Package elki.clustering.em.models

Class TextbookMultivariateGaussianModel

java.lang.Object

elki.clustering.em.models.TextbookMultivariateGaussianModel

All Implemented Interfaces:

EMClusterModel<NumberVector,EMModel>

public class TextbookMultivariateGaussianModel
extends java.lang.Object
implements EMClusterModel<NumberVector,EMModel>

Numerically problematic implementation of the GMM model, using the textbook algorithm. There is no reason to use this in practice, it is only useful to study the reliability of the textbook approach.

"Textbook" refers to the E[XY]-E[X]E[Y] equation for covariance, that is numerically not reliable with floating point math, but popular in textbooks.

Again, do not use this. Always prefer MultivariateGaussianModel.

Since:

0.7.5

Author:

Erich Schubert

Field Summary

Fields

Modifier and Type	Field	Description
(package private) CholeskyDecomposition	chol	Decomposition of covariance matrix.
(package private) double[][]	covariance	Covariance matrix.
(package private) double	logNorm	Normalization factor.
(package private) double	logNormDet	Normalization factor.
(package private) double[]	mean	Mean vector.
(package private) double[][]	priormatrix	Matrix for prior conditioning.
(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	Description
TextbookMultivariateGaussianModel(double weight, double[] mean)	Constructor.
TextbookMultivariateGaussianModel(double weight, double[] mean, double[][] covariance)	Constructor.

Method Summary

Modifier and Type	Method	Description
void	beginEStep()	Begin the E step.
void	calculateModelLimits(double[] min, double[] max, ConstrainedQuadraticProblemSolver solver, double ipiPow, double[] minpnt, double[] maxpnt, double[] ret)	Compute the weight of a Gaussian with respect to a bounding box.
void	clone(TextbookMultivariateGaussianModel other)	Copy the parameters of another model.
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.
double	getWeight()	Get the cluster weight.
double	mahalanobisDistance(NumberVector vec)	Compute the Mahalanobis distance from the centroid for a given vector.
void	setWeight(double weight)	Set the cluster weight.
void	updateE(double[] vec, double[][] covm, double sca, double wei)	Add a set of points with covariance information, for KDTreeEM.
void	updateE(NumberVector vec, double wei)	Process one data point in the E step

Methods inherited from class java.lang.Object

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

Methods inherited from interface elki.clustering.em.models.EMClusterModel

finalizeFirstPassE, firstPassE, needsTwoPass

Field Detail

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.

priormatrix

double[][] priormatrix

Matrix for prior conditioning.

Constructor Detail

TextbookMultivariateGaussianModel

public TextbookMultivariateGaussianModel(double weight,
                                         double[] mean)

Constructor.

Parameters:

weight - Cluster weight

mean - Initial mean

TextbookMultivariateGaussianModel

public TextbookMultivariateGaussianModel(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<NumberVector,EMModel>

updateE

public void updateE(NumberVector vec,
                    double wei)

Description copied from interface: EMClusterModel

Process one data point in the E step

Specified by:

updateE in interface EMClusterModel<NumberVector,EMModel>

Parameters:

vec - Vector to process

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

updateE

public void updateE(double[] vec,
                    double[][] covm,
                    double sca,
                    double wei)

Add a set of points with covariance information, for KDTreeEM.

Parameters:

vec - sum of new points

covm - sum of codeviates

sca - scaling factor applied to vec and covm instead of wei

wei - weight sum contribution

finalizeEStep

public void finalizeEStep(double weight,
                          double prior)

Description copied from interface: EMClusterModel

Finalize the E step.

Specified by:

finalizeEStep in interface EMClusterModel<NumberVector,EMModel>

Parameters:

weight - weight of the cluster

prior - MAP prior (0 for MLE)

mahalanobisDistance

public double mahalanobisDistance(NumberVector vec)

Compute the Mahalanobis distance from the centroid for a given vector.

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<NumberVector,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<NumberVector,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<NumberVector,EMModel>

Parameters:

weight - Cluster weight

finalizeCluster

public EMModel finalizeCluster()

Description copied from interface: EMClusterModel

Finalize a cluster model.

Specified by:

finalizeCluster in interface EMClusterModel<NumberVector,EMModel>

Returns:

Cluster model

clone

public void clone(TextbookMultivariateGaussianModel other)

Copy the parameters of another model.

Parameters:

other - Other

calculateModelLimits

public void calculateModelLimits(double[] min,
                                 double[] max,
                                 ConstrainedQuadraticProblemSolver solver,
                                 double ipiPow,
                                 double[] minpnt,
                                 double[] maxpnt,
                                 double[] ret)

Compute the weight of a Gaussian with respect to a bounding box.

Parameters:

min - Bounding box min will be modified

max - Bounding box max will be modified

solver - Quadratic solver

ipiPow - scaling constant

minpnt - result array for argmin

maxpnt - result array for argmax

ret - Return array