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

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

Type Parameters:

V - Vector Type

All Implemented Interfaces:

Algorithm<V,OutlierResult>, 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,Double>>
extends AbstractAlgorithm<V,OutlierResult>

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).

Author:

Lisa Reichert

Field Summary

private double	c Holds the value of C_PARAM.
static OptionID	C_ID OptionID for C_PARAM
private DoubleParameter	C_PARAM Parameter to specify the cutoff, Key: -mmo.c
private double	l Holds the value of L_PARAM.
static OptionID	L_ID OptionID for L_PARAM
private DoubleParameter	L_PARAM Parameter to specify the fraction of expected outliers, Key: -mmo.l
private double	logl log(l) precomputed
private double	logml log(1-l) precomputed
static AssociationID<Double>	MMOD_OFLAG The association id to associate the MMOD_OFLAF of an object for the GaussianUniformMixture algorithm.
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.logging.AbstractLoggable

debug, logger

Constructor Summary

GaussianUniformMixture(Parameterization config)
Constructor, adhering to Parameterizable

Method Summary

private double	loglikelihoodAnomalous(Collection<Integer> anomalousObjs) Loglikelihood anomalous objects.
private double	loglikelihoodNormal(Collection<Integer> objids, Database<V> database) Computes the loglikelihood of all normal objects.
protected OutlierResult	runInTime(Database<V> database) The run method encapsulated in measure of runtime.

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.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

Field Detail

MMOD_OFLAG

public static final AssociationID<Double> MMOD_OFLAG

The association id to associate the MMOD_OFLAF of an object for the GaussianUniformMixture algorithm.

L_ID

public static final OptionID L_ID

OptionID for L_PARAM

C_ID

public static final OptionID C_ID

OptionID for C_PARAM

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

L_PARAM

private final DoubleParameter L_PARAM

Parameter to specify the fraction of expected outliers,

Key: -mmo.l

l

private double l

Holds the value of L_PARAM.

C_PARAM

private final DoubleParameter C_PARAM

Parameter to specify the cutoff,

Key: -mmo.c

c

private double c

Holds the value of C_PARAM.

logl

private double logl

log(l) precomputed

logml

private double logml

log(1-l) precomputed

Constructor Detail

GaussianUniformMixture

public GaussianUniformMixture(Parameterization config)

Constructor, adhering to Parameterizable

Parameters:

config - Parameterization

Method Detail

runInTime

protected OutlierResult runInTime(Database<V> database)
                           throws IllegalStateException

Description copied from class: AbstractAlgorithm

The run method encapsulated in measure of runtime. An extending class needs not to take care of runtime itself.

Specified by:

runInTime in class AbstractAlgorithm<V extends NumberVector<V,Double>,OutlierResult>

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).

loglikelihoodAnomalous

private double loglikelihoodAnomalous(Collection<Integer> anomalousObjs)

Loglikelihood anomalous objects. Uniform distribution

Parameters:

anomalousObjs -

Returns:

loglikelihood for anomalous objects

loglikelihoodNormal

private double loglikelihoodNormal(Collection<Integer> objids,
                                   Database<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