de.lmu.ifi.dbs.elki.distance.distancefunction.probabilistic

Class SqrtJensenShannonDivergenceDistanceFunction

java.lang.Object

de.lmu.ifi.dbs.elki.distance.distancefunction.AbstractNumberVectorDistanceFunction

de.lmu.ifi.dbs.elki.distance.distancefunction.probabilistic.JeffreyDivergenceDistanceFunction

de.lmu.ifi.dbs.elki.distance.distancefunction.probabilistic.JensenShannonDivergenceDistanceFunction

de.lmu.ifi.dbs.elki.distance.distancefunction.probabilistic.SqrtJensenShannonDivergenceDistanceFunction

All Implemented Interfaces:

DistanceFunction<NumberVector>, NumberVectorDistanceFunction<NumberVector>, PrimitiveDistanceFunction<NumberVector>, SpatialPrimitiveDistanceFunction<NumberVector>

@Reference(authors="D. M. Endres, J. E. Schindelin",
           title="A new metric for probability distributions",
           booktitle="IEEE Transactions on Information Theory, 49(7)",
           url="https://doi.org/10.1109/TIT.2003.813506",
           bibkey="DBLP:journals/tit/EndresS03")
public class SqrtJensenShannonDivergenceDistanceFunction
extends JensenShannonDivergenceDistanceFunction

The square root of Jensen-Shannon divergence is a metric.

\[\sqrt{JS}(\vec{x},\vec{y}):=\sqrt{\tfrac12\sum\nolimits_i x_i\log\tfrac{2x_i}{x_i+y_i}+y_i\log\tfrac{2y_i}{x_i+y_i}} = \sqrt{JS(\vec{x},\vec{y})}\]

A proof of triangle inequality (for "\(D_{PQ}\)") can be found in Endres and Schindelin.

References:

D. M. Endres, J. E. Schindelin
A new metric for probability distributions
IEEE Transactions on Information Theory, 49(7)

Since:

0.6.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	SqrtJensenShannonDivergenceDistanceFunction.Parameterizer Parameterization class, using the static instance.

Field Summary

Fields

Modifier and Type	Field and Description
static SqrtJensenShannonDivergenceDistanceFunction	STATIC Static instance.

Constructor Summary

Constructors

Constructor and Description
SqrtJensenShannonDivergenceDistanceFunction() Deprecated. Use static instance!

Method Summary

Modifier and Type	Method and Description
double	distance(NumberVector v1, NumberVector v2) Computes the distance between two given DatabaseObjects according to this distance function.
boolean	isMetric() Is this distance function metric (satisfy the triangle inequality)
boolean	isSquared() Squared distances, that would become metric after square root.
double	minDist(SpatialComparable mbr1, SpatialComparable mbr2) Computes the distance between the two given MBRs according to this distance function.
java.lang.String	toString()

Methods inherited from class de.lmu.ifi.dbs.elki.distance.distancefunction.probabilistic.JeffreyDivergenceDistanceFunction

equals, hashCode

Methods inherited from class de.lmu.ifi.dbs.elki.distance.distancefunction.AbstractNumberVectorDistanceFunction

dimensionality, dimensionality, dimensionality, dimensionality, dimensionality, dimensionality, dimensionality, dimensionality, getInputTypeRestriction

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface de.lmu.ifi.dbs.elki.distance.distancefunction.SpatialPrimitiveDistanceFunction

instantiate

Methods inherited from interface de.lmu.ifi.dbs.elki.distance.distancefunction.PrimitiveDistanceFunction

getInputTypeRestriction

Methods inherited from interface de.lmu.ifi.dbs.elki.distance.distancefunction.DistanceFunction

isSymmetric

Field Detail

STATIC

public static final SqrtJensenShannonDivergenceDistanceFunction STATIC

Static instance. Use this!

Constructor Detail

SqrtJensenShannonDivergenceDistanceFunction

@Deprecated
public SqrtJensenShannonDivergenceDistanceFunction()

Deprecated. Use static instance!

Constructor for sqrt Jensen Shannon divergence.

Method Detail

distance

public double distance(NumberVector v1,
                       NumberVector v2)

Description copied from interface: PrimitiveDistanceFunction

Computes the distance between two given DatabaseObjects according to this distance function.

Specified by:

distance in interface NumberVectorDistanceFunction<NumberVector>

Specified by:

distance in interface PrimitiveDistanceFunction<NumberVector>

Overrides:

distance in class JensenShannonDivergenceDistanceFunction

Parameters:

v1 - first DatabaseObject

v2 - second DatabaseObject

Returns:

the distance between two given DatabaseObjects according to this distance function

minDist

public double minDist(SpatialComparable mbr1,
                      SpatialComparable mbr2)

Description copied from interface: SpatialPrimitiveDistanceFunction

Computes the distance between the two given MBRs according to this distance function.

Specified by:

minDist in interface SpatialPrimitiveDistanceFunction<NumberVector>

Overrides:

minDist in class JensenShannonDivergenceDistanceFunction

Parameters:

mbr1 - the first MBR object

mbr2 - the second MBR object

Returns:

the distance between the two given MBRs according to this distance function

isMetric

public boolean isMetric()

Description copied from interface: DistanceFunction

Is this distance function metric (satisfy the triangle inequality)

Returns:

true when metric.

isSquared

public boolean isSquared()

Description copied from interface: DistanceFunction

Squared distances, that would become metric after square root. E.g. squared Euclidean.

Specified by:

isSquared in interface DistanceFunction<NumberVector>

Overrides:

isSquared in class JeffreyDivergenceDistanceFunction

Returns:

true when squared.

toString

public java.lang.String toString()

Overrides:

toString in class JensenShannonDivergenceDistanceFunction