de.lmu.ifi.dbs.elki.math.linearalgebra.pca.filter

Class ProgressiveEigenPairFilter

java.lang.Object

de.lmu.ifi.dbs.elki.math.linearalgebra.pca.filter.ProgressiveEigenPairFilter

All Implemented Interfaces:

EigenPairFilter

@Title(value="Progressive Eigenpair Filter")
 @Description(value="Sorts the eigenpairs in decending order of their eigenvalues and returns the first eigenpairs, whose sum of eigenvalues explains more than the a certain percentage of the unexpected variance, where the percentage increases with subspace dimensionality.")
public class ProgressiveEigenPairFilter
extends java.lang.Object
implements EigenPairFilter

The ProgressiveEigenPairFilter sorts the eigenpairs in descending order of their eigenvalues and marks the first eigenpairs, whose sum of eigenvalues is higher than the given percentage of the sum of all eigenvalues as strong eigenpairs. In contrast to the PercentageEigenPairFilter, it will use a percentage which changes linearly with the subspace dimensionality. This makes the parameter more consistent for different dimensionalities and often gives better results when clusters of different dimensionality exist, since different percentage alpha levels might be appropriate for different dimensionalities.

Example calculations of alpha levels:

In a 3D space, a progressive alpha value of 0.5 equals:
- 1D subspace: 50 % + 1/3 of remainder = 0.667
- 2D subspace: 50 % + 2/3 of remainder = 0.833
In a 4D space, a progressive alpha value of 0.5 equals:
- 1D subspace: 50% + 1/4 of remainder = 0.625
- 2D subspace: 50% + 2/4 of remainder = 0.750
- 3D subspace: 50% + 3/4 of remainder = 0.875

Reasoning why this improves over PercentageEigenPairFilter:

In a 100 dimensional space, a single Eigenvector representing over 85% of the total variance is highly significant, whereas the strongest 85 Eigenvectors together will by definition always represent at least 85% of the variance. PercentageEigenPairFilter can thus not be used with these parameters and detect both dimensionalities correctly.

The second parameter introduced here, walpha, serves a different function: It prevents the eigenpair filter to use a statistically weak Eigenvalue just to reach the intended level, e.g. 84% + 1% >= 85% when 1% is statistically very weak.

Since:

0.2

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	ProgressiveEigenPairFilter.Parameterizer Parameterization class.

Field Summary

Fields

Modifier and Type	Field and Description
static double	DEFAULT_PALPHA The default value for alpha.
static double	DEFAULT_WALPHA The default value for alpha.
private double	palpha The threshold for strong eigenvectors: the strong eigenvectors explain a portion of at least alpha of the total variance.
private double	walpha The noise tolerance level for weak eigenvectors

Fields inherited from interface de.lmu.ifi.dbs.elki.math.linearalgebra.pca.filter.EigenPairFilter

PCA_EIGENPAIR_FILTER

Constructor Summary

Constructors

Constructor and Description
ProgressiveEigenPairFilter(double palpha, double walpha) Constructor.

Method Summary

Modifier and Type	Method and Description
int	filter(double[] eigenValues) Filter eigenpairs.

Methods inherited from class java.lang.Object

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

Field Detail

DEFAULT_PALPHA

public static final double DEFAULT_PALPHA

The default value for alpha.

See Also:

Constant Field Values

DEFAULT_WALPHA

public static final double DEFAULT_WALPHA

The default value for alpha.

See Also:

Constant Field Values

palpha

private double palpha

The threshold for strong eigenvectors: the strong eigenvectors explain a portion of at least alpha of the total variance.

walpha

private double walpha

The noise tolerance level for weak eigenvectors

Constructor Detail

ProgressiveEigenPairFilter

public ProgressiveEigenPairFilter(double palpha,
                                  double walpha)

Constructor.

Parameters:

palpha - palpha

walpha - walpha

Method Detail

filter

public int filter(double[] eigenValues)

Filter eigenpairs.

Specified by:

filter in interface EigenPairFilter

Parameters:

eigenValues - the array of eigenvalues, must be sorted descending

Returns:

the number of eigenvectors to keep