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

java.lang.Object
  de.lmu.ifi.dbs.elki.logging.AbstractLoggable
      de.lmu.ifi.dbs.elki.math.linearalgebra.pca.ProgressiveEigenPairFilter

All Implemented Interfaces:

EigenPairFilter, 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 AbstractLoggable
implements EigenPairFilter, Parameterizable

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.

Author:

Erich Schubert

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 OptionID for PALPHA_PARAM
private double	palpha The threshold for strong eigenvectors: the strong eigenvectors explain a portion of at least alpha of the total variance.
private DoubleParameter	PALPHA_PARAM Parameter progressive alpha.
private double	walpha The noise tolerance level for weak eigenvectors
private DoubleParameter	WALPHA_PARAM Parameter weak alpha.

Fields inherited from class de.lmu.ifi.dbs.elki.logging.AbstractLoggable

debug, logger

Constructor Summary

ProgressiveEigenPairFilter(Parameterization config)
Constructor, adhering to Parameterizable

Method Summary

FilteredEigenPairs

filter(SortedEigenPairs eigenPairs) Filter eigenpairs.

Methods inherited from class de.lmu.ifi.dbs.elki.logging.AbstractLoggable

debugFine, debugFiner, debugFinest, exception, progress, verbose, warning

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

OptionID for PALPHA_PARAM

DEFAULT_PALPHA

public static final double DEFAULT_PALPHA

The default value for alpha.

See Also:

Constant Field Values

PALPHA_PARAM

private final DoubleParameter PALPHA_PARAM

Parameter progressive alpha.

palpha

private double palpha

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

DEFAULT_WALPHA

public static final double DEFAULT_WALPHA

The default value for alpha.

See Also:

Constant Field Values

WALPHA_PARAM

private final DoubleParameter WALPHA_PARAM

Parameter weak alpha.

walpha

private double walpha

The noise tolerance level for weak eigenvectors

Constructor Detail

ProgressiveEigenPairFilter

public ProgressiveEigenPairFilter(Parameterization config)

Constructor, adhering to Parameterizable

Parameters:

config - Parameterization

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