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

Class HistogramMatchDistanceFunction

java.lang.Object

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

de.lmu.ifi.dbs.elki.distance.distancefunction.histogram.HistogramMatchDistanceFunction

All Implemented Interfaces:

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

@Reference(authors="L. N. Vaserstein",
           title="Markov processes over denumerable products of spaces describing large systems of automata",
           booktitle="Problemy Peredachi Informatsii 5.3 / Problems of Information Transmission, 5:3",
           url="http://mi.mathnet.ru/eng/ppi1811",
           bibkey="journals/misc/Vaserstein69")
public class HistogramMatchDistanceFunction
extends AbstractNumberVectorDistanceFunction
implements SpatialPrimitiveDistanceFunction<NumberVector>

Distance function based on histogram matching, i.e., Manhattan distance on the cumulative density function.

If your data is normalized to the 1-norm of 1, use ManhattanDistanceFunction instead, as this will be faster!

This distance function assumes there exist a natural order in the vectors, i.e., they should be some 1-dimensional histogram.

This is also known as Earth Movers Distance (EMD), 1st Mallows distance or 1st Wasserstein metric (also Vasershtein metric), for the special case of a one-dimensional histogram, where the cost is linear in the number of bins to transport.

Reference:

L. N. Vaserstein
Markov processes over denumerable products of spaces describing large systems of automata
Problemy Peredachi Informatsii 5.3 / Problems of Information Transmission 5:3

Since:

0.6.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

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

Field Summary

Fields

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

Constructor Summary

Constructors

Constructor and Description
HistogramMatchDistanceFunction() 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	isMetric() Is this distance function metric (satisfy the triangle inequality)
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

isSquared, isSymmetric

Field Detail

STATIC

public static final HistogramMatchDistanceFunction STATIC

Static instance. Use this!

Constructor Detail

HistogramMatchDistanceFunction

@Deprecated
public HistogramMatchDistanceFunction()

Deprecated. Use static instance!

Constructor for the Histogram match distance function.

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

isMetric

public boolean isMetric()

Description copied from interface: DistanceFunction

Is this distance function metric (satisfy the triangle inequality)

Specified by:

isMetric in interface DistanceFunction<NumberVector>

Returns:

true when metric.

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