## Class ProgressiveEigenPairFilter

• java.lang.Object
• elki.math.linearalgebra.pca.filter.ProgressiveEigenPairFilter
• All Implemented Interfaces:
EigenPairFilter

@Title("Progressive Eigenpair Filter")
@Description("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 Description
static class  ProgressiveEigenPairFilter.Par
Parameterization class.
• ### Field Summary

Fields
Modifier and Type Field 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 elki.math.linearalgebra.pca.filter.EigenPairFilter

PCA_EIGENPAIR_FILTER
• ### Constructor Summary

Constructors
Constructor Description
ProgressiveEigenPairFilter​(double palpha, double walpha)
Constructor.
• ### Method Summary

All Methods
Modifier and Type Method Description
int filter​(double[] eigenValues)
Filters the specified eigenvalues into strong and weak eigenvalues, where strong eigenvalues have high variance and weak eigenvalues have small variance.
• ### 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.
Constant Field Values
• #### DEFAULT_WALPHA

public static final double DEFAULT_WALPHA
The default value for alpha.
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)
Description copied from interface: EigenPairFilter
Filters the specified eigenvalues into strong and weak eigenvalues, where strong eigenvalues have high variance and weak eigenvalues have small variance.
Specified by:
filter in interface EigenPairFilter
Parameters:
eigenValues - the array of eigenvalues, must be sorted descending
Returns:
the number of eigenvectors to keep