de.lmu.ifi.dbs.elki.utilities.scaling.outlier

Class SqrtStandardDeviationScaling

java.lang.Object

de.lmu.ifi.dbs.elki.utilities.scaling.outlier.SqrtStandardDeviationScaling

All Implemented Interfaces:

OutlierScaling, ScalingFunction

@Reference(authors="Hans-Peter Kriegel, Peer Kr\u00f6ger, Erich Schubert, Arthur Zimek",
           title="Interpreting and Unifying Outlier Scores",
           booktitle="Proc. 11th SIAM International Conference on Data Mining (SDM 2011)",
           url="https://doi.org/10.1137/1.9781611972818.2",
           bibkey="DBLP:conf/sdm/KriegelKSZ11")
public class SqrtStandardDeviationScaling
extends java.lang.Object
implements OutlierScaling

Scaling that can map arbitrary values to a probability in the range of [0:1].

Transformation is done using the formulas \[y = \sqrt{x - \min}\] \[s = \max\{0, \textrm{erf}(\lambda \frac{y-\mu}{\sigma\sqrt{2}})\}\]

Where min and mean \(\mu\) can be fixed to a given value, and stddev \(\sigma\) is then computed against this mean.

Reference:

Hans-Peter Kriegel, Peer Kröger, Erich Schubert, Arthur Zimek
Interpreting and Unifying Outlier Scores
Proc. 11th SIAM International Conference on Data Mining (SDM 2011)

Since:

0.3

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	SqrtStandardDeviationScaling.Parameterizer Parameterization class.

Field Summary

Fields

Modifier and Type	Field and Description
(package private) double	factor Effective parameters.
(package private) double	mean Effective parameters.
(package private) double	min Effective parameters.
(package private) double	plambda Predefined lambda scaling factor.
(package private) double	pmean Pre-fixed minimum and mean.
(package private) double	pmin Pre-fixed minimum and mean.

Constructor Summary

Constructors

Constructor and Description
SqrtStandardDeviationScaling(double pmin, double pmean, double plambda) Constructor.

Method Summary

Modifier and Type	Method and Description
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

min

double min

Effective parameters.

mean

double mean

Effective parameters.

factor

double factor

Effective parameters.

pmin

double pmin

Pre-fixed minimum and mean.

pmean

double pmean

Pre-fixed minimum and mean.

plambda

double plambda

Predefined lambda scaling factor.

Constructor Detail

SqrtStandardDeviationScaling

public SqrtStandardDeviationScaling(double pmin,
                                    double pmean,
                                    double plambda)

Constructor.

Parameters:

pmin - Predefined minimum

pmean - Predefined mean

plambda - Lambda parameter

Method Detail

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

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

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.

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.