de.lmu.ifi.dbs.elki.algorithm.outlier

Class GaussianUniformMixture<V extends NumberVector>

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

@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="E. Eskin",
           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>
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:

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

Author:

Lisa Reichert

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	GaussianUniformMixture.Parameterizer<V extends NumberVector> Parameterization class.

Field Summary

Fields

Modifier and Type	Field and Description
private double	c Holds the cutoff value.
private static Logging	LOG 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

Constructors

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

Method Summary

Methods

Modifier and Type	Method and Description
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) Run the algorithm

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

LOG

private static final Logging LOG

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

c

private double c

Holds the cutoff value.

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)

Run the algorithm

Parameters:

relation - Data relation

Returns:

Outlier result

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