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

java.lang.Object
  extended by de.lmu.ifi.dbs.elki.math.linearalgebra.pca.ProgressiveEigenPairFilter
All Implemented Interfaces:
EigenPairFilter, InspectionUtilFrequentlyScanned, Parameterizable

@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 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.


Nested Class Summary
static class ProgressiveEigenPairFilter.Parameterizer
          Parameterization class.
 
Field Summary
static double DEFAULT_PALPHA
          The default value for alpha.
static double DEFAULT_WALPHA
          The default value for alpha.
static OptionID EIGENPAIR_FILTER_PALPHA
          Parameter progressive 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
 
Constructor Summary
ProgressiveEigenPairFilter(double palpha, double walpha)
          Constructor.
 
Method Summary
 FilteredEigenPairs filter(SortedEigenPairs eigenPairs)
          Filter eigenpairs.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

EIGENPAIR_FILTER_PALPHA

public static final OptionID EIGENPAIR_FILTER_PALPHA
Parameter progressive alpha.


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 FilteredEigenPairs filter(SortedEigenPairs eigenPairs)
Filter eigenpairs.

Specified by:
filter in interface EigenPairFilter
Parameters:
eigenPairs - the eigenPairs (i.e. the eigenvectors and
Returns:
the filtered eigenpairs

Release 0.4.0 (2011-09-20_1324)