de.lmu.ifi.dbs.elki.math.linearalgebra.pca
Class WeightedCovarianceMatrixBuilder<V extends NumberVector<V,?>,D extends NumberDistance<D,?>>

java.lang.Object
  de.lmu.ifi.dbs.elki.logging.AbstractLoggable
      de.lmu.ifi.dbs.elki.math.linearalgebra.pca.CovarianceMatrixBuilder<V,D>
          de.lmu.ifi.dbs.elki.math.linearalgebra.pca.WeightedCovarianceMatrixBuilder<V,D>

Type Parameters:

V - Vector class to use

D - Distance type

All Implemented Interfaces:

Parameterizable

@Title(value="Weighted Covariance Matrix / PCA")
@Description(value="A PCA modification by using weights while building the covariance matrix, to obtain more stable results")
@Reference(authors="H.-P. Kriegel, P. Kr\u00f6ger, E. Schubert, A. Zimek",
           title="A General Framework for Increasing the Robustness of PCA-based Correlation Clustering Algorithms",
           booktitle="Proceedings of the 20th International Conference on Scientific and Statistical Database Management (SSDBM), Hong Kong, China, 2008",
           url="http://dx.doi.org/10.1007/978-3-540-69497-7_27")
public class WeightedCovarianceMatrixBuilder<V extends NumberVector<V,?>,D extends NumberDistance<D,?>>
extends CovarianceMatrixBuilder<V,D>

CovarianceMatrixBuilder with weights. This builder uses a weight function to weight points differently during build a covariance matrix. Covariance can be canonically extended with weights, as shown in the article A General Framework for Increasing the Robustness of PCA-Based Correlation Clustering Algorithms Hans-Peter Kriegel and Peer Kröger and Erich Schubert and Arthur Zimek In: Proc. 20th Int. Conf. on Scientific and Statistical Database Management (SSDBM), 2008, Hong Kong Lecture Notes in Computer Science 5069, Springer

Author:

Erich Schubert

Field Summary

static OptionID	WEIGHT_ID OptionID for WEIGHT_PARAM
private ObjectParameter<WeightFunction>	WEIGHT_PARAM Parameter to specify the weight function to use in weighted PCA, must implement WeightFunction .
private DistanceFunction<V,DoubleDistance>	weightDistance Holds the distance function used for weight calculation
WeightFunction	weightfunction Holds the weight function.

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

debug, logger

Constructor Summary

WeightedCovarianceMatrixBuilder(Parameterization config)
Constructor, adhering to Parameterizable

Method Summary

private double[][]	finishCovarianceMatrix(double[] sums, double[][] squares, double weightsum) Finish the Covariance matrix in array "squares".
Matrix	processIds(Collection<Integer> ids, Database<V> database) Weighted Covariance Matrix for a set of IDs.
Matrix	processQueryResults(Collection<DistanceResultPair<D>> results, Database<V> database, int k) Compute Covariance Matrix for a QueryResult Collection By default it will just collect the ids and run processIds

Methods inherited from class de.lmu.ifi.dbs.elki.math.linearalgebra.pca.CovarianceMatrixBuilder

processDatabase, processQueryResults

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

WEIGHT_ID

public static final OptionID WEIGHT_ID

OptionID for WEIGHT_PARAM

WEIGHT_PARAM

private final ObjectParameter<WeightFunction> WEIGHT_PARAM

Parameter to specify the weight function to use in weighted PCA, must implement WeightFunction .

Key: -pca.weight

weightfunction

public WeightFunction weightfunction

Holds the weight function.

weightDistance

private DistanceFunction<V extends NumberVector<V,?>,DoubleDistance> weightDistance

Holds the distance function used for weight calculation

Constructor Detail

WeightedCovarianceMatrixBuilder

public WeightedCovarianceMatrixBuilder(Parameterization config)

Constructor, adhering to Parameterizable

Parameters:

config - Parameterization

Method Detail

processIds

public Matrix processIds(Collection<Integer> ids,
                         Database<V> database)

Weighted Covariance Matrix for a set of IDs. Since we are not supplied any distance information, we'll need to compute it ourselves. Covariance is tied to Euclidean distance, so it probably does not make much sense to add support for other distance functions?

Specified by:

processIds in class CovarianceMatrixBuilder<V extends NumberVector<V,?>,D extends NumberDistance<D,?>>

Parameters:

ids - a collection of ids

database - the database used

Returns:

Covariance Matrix

processQueryResults

public Matrix processQueryResults(Collection<DistanceResultPair<D>> results,
                                  Database<V> database,
                                  int k)

Compute Covariance Matrix for a QueryResult Collection By default it will just collect the ids and run processIds

Overrides:

processQueryResults in class CovarianceMatrixBuilder<V extends NumberVector<V,?>,D extends NumberDistance<D,?>>

Parameters:

results - a collection of QueryResults

database - the database used

k - number of elements to process

Returns:

Covariance Matrix

finishCovarianceMatrix

private double[][] finishCovarianceMatrix(double[] sums,
                                          double[][] squares,
                                          double weightsum)

Finish the Covariance matrix in array "squares".

Parameters:

sums - Sums of values.

squares - Sums of squares. Contents are destroyed and replaced with Covariance Matrix!

weightsum - Sum of weights.

Returns:

modified squares array