jsat.datatransform.kernel

Class KernelPCA

java.lang.Object

jsat.datatransform.DataTransformBase

jsat.datatransform.kernel.KernelPCA

All Implemented Interfaces:

Serializable, Cloneable, DataTransform, Parameterized

public class KernelPCA
extends DataTransformBase

A kernelized implementation of PCA. Because this works in a different feature space, it will do its own centering in the kernel space.

KernelPCA is expensive to compute at O(n³) work, where n is the number of data points. For this reason, sampling from Nystrom is used to reduce the data set to a reasonable approximation.

See: Schölkopf, B., Smola, A.,&Müller, K.-R. (1998). Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation, 10(5), 1299–1319. doi:10.1162/089976698300017467

Author:

Edward Raff

See Also:

Nystrom.SamplingMethod, Serialized Form

Constructor Summary

Constructors

Modifier	Constructor and Description
	KernelPCA() Creates a new Kernel PCA transform object using the RBF Kernel and 100 dimensions
	KernelPCA(int dimensions) Creates a new Kernel PCA transform object using the RBF Kernel
protected	KernelPCA(KernelPCA toCopy) Copy constructor
	KernelPCA(KernelTrick k, DataSet ds, int dimensions, int basisSize, Nystrom.SamplingMethod samplingMethod) Creates a new Kernel PCA transform object
	KernelPCA(KernelTrick k, int dimensions) Creates a new Kernel PCA transform object
	KernelPCA(KernelTrick k, int dimensions, int basisSize, Nystrom.SamplingMethod samplingMethod) Creates a new Kernel PCA transform object

Method Summary

Modifier and Type	Method and Description
KernelPCA	clone()
void	fit(DataSet ds) Fits this transform to the given dataset.
Nystrom.SamplingMethod	getBasisSamplingMethod() Returns the method of selecting the basis vectors
int	getBasisSize() Returns the number of basis vectors to use
int	getDimensions() Returns the number of dimensions to project down too
KernelTrick	getKernel()
static Distribution	guessDimensions(DataSet d)
void	setBasisSamplingMethod(Nystrom.SamplingMethod method) Sets the method of selecting the basis vectors
void	setBasisSize(int basisSize) Sets the basis size for the Kernel PCA to be learned from.
void	setDimensions(int dimensions) Sets the dimension of the new feature space, which is the number of principal components to select from the kernelized feature space.
void	setKernel(KernelTrick k)
DataPoint	transform(DataPoint dp) Returns a new data point that is a transformation of the original data point.

Methods inherited from class jsat.datatransform.DataTransformBase

getParameter, getParameters

Methods inherited from class java.lang.Object

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

Constructor Detail

KernelPCA

public KernelPCA()

Creates a new Kernel PCA transform object using the RBF Kernel and 100 dimensions

KernelPCA

public KernelPCA(int dimensions)

Creates a new Kernel PCA transform object using the RBF Kernel

Parameters:

dimensions - the number of dimensions to project down to. Must be less than than the basis size

KernelPCA

public KernelPCA(KernelTrick k,
                 int dimensions)

Creates a new Kernel PCA transform object

Parameters:

k - the kernel trick to use

dimensions - the number of dimensions to project down to. Must be less than than the basis size

KernelPCA

public KernelPCA(KernelTrick k,
                 int dimensions,
                 int basisSize,
                 Nystrom.SamplingMethod samplingMethod)

Creates a new Kernel PCA transform object

Parameters:

k - the kernel trick to use

dimensions - the number of dimensions to project down to. Must be less than than the basis size

basisSize - the number of points from the data set to select. If larger than the number of data points in the data set, the whole data set will be used.

samplingMethod - the sampling method to select the basis vectors

KernelPCA

public KernelPCA(KernelTrick k,
                 DataSet ds,
                 int dimensions,
                 int basisSize,
                 Nystrom.SamplingMethod samplingMethod)

Creates a new Kernel PCA transform object

Parameters:

k - the kernel trick to use

ds - the data set to form the data transform from

dimensions - the number of dimensions to project down to. Must be less than than the basis size

basisSize - the number of points from the data set to select. If larger than the number of data points in the data set, the whole data set will be used.

samplingMethod - the sampling method to select the basis vectors

KernelPCA

protected KernelPCA(KernelPCA toCopy)

Copy constructor

Parameters:

toCopy - the object to copy

Method Detail

fit

public void fit(DataSet ds)

Description copied from interface: DataTransform

Fits this transform to the given dataset. Some transforms can only be learned from classification or regression datasets. If an incompatible dataset type is given, a FailedToFitException exception may be thrown.

Parameters:

ds - the dataset to fir this transform to

transform

public DataPoint transform(DataPoint dp)

Description copied from interface: DataTransform

Returns a new data point that is a transformation of the original data point. This new data point is a different object, but may contain the same references as the original data point. It is not guaranteed that you can mutate the transformed point without having a side effect on the original point.

Parameters:

dp - the data point to apply a transformation to

Returns:

a transformed data point

clone

public KernelPCA clone()

Specified by:

clone in interface DataTransform

Specified by:

clone in class DataTransformBase

setKernel

public void setKernel(KernelTrick k)

Parameters:

k - the kernel trick to use

getKernel

public KernelTrick getKernel()

Returns:

the kernel trick to use

setBasisSize

public void setBasisSize(int basisSize)

Sets the basis size for the Kernel PCA to be learned from. Increasing the basis increase the accuracy of the transform, but increased the training time at a cubic rate.

Parameters:

basisSize - the number of basis vectors to build Kernel PCA from

getBasisSize

public int getBasisSize()

Returns the number of basis vectors to use

Returns:

the number of basis vectors to use

setDimensions

public void setDimensions(int dimensions)

Sets the dimension of the new feature space, which is the number of principal components to select from the kernelized feature space.

Parameters:

dimensions - the number of dimensions to project down too

getDimensions

public int getDimensions()

Returns the number of dimensions to project down too

Returns:

the number of dimensions to project down too

setBasisSamplingMethod

public void setBasisSamplingMethod(Nystrom.SamplingMethod method)

Sets the method of selecting the basis vectors

Parameters:

method - the method of selecting the basis vectors

getBasisSamplingMethod

public Nystrom.SamplingMethod getBasisSamplingMethod()

Returns the method of selecting the basis vectors

Returns:

the method of selecting the basis vectors

guessDimensions

public static Distribution guessDimensions(DataSet d)