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

java.lang.Object
  de.lmu.ifi.dbs.elki.logging.AbstractLoggable
      de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizable
          de.lmu.ifi.dbs.elki.algorithm.AbstractAlgorithm<V,Clustering<EMModel<V>>>
              de.lmu.ifi.dbs.elki.algorithm.clustering.EM<V>

Type Parameters:

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

All Implemented Interfaces:

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

public class EM<V extends RealVector<V,?>>
extends AbstractAlgorithm<V,Clustering<EMModel<V>>>
implements ClusteringAlgorithm<Clustering<EMModel<V>>,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

Author:

Arthur Zimek

Field Summary

private double	delta Holds the value of DELTA_PARAM.
static OptionID	DELTA_ID OptionID for DELTA_PARAM
private DoubleParameter	DELTA_PARAM 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_PARAM.
static OptionID	K_ID OptionID for K_PARAM
private IntParameter	K_PARAM Parameter to specify the number of clusters to find, must be an integer greater than 0.
private static double	MIN_LOGLIKELIHOOD
private Clustering<EMModel<V>>	result Keeps the result.
private static double	SINGULARITY_CHEAT Small value to increment diagonally of a matrix in order to avoid singularity before building the inverse.

Fields inherited from class de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizable

optionHandler

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

debug, logger

Constructor Summary

EM()
Provides the EM algorithm (clustering by expectation maximization), adding parameters K_PARAM and DELTA_PARAM to the option handler additionally to parameters of super class.

Method Summary

protected void	assignProbabilitiesToInstances(Database<V> database, List<Double> normDistrFactor, List<V> means, List<Matrix> invCovMatr, List<Double> clusterWeights) Assigns the current probability values to the instances in the database.
protected double	expectationOfMixture(Database<V> database) The expectation value of the current mixture of distributions.
Description	getDescription() Returns a description of the algorithm.
Clustering<EMModel<V>>	getResult() Retrieve the result.
protected List<V>	initialMeans(Database<V> database) Creates k random points distributed uniformly within the attribute ranges of the given database.
protected Clustering<EMModel<V>>	runInTime(Database<V> database) Performs the EM clustering algorithm on the given database.
List<String>	setParameters(List<String> args) Calls the super method and sets additionally the values of the parameters K_PARAM and DELTA_PARAM.

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

isTime, isVerbose, run, setTime, setVerbose

Methods inherited from class de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizable

addOption, addParameterizable, addParameterizable, checkGlobalParameterConstraints, collectOptions, getAttributeSettings, getParameters, rememberParametersExcept, removeOption, removeParameterizable, shortDescription

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

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

run

Methods inherited from interface de.lmu.ifi.dbs.elki.algorithm.Algorithm

setTime, setVerbose

Methods inherited from interface de.lmu.ifi.dbs.elki.utilities.optionhandling.Parameterizable

checkGlobalParameterConstraints, collectOptions, getParameters, shortDescription

Field Detail

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

OptionID for K_PARAM

K_PARAM

private final IntParameter K_PARAM

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

Key: -em.k

k

private int k

Holds the value of K_PARAM.

DELTA_ID

public static final OptionID DELTA_ID

OptionID for DELTA_PARAM

MIN_LOGLIKELIHOOD

private static final double MIN_LOGLIKELIHOOD

See Also:

Constant Field Values

DELTA_PARAM

private final DoubleParameter DELTA_PARAM

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.

Default value: 0.0

Key: -em.delta

delta

private double delta

Holds the value of DELTA_PARAM.

result

private Clustering<EMModel<V extends RealVector<V,?>>> result

Keeps the result.

Constructor Detail

EM

public EM()

Provides the EM algorithm (clustering by expectation maximization), adding parameters K_PARAM and DELTA_PARAM to the option handler additionally to parameters of super class.

Method Detail

runInTime

protected Clustering<EMModel<V>> runInTime(Database<V> database)
                                                            throws IllegalStateException

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.

Specified by:

runInTime in class AbstractAlgorithm<V extends RealVector<V,?>,Clustering<EMModel<V extends RealVector<V,?>>>>

Parameters:

database - the database to run the algorithm on

Returns:

the Result computed by this algorithm

Throws:

IllegalStateException - if the algorithm has not been initialized properly (e.g. the setParameters(String[]) method has been failed to be called).

assignProbabilitiesToInstances

protected void assignProbabilitiesToInstances(Database<V> database,
                                              List<Double> normDistrFactor,
                                              List<V> means,
                                              List<Matrix> invCovMatr,
                                              List<Double> clusterWeights)

Assigns the current probability values to the instances in the database.

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

expectationOfMixture

protected double expectationOfMixture(Database<V> database)

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 where the prior probability of each instance is associated

Returns:

the expectation value of the current mixture of distributions

initialMeans

protected List<V> initialMeans(Database<V> database)

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

Parameters:

database - 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

getDescription

public Description getDescription()

Description copied from interface: Algorithm

Returns a description of the algorithm.

Specified by:

getDescription in interface Algorithm<V extends RealVector<V,?>,Clustering<EMModel<V extends RealVector<V,?>>>>

Returns:

a description of the algorithm

getResult

public Clustering<EMModel<V>> getResult()

Description copied from interface: ClusteringAlgorithm

Retrieve the result.

Specified by:

getResult in interface Algorithm<V extends RealVector<V,?>,Clustering<EMModel<V extends RealVector<V,?>>>>

Specified by:

getResult in interface ClusteringAlgorithm<Clustering<EMModel<V extends RealVector<V,?>>>,V extends RealVector<V,?>>

Returns:

the result of the algorithm

setParameters

public List<String> setParameters(List<String> args)
                           throws ParameterException

Calls the super method and sets additionally the values of the parameters K_PARAM and DELTA_PARAM.

Specified by:

setParameters in interface Parameterizable

Overrides:

setParameters in class AbstractAlgorithm<V extends RealVector<V,?>,Clustering<EMModel<V extends RealVector<V,?>>>>

Parameters:

args - parameters to set the attributes accordingly to

Returns:

a list containing the unused parameters

Throws:

ParameterException - in case of wrong parameter-setting