Package elki.distance.probabilistic

Class TriangularDiscriminationDistance

java.lang.Object

elki.distance.AbstractNumberVectorDistance

elki.distance.probabilistic.TriangularDiscriminationDistance

All Implemented Interfaces:

Distance<NumberVector>, NumberVectorDistance<NumberVector>, PrimitiveDistance<NumberVector>, SpatialPrimitiveDistance<NumberVector>

Direct Known Subclasses:

TriangularDistance

@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")
public class TriangularDiscriminationDistance
extends AbstractNumberVectorDistance
implements SpatialPrimitiveDistance<NumberVector>

Triangular Discrimination has relatively tight upper and lower bounds to the Jensen-Shannon divergence, but is much less expensive.

$$\text{Triangular-Discrimination}(\vec{x},\vec{y}):= \sum\nolimits_i \tfrac{|x_i-y_i|^2}{x_i+y_i}$$

This distance function is meant for distribution vectors that sum to 1, and does not work on negative values.

See also TriangularDistance for a metric version.

Reference:

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

TODO: support sparse vectors, varying length

Since:

0.7.5

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	TriangularDiscriminationDistance.Par	Parameterization class, using the static instance.

Field Summary

Fields

Modifier and Type	Field	Description
static TriangularDiscriminationDistance	STATIC	Static instance.

Constructor Summary

Constructors

Constructor	Description
TriangularDiscriminationDistance()	Deprecated. Use static instance!

Method Summary

Modifier and Type	Method	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 elki.distance.AbstractNumberVectorDistance

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 elki.distance.Distance

isMetric, isSymmetric

Methods inherited from interface elki.distance.PrimitiveDistance

getInputTypeRestriction

Methods inherited from interface elki.distance.SpatialPrimitiveDistance

instantiate

Field Detail

STATIC

public static final TriangularDiscriminationDistance STATIC

Static instance. Use this!

Constructor Detail

TriangularDiscriminationDistance

@Deprecated
public TriangularDiscriminationDistance()

Deprecated.

Use static instance!

Constructor for the Triangular Discrimination - use STATIC instead.

Method Detail

distance

public double distance(NumberVector v1,
                       NumberVector v2)

Description copied from interface: PrimitiveDistance

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

Specified by:

distance in interface NumberVectorDistance<NumberVector>

Specified by:

distance in interface PrimitiveDistance<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: SpatialPrimitiveDistance

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

Specified by:

minDist in interface SpatialPrimitiveDistance<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: Distance

Squared distances, that would become metric after square root.

E.g. squared Euclidean.

Specified by:

isSquared in interface Distance<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