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

Class JensenShannonDivergenceDistanceFunction

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

All Implemented Interfaces:

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

Direct Known Subclasses:

SqrtJensenShannonDivergenceDistanceFunction

@Reference(authors="J. Lin",title="Divergence measures based on the Shannon entropy",booktitle="IEEE Transactions on Information Theory 37(1)",url="https://doi.org/10.1109/18.61115",bibkey="DBLP:journals/tit/Lin91") @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") @Reference(authors="M.-M. Deza, E. Deza",title="Dictionary of distances",booktitle="Dictionary of distances",url="https://doi.org/10.1007/978-3-642-00234-2",bibkey="doi:10.1007/978-3-642-00234-2")
public class JensenShannonDivergenceDistanceFunction
extends JeffreyDivergenceDistanceFunction

Jensen-Shannon Divergence for NumberVectors is a symmetric, smoothened version of the KullbackLeiblerDivergenceAsymmetricDistanceFunction.

It essentially is the same as JeffreyDivergenceDistanceFunction, only scaled by half. For completeness, we include both.

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

There exists a variable definition where the two vectors are weighted with \(\beta\) and \(1-\beta\), which for the common choice of \(\beta=\tfrac12\) yields this version.

Reference:

J. Lin
Divergence measures based on the Shannon entropy
IEEE Transactions on Information Theory 37(1)

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

M.-M. Deza, E. Deza
Dictionary of distances

Since:

0.6.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

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

Field Summary

Fields

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

Constructor Summary

Constructors

Constructor and Description
JensenShannonDivergenceDistanceFunction() 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.
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, isSquared

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

isMetric, isSymmetric

Field Detail

STATIC

public static final JensenShannonDivergenceDistanceFunction STATIC

Static instance. Use this!

Constructor Detail

JensenShannonDivergenceDistanceFunction

@Deprecated
public JensenShannonDivergenceDistanceFunction()

Deprecated. Use static instance!

Constructor for the 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 JeffreyDivergenceDistanceFunction

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 JeffreyDivergenceDistanceFunction

Parameters:

mbr1 - the first MBR object

mbr2 - the second MBR object

Returns:

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

toString

public java.lang.String toString()

Overrides:

toString in class JeffreyDivergenceDistanceFunction