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

Class TriangularDistanceFunction

java.lang.Object

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

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

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

All Implemented Interfaces:

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

@Reference(authors="R. Connor, F. A. Cardillo, L. Vadicamo, F. Rabitti",
           title="Hilbert Exclusion: Improved Metric Search through Finite Isometric Embeddings",
           booktitle="arXiv preprint arXiv:1604.08640",
           url="http://arxiv.org/abs/1604.08640",
           bibkey="DBLP:journals/corr/ConnorCVR16")
public class TriangularDistanceFunction
extends TriangularDiscriminationDistanceFunction

Triangular Distance has relatively tight upper and lower bounds to the (square root of the) Jensen-Shannon divergence, but is much less expensive.

\[\text{Triangular-Distance}(\vec{x},\vec{y}):=\sqrt{ \sum\nolimits_i \tfrac{|x_i-y_i|^2}{x_i+y_i}}\]

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

This differs from TriangularDistanceFunction simply by the square root, which makes it a proper metric and a good approximation for the much more expensive SqrtJensenShannonDivergenceDistanceFunction.

Reference:

R. Connor, F. A. Cardillo, L. Vadicamo, F. Rabitti
Hilbert Exclusion: Improved Metric Search through Finite Isometric Embeddings
arXiv preprint arXiv:1604.08640

TODO: support sparse vectors, varying length

Since:

0.7.5

Author:

Erich Schubert

Nested Class Summary

Nested Classes

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

Field Summary

Fields

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

Constructor Summary

Constructors

Modifier	Constructor and Description
private	TriangularDistanceFunction() Deprecated.

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	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.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 TriangularDistanceFunction STATIC

Static instance. Use this!

Constructor Detail

TriangularDistanceFunction

@Deprecated
private TriangularDistanceFunction()

Deprecated.

Deprecated constructor: use the static instance 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>

Overrides:

distance in class TriangularDiscriminationDistanceFunction

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 TriangularDiscriminationDistanceFunction

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>

Overrides:

isSquared in class TriangularDiscriminationDistanceFunction

Returns:

true when squared.

isMetric

public boolean isMetric()

Description copied from interface: DistanceFunction

Is this distance function metric (satisfy the triangle inequality)

Returns:

true when metric.

toString

public java.lang.String toString()

Overrides:

toString in class TriangularDiscriminationDistanceFunction

equals

public boolean equals(java.lang.Object obj)

Overrides:

equals in class TriangularDiscriminationDistanceFunction

hashCode

public int hashCode()

Overrides:

hashCode in class TriangularDiscriminationDistanceFunction