uk.ac.gla.dcs.renaissance.kqpr
Class KernelEigenDecomposition<T extends KernelVector>

java.lang.Object
  uk.ac.gla.dcs.renaissance.kqpr.KernelEigenDecomposition<T>

All Implemented Interfaces:

Serializable

Direct Known Subclasses:

Density, Subspace

public class KernelEigenDecomposition<T extends KernelVector>
extends Object
implements Serializable

Common class shared by fuzzy subspaces and densities

The underlying density/subspace is represented by

• A set of base vectors provided by KernelVectorList X
• A linear combination matrix Y
• A diagonal matrix S

such as A X is usually (i.e. AXXTAT is the identity), and the density rho is expressed as

rho = A U S2 UT AT

Author:

B. Piwowarski

See Also:

Serialized Form

Field Summary

bpiwowar.maths.matrix.DiagonalDoubleMatrix	mS The singular values
bpiwowar.maths.matrix.DoubleMatrix2D	mY The basis of the subspace

Constructor Summary

KernelEigenDecomposition(KernelEVD<T> evd, boolean deepCopy)
Creates an object given a Kernel EVD

KernelEigenDecomposition(KernelVectorList<T> list)
Creates a one dimensional eigen-decomposition representation

Method Summary

int	getRank()
double	normalise() Normalise with the L2 norm
double	normalise(boolean orthonormalU) Normalise the decomposition so that || U x S || = 1
void	trim(int newRank) Trim the eigenvalue decomposition to a lower rank

Methods inherited from class java.lang.Object

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

Field Detail

mY

public bpiwowar.maths.matrix.DoubleMatrix2D mY

The basis of the subspace

mS

public bpiwowar.maths.matrix.DiagonalDoubleMatrix mS

The singular values

Constructor Detail

KernelEigenDecomposition

public KernelEigenDecomposition(KernelEVD<T> evd,
                                boolean deepCopy)

Creates an object given a Kernel EVD

Parameters:

evd -

deepCopy -

KernelEigenDecomposition

public KernelEigenDecomposition(KernelVectorList<T> list)

Creates a one dimensional eigen-decomposition representation

Parameters:

list - A list for vector v

Method Detail

normalise

public double normalise()

Normalise with the L2 norm

normalise

public double normalise(boolean orthonormalU)

Normalise the decomposition so that || U x S || = 1

Parameters:

orthonormalU - Should we expect U to be orthonormal (which should be the case normally)?

Returns:

The norm of the matrix

trim

public void trim(int newRank)

Trim the eigenvalue decomposition to a lower rank

Parameters:

newRank - The new rank of the subspace

getRank

public int getRank()