de.lmu.ifi.dbs.elki.algorithm.clustering.em

Class TwoPassMultivariateGaussianModel

java.lang.Object

de.lmu.ifi.dbs.elki.algorithm.clustering.em.TwoPassMultivariateGaussianModel

All Implemented Interfaces:

EMClusterModel<EMModel>

public class TwoPassMultivariateGaussianModel
extends java.lang.Object
implements EMClusterModel<EMModel>

Model for a single Gaussian cluster, using two-passes for slightly better numerics. This is the more classic approach, but the savings in numerical precision are usually negligible, since we already use a very stable and fast approach.

Since:

0.7.5

Author:

Erich Schubert

Field Summary

Fields

Modifier and Type	Field and Description
(package private) CholeskyDecomposition	chol Decomposition of covariance matrix.
(package private) double[][]	covariance Covariance matrix.
private static Logging	LOG Class logger.
(package private) double	logNorm Normalization factor.
(package private) double	logNormDet Normalization factor.
(package private) double[]	mean Mean vector.
(package private) double	prior MAP prior / MLE prior.
(package private) double[][]	priormatrix Matrix for prior conditioning.
private static double	SINGULARITY_CHEAT Constant to avoid singular matrixes.
(package private) double[]	tmp Temporary storage, to avoid reallocations.
(package private) double	weight Weight aggregation sum
(package private) double	wsum Weight aggregation sum

Constructor Summary

Constructors

Constructor and Description
TwoPassMultivariateGaussianModel(double weight, double[] mean) Constructor.
TwoPassMultivariateGaussianModel(double weight, double[] mean, double[][] covariance) Constructor.

Method Summary

Modifier and Type	Method and Description
void	beginEStep() Begin the E step.
double	estimateLogDensity(NumberVector vec) Estimate the log likelihood of a vector.
EMModel	finalizeCluster() Finalize a cluster model.
void	finalizeEStep(double weight, double prior) Finalize the E step.
void	finalizeFirstPassE() Finish computation of the mean.
void	firstPassE(NumberVector vec, double wei) First pass: update the mean only.
private double	getHalfLogDeterminant(CholeskyDecomposition chol) Get 0.5 * log(det) of a cholesky decomposition.
double	getWeight() Get the cluster weight.
double	mahalanobisDistance(NumberVector vec) Compute the Mahalanobis distance from the centroid for a given vector.
boolean	needsTwoPass() True, if the model needs two passes in the E step.
void	setWeight(double weight) Set the cluster weight.
private void	updateCholesky() Update the cholesky decomposition.
void	updateE(NumberVector vec, double wei) Second pass: compute the covariance matrix.

Methods inherited from class java.lang.Object

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

Field Detail

LOG

private static Logging LOG

Class logger.

SINGULARITY_CHEAT

private static final double SINGULARITY_CHEAT

Constant to avoid singular matrixes.

See Also:

Constant Field Values

mean

double[] mean

Mean vector.

covariance

double[][] covariance

Covariance matrix.

chol

CholeskyDecomposition chol

Decomposition of covariance matrix.

tmp

double[] tmp

Temporary storage, to avoid reallocations.

logNorm

double logNorm

Normalization factor.

logNormDet

double logNormDet

Normalization factor.

weight

double weight

Weight aggregation sum

wsum

double wsum

Weight aggregation sum

prior

double prior

MAP prior / MLE prior.

priormatrix

double[][] priormatrix

Matrix for prior conditioning.

Constructor Detail

TwoPassMultivariateGaussianModel

public TwoPassMultivariateGaussianModel(double weight,
                                        double[] mean)

Constructor.

Parameters:

weight - Cluster weight

mean - Initial mean

TwoPassMultivariateGaussianModel

public TwoPassMultivariateGaussianModel(double weight,
                                        double[] mean,
                                        double[][] covariance)

Constructor.

Parameters:

weight - Cluster weight

mean - Initial mean

covariance - initial covariance matrix.

Method Detail

beginEStep

public void beginEStep()

Description copied from interface: EMClusterModel

Begin the E step.

Specified by:

beginEStep in interface EMClusterModel<EMModel>

needsTwoPass

public boolean needsTwoPass()

Description copied from interface: EMClusterModel

True, if the model needs two passes in the E step.

Specified by:

needsTwoPass in interface EMClusterModel<EMModel>

Returns:

true when an initial pass is needed.

firstPassE

public void firstPassE(NumberVector vec,
                       double wei)

First pass: update the mean only.

Specified by:

firstPassE in interface EMClusterModel<EMModel>

Parameters:

vec - Vector to process

wei - Weight of point ("responsibility" of the cluster)

finalizeFirstPassE

public void finalizeFirstPassE()

Finish computation of the mean.

Specified by:

finalizeFirstPassE in interface EMClusterModel<EMModel>

updateE

public void updateE(NumberVector vec,
                    double wei)

Second pass: compute the covariance matrix.

Specified by:

updateE in interface EMClusterModel<EMModel>

Parameters:

vec - Vector to process

wei - Weight of point ("responsibility" of the cluster)

finalizeEStep

public void finalizeEStep(double weight,
                          double prior)

Description copied from interface: EMClusterModel

Finalize the E step.

Specified by:

finalizeEStep in interface EMClusterModel<EMModel>

Parameters:

weight - weight of the cluster

prior - MAP prior (0 for MLE)

updateCholesky

private void updateCholesky()

Update the cholesky decomposition.

getHalfLogDeterminant

private double getHalfLogDeterminant(CholeskyDecomposition chol)

Get 0.5 * log(det) of a cholesky decomposition.

Parameters:

chol - Cholesky Decomposition

Returns:

log determinant.

mahalanobisDistance

public double mahalanobisDistance(NumberVector vec)

Compute the Mahalanobis distance from the centroid for a given vector. Note: used by P3C.

Parameters:

vec - Vector

Returns:

Mahalanobis distance

estimateLogDensity

public double estimateLogDensity(NumberVector vec)

Description copied from interface: EMClusterModel

Estimate the log likelihood of a vector.

Specified by:

estimateLogDensity in interface EMClusterModel<EMModel>

Parameters:

vec - Vector

Returns:

log likelihood.

getWeight

public double getWeight()

Description copied from interface: EMClusterModel

Get the cluster weight.

Specified by:

getWeight in interface EMClusterModel<EMModel>

Returns:

Cluster weight

setWeight

public void setWeight(double weight)

Description copied from interface: EMClusterModel

Set the cluster weight.

Specified by:

setWeight in interface EMClusterModel<EMModel>

Parameters:

weight - Cluster weight

finalizeCluster

public EMModel finalizeCluster()

Description copied from interface: EMClusterModel

Finalize a cluster model.

Specified by:

finalizeCluster in interface EMClusterModel<EMModel>

Returns:

Cluster model