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

Class JeffreyDivergenceDistanceFunction

java.lang.Object

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

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

All Implemented Interfaces:

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

Direct Known Subclasses:

JensenShannonDivergenceDistanceFunction

@Reference(authors="H. Jeffreys",title="An invariant form for the prior probability in estimation problems",booktitle="Proc. Royal Society A: Mathematical, Physical and Engineering Sciences 186(1007)",url="https://doi.org/10.1098/rspa.1946.0056",bibkey="doi:10.1098/rspa.1946.0056") @Reference(authors="J. Puzicha, J. M. Buhmann, Y. Rubner, C. Tomasi",title="Empirical evaluation of dissimilarity measures for color and texture",booktitle="Proc. 7th IEEE International Conference on Computer Vision",url="https://doi.org/10.1109/ICCV.1999.790412",bibkey="DBLP:conf/iccv/PuzichaRTB99") @Reference(authors="F. Tops\u00f8e",title="Some inequalities for information divergence and related measures of discrimination",booktitle="IEEE Transactions on information theory, 46(4)",url="https://doi.org/10.1109/18.850703",bibkey="DBLP:journals/tit/Topsoe00") @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")
 @Alias(value="j-divergence")
public class JeffreyDivergenceDistanceFunction
extends AbstractNumberVectorDistanceFunction
implements SpatialPrimitiveDistanceFunction<NumberVector>

Jeffrey Divergence for NumberVectors is a symmetric, smoothened version of the KullbackLeiblerDivergenceAsymmetricDistanceFunction. Topsøe called this "capacitory discrimination".

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

Reference:

H. Jeffreys
An invariant form for the prior probability in estimation problems
Proc. Royal Society A: Mathematical, Physical and Engineering Sciences 186(1007)

J. Puzicha, J. M. Buhmann, Y. Rubner, C. Tomasi
Empirical evaluation of dissimilarity measures for color and texture
Proc. 7th IEEE International Conference on Computer Vision

F. Topsøe
Some inequalities for information divergence and related measures of discrimination
IEEE Transactions on information theory, 46(4)

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

TODO: add support for sparse vectors + varying length

Since:

0.5.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

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

Field Summary

Fields

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

Constructor Summary

Constructors

Constructor and Description
JeffreyDivergenceDistanceFunction() 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	equals(java.lang.Object obj)
int	hashCode()
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.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 JeffreyDivergenceDistanceFunction STATIC

Static instance. Use this!

Constructor Detail

JeffreyDivergenceDistanceFunction

@Deprecated
public JeffreyDivergenceDistanceFunction()

Deprecated. Use static instance!

Constructor for the Jeffrey divergence - use STATIC instead.

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>

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>

Parameters:

mbr1 - the first MBR object

mbr2 - the second MBR object

Returns:

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

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>

Returns:

true when squared.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

equals

public boolean equals(java.lang.Object obj)

Overrides:

equals in class java.lang.Object

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object