Package elki.clustering.em

Class KDTreeEM

java.lang.Object

elki.clustering.em.KDTreeEM

All Implemented Interfaces:

elki.Algorithm, ClusteringAlgorithm<Clustering<EMModel>>

@Description("Gaussian mixture modeling accelerated using a kd-tree")
@Reference(authors="Andrew W. Moore",
           booktitle="Advances in Neural Information Processing Systems 11 (NIPS 1998)",
           title="Very Fast EM-based Mixture Model Clustering using Multiresolution kd-trees",
           bibkey="DBLP:conf/nips/Moore98")
public class KDTreeEM
extends java.lang.Object
implements ClusteringAlgorithm<Clustering<EMModel>>

Clustering by expectation maximization (EM-Algorithm), also known as Gaussian Mixture Modeling (GMM), calculated on a kd-tree. If supported, tries to prune during calculation.

Reference:

A. W. Moore:
Very Fast EM-based Mixture Model Clustering using Multiresolution kd-trees.
Neural Information Processing Systems (NIPS 1998)

Since:

0.8.0

Author:

Robert Gehde

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
(package private) static class	KDTreeEM.KDTree	KDTree class with the statistics needed for EM clustering.
static class	KDTreeEM.Par	Parameterization class.

Nested classes/interfaces inherited from interface elki.Algorithm

elki.Algorithm.Utils

Field Summary

Fields

Modifier and Type	Field	Description
private double	delta	Delta parameter
protected boolean	exactAssign	Perform exact cluster assignments
private double	ipiPow	Gaussian scaling factor for likelihood.
private int	k	number of models
private static elki.logging.Logging	LOG	Logging object
private int	maxiter	maximum amount of iterations
private double	mbw	minimum leaf size
private TextbookMultivariateGaussianModelFactory	mfactory	Factory for producing the initial cluster model.
private int	miniter	minimum amount of iterations
private java.util.List<TextbookMultivariateGaussianModel>	models	Current clusters.
private java.util.List<TextbookMultivariateGaussianModel>	newmodels	Models for next iteration.
private boolean	soft	Retain soft assignments.
static elki.data.type.SimpleTypeInformation<double[]>	SOFT_TYPE	Soft assignment result type.
private elki.math.linearalgebra.ConstrainedQuadraticProblemSolver	solver	Solver for quadratic problems
protected elki.database.ids.ArrayModifiableDBIDs	sorted	kd-tree object order
private double	tau	tau, low for precise, high for fast results.
private double	tauClass	Drop one class if the maximum weight of a class in the bounding box is lower than tauClass * wmin_max, where wmin_max is the maximum minimum weight of all classes
private double[]	wsum	Cluster weights

Constructor Summary

Constructors

Constructor	Description
KDTreeEM(int k, double mbw, double tau, double tauclass, double delta, TextbookMultivariateGaussianModelFactory mfactory, int miniter, int maxiter, boolean soft, boolean exactAssign)	Constructor.

Method Summary

Modifier and Type	Method	Description
private double[]	analyseDimWidth(elki.database.relation.Relation<? extends elki.data.NumberVector> relation)	Helper method to retrieve the widths of all data in all dimensions.
private void	calculateModelLimits(KDTreeEM.KDTree node, TextbookMultivariateGaussianModel model, double[] minpnt, double[] maxpnt, double[] ret)	Calculates the model limits inside this node by translating the Gaussian model into a squared function.
private int[]	checkStoppingCondition(KDTreeEM.KDTree node, int[] indices)	This methods checks the different stopping conditions given in the paper, thus calculating the Dimensions, that will be considered for child-trees.
elki.data.type.TypeInformation[]	getInputTypeRestriction()
private double	makeStats(KDTreeEM.KDTree node, int[] indices, elki.database.datastore.WritableDataStore<double[]> probs)	Calculates the statistics on the kd-tree needed for the calculation of the new models
Clustering<EMModel>	run(elki.database.relation.Relation<? extends elki.data.NumberVector> relation)	Calculates the EM Clustering with the given values by calling makeStats and calculation the new models from the given results

