de.lmu.ifi.dbs.elki.algorithm.clustering
Class EM<V extends NumberVector<V,?>>

java.lang.Object
  de.lmu.ifi.dbs.elki.algorithm.AbstractAlgorithm<Clustering<EMModel<V>>>
      de.lmu.ifi.dbs.elki.algorithm.clustering.EM<V>

Type Parameters:

V - a type of NumberVector as a suitable datatype for this algorithm

All Implemented Interfaces:

Algorithm, ClusteringAlgorithm<Clustering<EMModel<V>>>, InspectionUtilFrequentlyScanned, Parameterizable

@Title(value="EM-Clustering: Clustering by Expectation Maximization")
@Description(value="Provides k Gaussian mixtures maximizing the probability of the given data")
@Reference(authors="A. P. Dempster, N. M. Laird, D. B. Rubin",
           title="Maximum Likelihood from Incomplete Data via the EM algorithm",
           booktitle="Journal of the Royal Statistical Society, Series B, 39(1), 1977, pp. 1-31",
           url="http://www.jstor.org/stable/2984875")
public class EM<V extends NumberVector<V,?>>
extends AbstractAlgorithm<Clustering<EMModel<V>>>
implements ClusteringAlgorithm<Clustering<EMModel<V>>>

Provides the EM algorithm (clustering by expectation maximization).

Initialization is implemented as random initialization of means (uniformly distributed within the attribute ranges of the given database) and initial zero-covariance and variance=1 in covariance matrices.

Reference: A. P. Dempster, N. M. Laird, D. B. Rubin: Maximum Likelihood from Incomplete Data via the EM algorithm.
In Journal of the Royal Statistical Society, Series B, 39(1), 1977, pp. 1-31

Nested Class Summary

static class

EM.Parameterizer<V extends NumberVector<V,?>> Parameterization class.

Field Summary

private double	delta Holds the value of DELTA_ID.
static OptionID	DELTA_ID Parameter to specify the termination criterion for maximization of E(M): E(M) - E(M') < em.delta, must be a double equal to or greater than 0.
private int	k Holds the value of K_ID.
static OptionID	K_ID Parameter to specify the number of clusters to find, must be an integer greater than 0.
private static Logging	logger The logger for this class.
private static double	MIN_LOGLIKELIHOOD
private WritableDataStore<double[]>	probClusterIGivenX Store the individual probabilities, for use by EMOutlierDetection etc.
private Long	seed Holds the value of SEED_ID.
static OptionID	SEED_ID Parameter to specify the random generator seed.
private static double	SINGULARITY_CHEAT Small value to increment diagonally of a matrix in order to avoid singularity before building the inverse.

Constructor Summary

EM(int k, double delta, Long seed)
Constructor.

Method Summary

protected double	assignProbabilitiesToInstances(Relation<V> database, List<Double> normDistrFactor, List<V> means, List<Matrix> invCovMatr, List<Double> clusterWeights, WritableDataStore<double[]> probClusterIGivenX) Assigns the current probability values to the instances in the database and compute the expectation value of the current mixture of distributions.
TypeInformation[]	getInputTypeRestriction() Get the input type restriction used for negotiating the data query.
protected Logging	getLogger() Get the (STATIC) logger for this class.
double[]	getProbClusterIGivenX(DBID index) Get the probabilities for a given point.
protected List<V>	initialMeans(Relation<V> relation) Creates k random points distributed uniformly within the attribute ranges of the given database.
Clustering<EMModel<V>>	run(Database database, Relation<V> relation) Performs the EM clustering algorithm on the given database.

Methods inherited from class de.lmu.ifi.dbs.elki.algorithm.AbstractAlgorithm

makeParameterDistanceFunction, run

Methods inherited from class java.lang.Object

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

Methods inherited from interface de.lmu.ifi.dbs.elki.algorithm.clustering.ClusteringAlgorithm

run

Field Detail

logger

private static final Logging logger

The logger for this class.

SINGULARITY_CHEAT

private static final double SINGULARITY_CHEAT

Small value to increment diagonally of a matrix in order to avoid singularity before building the inverse.

See Also:

Constant Field Values

K_ID

public static final OptionID K_ID

Parameter to specify the number of clusters to find, must be an integer greater than 0.

k

private int k

Holds the value of K_ID.

DELTA_ID

public static final OptionID DELTA_ID

Parameter to specify the termination criterion for maximization of E(M): E(M) - E(M') < em.delta, must be a double equal to or greater than 0.

MIN_LOGLIKELIHOOD

private static final double MIN_LOGLIKELIHOOD

See Also:

Constant Field Values

delta

private double delta

Holds the value of DELTA_ID.

SEED_ID

public static final OptionID SEED_ID

Parameter to specify the random generator seed.

seed

private Long seed

Holds the value of SEED_ID.

probClusterIGivenX

private WritableDataStore<double[]> probClusterIGivenX

Store the individual probabilities, for use by EMOutlierDetection etc.

Constructor Detail

EM

public EM(int k,
          double delta,
          Long seed)

Constructor.

Parameters:

k - k parameter

delta - delta parameter

seed - Seed parameter

Method Detail

run

public Clustering<EMModel<V>> run(Database database,
                                  Relation<V> relation)

Performs the EM clustering algorithm on the given database.

Finally a hard clustering is provided where each clusters gets assigned the points exhibiting the highest probability to belong to this cluster. But still, the database objects hold associated the complete probability-vector for all models.

Parameters:

database - Database

relation - Relation

Returns:

Result

assignProbabilitiesToInstances

protected double assignProbabilitiesToInstances(Relation<V> database,
                                                List<Double> normDistrFactor,
                                                List<V> means,
                                                List<Matrix> invCovMatr,
                                                List<Double> clusterWeights,
                                                WritableDataStore<double[]> probClusterIGivenX)

Assigns the current probability values to the instances in the database and compute the expectation value of the current mixture of distributions. Computed as the sum of the logarithms of the prior probability of each instance.

Parameters:

database - the database used for assignment to instances

normDistrFactor - normalization factor for density function, based on current covariance matrix

means - the current means

invCovMatr - the inverse covariance matrices

clusterWeights - the weights of the current clusters

Returns:

the expectation value of the current mixture of distributions

initialMeans

protected List<V> initialMeans(Relation<V> relation)

Creates k random points distributed uniformly within the attribute ranges of the given database.

Parameters:

relation - the database must contain enough points in order to ascertain the range of attribute values. Less than two points would make no sense. The content of the database is not touched otherwise.

Returns:

a list of k random points distributed uniformly within the attribute ranges of the given database

getProbClusterIGivenX

public double[] getProbClusterIGivenX(DBID index)

Get the probabilities for a given point.

Parameters:

index - Point ID

Returns:

Probabilities of given point

getInputTypeRestriction

public TypeInformation[] getInputTypeRestriction()

Description copied from class: AbstractAlgorithm

Get the input type restriction used for negotiating the data query.

Specified by:

getInputTypeRestriction in interface Algorithm

Specified by:

getInputTypeRestriction in class AbstractAlgorithm<Clustering<EMModel<V extends NumberVector<V,?>>>>

Returns:

Type restriction

getLogger

protected Logging getLogger()

Description copied from class: AbstractAlgorithm

Get the (STATIC) logger for this class.

Specified by:

getLogger in class AbstractAlgorithm<Clustering<EMModel<V extends NumberVector<V,?>>>>

Returns:

the static logger