector to the list of cache values. This method is present for online style kernel learning algorithms, where the set of vectors is not known in advance. When a vector is added to the set of kernel vectors, its cache values can be added using this method.

The results of calling this sequentially on a lit of vectors starting with an empty double list is equivalent to getting the results from calling getAccelerationCache(java.util.List)

If this kernel does not support acceleration, this method call will function as a nop.

Parameters:

newVec - the new vector to add to the cache values

cache - the original list of cache values to add to

eval

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 getQueryInfo(jsat.linear.Vec).
If the cache input is null, then 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

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 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

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 eval(jsat.linear.Vec, jsat.linear.Vec)

evalSum

double evalSum(List<? extends Vec> finalSet,
               List<Double> cache,
               double[] alpha,
               Vec y,
               int start,
               int end)

Performs an efficient summation of kernel products of the form
∑ α_i k(x_i, y)
where x are the final set of vectors, and α the associated scalar multipliers

Parameters:

finalSet - the final set of vectors

cache - the cache associated with the final set of vectors

alpha - the coefficients associated with each vector

y - the vector to perform the summed kernel products against

start - the starting index (inclusive) to sum from

end - the ending index (exclusive) to sum from

Returns:

the sum of the multiplied kernel products

evalSum

double evalSum(List<? extends Vec> finalSet,
               List<Double> cache,
               double[] alpha,
               Vec y,
               List<Double> qi,
               int start,
               int end)

Performs an efficient summation of kernel products of the form
∑ α_i k(x_i, y)
where x are the final set of vectors, and α the associated scalar multipliers

Parameters:

finalSet - the final set of vectors

cache - the cache associated with the final set of vectors

alpha - the coefficients associated with each vector

y - the vector to perform the summed kernel products against

qi - the query information about y

start - the starting index (inclusive) to sum from

end - the ending index (exclusive) to sum from

Returns:

the sum of the multiplied kernel products

normalized

boolean normalized()

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.