Methods inherited from class java.lang.Object

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

Methods inherited from interface elki.clustering.ClusteringAlgorithm

autorun

Field Detail

LOG

private static final elki.logging.Logging LOG

Logging object

mfactory

private TextbookMultivariateGaussianModelFactory mfactory

Factory for producing the initial cluster model.

soft

private boolean soft

Retain soft assignments.

delta

private double delta

Delta parameter

SOFT_TYPE

public static final elki.data.type.SimpleTypeInformation<double[]> SOFT_TYPE

Soft assignment result type.

k

private int k

number of models

mbw

private double mbw

minimum leaf size

tau

private double tau

tau, low for precise, high for fast results.

tauClass

private double tauClass

Drop one class if the maximum weight of a class in the bounding box is lower than tauClass * wmin_max, where wmin_max is the maximum minimum weight of all classes

miniter

private int miniter

minimum amount of iterations

maxiter

private int maxiter

maximum amount of iterations

sorted

protected elki.database.ids.ArrayModifiableDBIDs sorted

kd-tree object order

models

private java.util.List<TextbookMultivariateGaussianModel> models

Current clusters.

newmodels

private java.util.List<TextbookMultivariateGaussianModel> newmodels

Models for next iteration.

solver

private elki.math.linearalgebra.ConstrainedQuadraticProblemSolver solver

Solver for quadratic problems

ipiPow

private double ipiPow

Gaussian scaling factor for likelihood.

wsum

private double[] wsum

Cluster weights

exactAssign

protected boolean exactAssign

Perform exact cluster assignments

Constructor Detail

KDTreeEM

public KDTreeEM(int k,
                double mbw,
                double tau,
                double tauclass,
                double delta,
                TextbookMultivariateGaussianModelFactory mfactory,
                int miniter,
                int maxiter,
                boolean soft,
                boolean exactAssign)

Constructor.

Parameters:

k - number of classes

mbw - minimum relative size of leaf nodes

tau - pruning parameter

tauclass - pruning parameter for single classes

delta - delta parameter

mfactory - EM cluster model factory

miniter - Minimum number of iterations

maxiter - Maximum number of iterations

soft - Include soft assignments

exactAssign - Perform exact assignments at the end

Method Detail

run

public Clustering<EMModel> run(elki.database.relation.Relation<? extends elki.data.NumberVector> relation)

Calculates the EM Clustering with the given values by calling makeStats and calculation the new models from the given results

Parameters:

relation - Data Relation

Returns:

Clustering KDTreeEM Clustering

analyseDimWidth

private double[] analyseDimWidth(elki.database.relation.Relation<? extends elki.data.NumberVector> relation)

Helper method to retrieve the widths of all data in all dimensions.

Parameters:

relation - Relation to analyze

Returns:

width of each dimension

checkStoppingCondition

private int[] checkStoppingCondition(KDTreeEM.KDTree node,
                                     int[] indices)

This methods checks the different stopping conditions given in the paper, thus calculating the Dimensions, that will be considered for child-trees. If this method returns a non-empty subset of the input dimension set, it means that missing dimensions are dropped because their weight was too small. If it returns a null array it means that the expected error of all remaining models is small enough to consider this node a leaf node.

Parameters:

node - kd tree node

indices - list of indices to check

Returns:

indices that are not pruned, null if everything was pruned

calculateModelLimits

private void calculateModelLimits(KDTreeEM.KDTree node,
                                  TextbookMultivariateGaussianModel model,
                                  double[] minpnt,
                                  double[] maxpnt,
                                  double[] ret)

Calculates the model limits inside this node by translating the Gaussian model into a squared function.

Parameters:

model - model to calculate the limits for

minpnt - result array for argmin

maxpnt - result array for argmax

ret - Return array

makeStats

private double makeStats(KDTreeEM.KDTree node,
                         int[] indices,
                         elki.database.datastore.WritableDataStore<double[]> probs)

Calculates the statistics on the kd-tree needed for the calculation of the new models

Parameters:

node - next node

indices - list of indices to use in calculation, initially all

probs - cluster assignment

Returns:

log likelihood of the model

getInputTypeRestriction

public elki.data.type.TypeInformation[] getInputTypeRestriction()

Specified by:

getInputTypeRestriction in interface elki.Algorithm