Package elki.utilities.scaling.outlier

Class MixtureModelOutlierScaling

java.lang.Object

elki.utilities.scaling.outlier.MixtureModelOutlierScaling

All Implemented Interfaces:

OutlierScaling, ScalingFunction

@Reference(authors="J. Gao, P.-N. Tan",
           title="Converting Output Scores from Outlier Detection Algorithms into Probability Estimates",
           booktitle="Proc. Sixth International Conference on Data Mining, 2006. ICDM\'06.",
           url="https://doi.org/10.1109/ICDM.2006.43",
           bibkey="DBLP:conf/icdm/GaoT06")
public class MixtureModelOutlierScaling
extends java.lang.Object
implements OutlierScaling

Tries to fit a mixture model (exponential for inliers and gaussian for outliers) to the outlier score distribution.

Note: we found this method to often fail, and fit the normal distribution to the inliers instead of the outliers, yielding reversed results.

Reference:

J. Gao, P.-N. Tan
Converting Output Scores from Outlier Detection Algorithms into Probability Estimates
Proc. Sixth International Conference on Data Mining, 2006. ICDM'06.

Since:

0.4.0

Author:

Erich Schubert

Field Summary

Fields

Modifier and Type	Field	Description
protected double	alpha	Mixing parameter alpha
private static double	DELTA	Convergence parameter
protected double	lambda	Parameter lambda of the exponential distribution (inliers)
private static Logging	LOG	The logger for this class.
protected double	mu	Parameter mu of the gaussian distribution (outliers)
static double	ONEBYSQRT2PI	Precomputed static value
protected double	sigma	Parameter sigma of the gaussian distribution (outliers)

Constructor Summary

Constructors

Constructor	Description
MixtureModelOutlierScaling()

Method Summary

Modifier and Type	Method	Description
protected static double	calcP_i(double f, double mu, double sigma)	Compute p_i (Gaussian distribution, outliers)
protected static double	calcPosterior(double f, double alpha, double mu, double sigma, double lambda)	Compute the a posterior probability for the given parameters.
protected static double	calcQ_i(double f, double lambda)	Compute q_i (Exponential distribution, inliers)
double	getMax()	Get maximum resulting value.
double	getMin()	Get minimum resulting value.
double	getScaled(double value)	Transform a given value using the scaling function.
<A> void	prepare(A array, NumberArrayAdapter<?,A> adapter)	Prepare is called once for each data set, before getScaled() will be called.
void	prepare(OutlierResult or)	Prepare is called once for each data set, before getScaled() will be called.

Methods inherited from class java.lang.Object

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

Field Detail

LOG

private static final Logging LOG

The logger for this class.

mu

protected double mu

Parameter mu of the gaussian distribution (outliers)

sigma

protected double sigma

Parameter sigma of the gaussian distribution (outliers)

lambda

protected double lambda

Parameter lambda of the exponential distribution (inliers)

alpha

protected double alpha

Mixing parameter alpha

ONEBYSQRT2PI

public static final double ONEBYSQRT2PI

Precomputed static value

DELTA

private static final double DELTA

Convergence parameter

See Also:

Constant Field Values

Constructor Detail

MixtureModelOutlierScaling

public MixtureModelOutlierScaling()

Method Detail

calcP_i

protected static double calcP_i(double f,
                                double mu,
                                double sigma)

Compute p_i (Gaussian distribution, outliers)

Parameters:

f - value

mu - Mu parameter

sigma - Sigma parameter

Returns:

probability

calcQ_i

protected static double calcQ_i(double f,
                                double lambda)

Compute q_i (Exponential distribution, inliers)

Parameters:

f - value

lambda - Lambda parameter

Returns:

probability

calcPosterior

protected static double calcPosterior(double f,
                                      double alpha,
                                      double mu,
                                      double sigma,
                                      double lambda)

Compute the a posterior probability for the given parameters.

Parameters:

f - value

alpha - Alpha (mixing) parameter

mu - Mu (for gaussian)

sigma - Sigma (for gaussian)

lambda - Lambda (for exponential)

Returns:

Probability

prepare

public void prepare(OutlierResult or)

Description copied from interface: OutlierScaling

Prepare is called once for each data set, before getScaled() will be called. This function can be used to extract global parameters such as means, minimums or maximums from the outlier scores.

Specified by:

prepare in interface OutlierScaling

Parameters:

or - Outlier result to use

prepare

public <A> void prepare(A array,
                        NumberArrayAdapter<?,A> adapter)

Description copied from interface: OutlierScaling

Prepare is called once for each data set, before getScaled() will be called. This function can be used to extract global parameters such as means, minimums or maximums from the score array. The method using a full OutlierResult is preferred, as it will allow access to the metadata.

Specified by:

prepare in interface OutlierScaling

Parameters:

array - Data to process

adapter - Array adapter

getMax

public double getMax()

Description copied from interface: ScalingFunction

Get maximum resulting value. May be Double.NaN or Double.POSITIVE_INFINITY.

Specified by:

getMax in interface ScalingFunction

Returns:

Maximum resulting value.

getMin

public double getMin()

Description copied from interface: ScalingFunction

Get minimum resulting value. May be Double.NaN or Double.NEGATIVE_INFINITY.

Specified by:

getMin in interface ScalingFunction

Returns:

Minimum resulting value.

getScaled

public double getScaled(double value)

Description copied from interface: ScalingFunction

Transform a given value using the scaling function.

Specified by:

getScaled in interface ScalingFunction

Parameters:

value - Original value

Returns:

Scaled value