jsat.distributions.kernels

Class BaseL2Kernel

java.lang.Object

jsat.distributions.kernels.BaseL2Kernel

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable, KernelTrick, Parameterized

Direct Known Subclasses:

PukKernel, RationalQuadraticKernel, RBFKernel

public abstract class BaseL2Kernel
extends java.lang.Object
implements KernelTrick

Many Kernels can be described in terms the L2 norm with some operations performed on it. For example, the RBFKernel and RationalQuadraticKernel can both be expressed in terms of the L₂ norm of the two inputs. To simplify the addition of other kernels based on the same norm, this base class exists.

All Kernels extending this base kernel support acceleration. This is done making use of the fact that || x - y ||² = x x' +y y' - 2 x y'
Thus the cached value for each vector is its self dot product.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
BaseL2Kernel()

Method Summary

Modifier and Type	Method and Description
void	addToCache(Vec newVec, java.util.List<java.lang.Double> cache) Appends the new cache values for the given vector to the list of cache values.
abstract KernelTrick	clone()
abstract double	eval(int a, int b, java.util.List<? extends Vec> trainingSet, java.util.List<java.lang.Double> cache) Produces the correct kernel evaluation given the training set and the cache generated by KernelTrick.getAccelerationCache(List).
abstract double	eval(int a, Vec b, java.util.List<java.lang.Double> qi, java.util.List<? extends Vec> vecs, java.util.List<java.lang.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).
abstract double	eval(Vec a, Vec b) Evaluate this kernel function for the two given vectors.
double	evalSum(java.util.List<? extends Vec> finalSet, java.util.List<java.lang.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(java.util.List<? extends Vec> finalSet, java.util.List<java.lang.Double> cache, double[] alpha, Vec y, java.util.List<java.lang.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
java.util.List<java.lang.Double>	getAccelerationCache(java.util.List<? extends Vec> trainingSet) Creates a new list cache values from a given list of training set vectors.
java.util.List<java.lang.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 KernelTrick.getAccelerationCache(java.util.List) .
boolean	supportsAcceleration() Indicates if this kernel supports building an acceleration cache using the KernelTrick.getAccelerationCache(List) and associated cache accelerated methods.

Methods inherited from class java.lang.Object

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

Methods inherited from interface jsat.distributions.kernels.KernelTrick

normalized, toString

Methods inherited from interface jsat.parameters.Parameterized

getParameter, getParameters

Constructor Detail

BaseL2Kernel

public BaseL2Kernel()

Method Detail

eval

public abstract 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

Parameters:

a - the first vector

b - the first vector

Returns:

the evaluation

clone

public abstract KernelTrick clone()

Specified by:

clone in interface KernelTrick

Overrides:

clone in class java.lang.Object

supportsAcceleration

public boolean supportsAcceleration()

Description copied from interface: KernelTrick

Indicates if this kernel supports building an acceleration cache using the KernelTrick.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 KernelTrick.eval(int, Vec, List, List, List) and KernelTrick.eval(int, int, List, List) to perform kernel products.

Specified by:

supportsAcceleration in interface KernelTrick

Returns:

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

getAccelerationCache

public java.util.List<java.lang.Double> getAccelerationCache(java.util.List<? extends Vec> trainingSet)

Description copied from interface: KernelTrick

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.

Specified by:

getAccelerationCache in interface KernelTrick

Parameters:

trainingSet - the list of training set vectors

Returns:

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

getQueryInfo

public java.util.List<java.lang.Double> getQueryInfo(Vec q)

Description copied from interface: KernelTrick

Pre computes query information that would have be generated if the query was a member of the original list of vectors when calling KernelTrick.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.

Specified by:

getQueryInfo in interface KernelTrick

Parameters:

q - the query point to generate cache information for

Returns:

the cache information for the query point

addToCache

public void addToCache(Vec newVec,
                       java.util.List<java.lang.Double> cache)

Description copied from interface: KernelTrick

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 KernelTrick.getAccelerationCache(java.util.List)

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

Specified by:

addToCache in interface KernelTrick

Parameters:

newVec - the new vector to add to the cache values

cache - the original list of cache values to add to

eval

public abstract double eval(int a,
                            Vec b,
                            java.util.List<java.lang.Double> qi,
                            java.util.List<? extends Vec> vecs,
                            java.util.List<java.lang.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

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 abstract double eval(int a,
                            int b,
                            java.util.List<? extends Vec> trainingSet,
                            java.util.List<java.lang.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

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)

evalSum

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

Description copied from interface: KernelTrick

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

Specified by:

evalSum in interface KernelTrick

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

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

Description copied from interface: KernelTrick

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

Specified by:

evalSum in interface KernelTrick

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