de.lmu.ifi.dbs.elki.algorithm.outlier
Class GaussianUniformMixture<V extends NumberVector<V,?>>

java.lang.Object
  de.lmu.ifi.dbs.elki.algorithm.AbstractAlgorithm<OutlierResult>
      de.lmu.ifi.dbs.elki.algorithm.outlier.GaussianUniformMixture<V>

Type Parameters:

V - Vector Type

All Implemented Interfaces:

Algorithm, OutlierAlgorithm, InspectionUtilFrequentlyScanned, Parameterizable

@Title(value="Gaussian-Uniform Mixture Model Outlier Detection")
@Description(value="Fits a mixture model consisting of a Gaussian and a uniform distribution to the data.")
@Reference(prefix="Generalization using the likelihood gain as outlier score of",
           authors="Eskin, Eleazar",
           title="Anomaly detection over noisy data using learned probability distributions",
           booktitle="Proc. of the Seventeenth International Conference on Machine Learning (ICML-2000)")
public class GaussianUniformMixture<V extends NumberVector<V,?>>
extends AbstractAlgorithm<OutlierResult>
implements OutlierAlgorithm

Outlier detection algorithm using a mixture model approach. The data is modeled as a mixture of two distributions, a Gaussian distribution for ordinary data and a uniform distribution for outliers. At first all Objects are in the set of normal objects and the set of anomalous objects is empty. An iterative procedure then transfers objects from the ordinary set to the anomalous set if the transfer increases the overall likelihood of the data.

Reference:
Eskin, Eleazar: Anomaly detection over noisy data using learned probability distributions. In Proc. of the Seventeenth International Conference on Machine Learning (ICML-2000).

Nested Class Summary

static class

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

Field Summary

private double	c Holds the value of C_ID.
static OptionID	C_ID Parameter to specify the cutoff.
static OptionID	L_ID Parameter to specify the fraction of expected outliers.
private static Logging	logger The logger for this class.
private double	logl log(l) precomputed
private double	logml log(1-l) precomputed
private static double	SINGULARITY_CHEAT Small value to increment diagonally of a matrix in order to avoid singularity before building the inverse.

Constructor Summary

GaussianUniformMixture(double l, double c)
Constructor with parameters.

Method Summary

TypeInformation[]	getInputTypeRestriction() Get the input type restriction used for negotiating the data query.
protected Logging	getLogger() Get the (STATIC) logger for this class.
private double	loglikelihoodAnomalous(DBIDs anomalousObjs) Loglikelihood anomalous objects.
private double	loglikelihoodNormal(DBIDs objids, Relation<V> database) Computes the loglikelihood of all normal objects.
OutlierResult	run(Relation<V> relation)

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.outlier.OutlierAlgorithm

run

Field Detail

logger

private static final Logging logger

The logger for this class.

L_ID

public static final OptionID L_ID

Parameter to specify the fraction of expected outliers.

C_ID

public static final OptionID C_ID

Parameter to specify the cutoff.

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

c

private double c

Holds the value of C_ID.

logl

private double logl

log(l) precomputed

logml

private double logml

log(1-l) precomputed

Constructor Detail

GaussianUniformMixture

public GaussianUniformMixture(double l,
                              double c)

Constructor with parameters.

Parameters:

l - l value

c - c value

Method Detail

run

public OutlierResult run(Relation<V> relation)
                  throws IllegalStateException

Throws:

IllegalStateException

loglikelihoodAnomalous

private double loglikelihoodAnomalous(DBIDs anomalousObjs)

Loglikelihood anomalous objects. Uniform distribution

Parameters:

anomalousObjs -

Returns:

loglikelihood for anomalous objects

loglikelihoodNormal

private double loglikelihoodNormal(DBIDs objids,
                                   Relation<V> database)

Computes the loglikelihood of all normal objects. Gaussian model

Parameters:

objids - Object IDs for 'normal' objects.

database - Database

Returns:

loglikelihood for normal objects

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<OutlierResult>

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<OutlierResult>

Returns:

the static logger