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

Class HellingerDistanceFunction

java.lang.Object

de.lmu.ifi.dbs.elki.distance.distancefunction.AbstractPrimitiveDistanceFunction<NumberVector>

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

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

All Implemented Interfaces:

DistanceFunction<NumberVector>, NumberVectorDistanceFunction<NumberVector>, PrimitiveDistanceFunction<NumberVector>, PrimitiveSimilarityFunction<NumberVector>, SimilarityFunction<NumberVector>

@Reference(authors="E. Hellinger",
           title="Neue Begr\u00fcndung der Theorie quadratischer Formen von unendlichvielen Ver\u00e4nderlichen",
           booktitle="Journal f\u00fcr die reine und angewandte Mathematik ",
           url="http://resolver.sub.uni-goettingen.de/purl?GDZPPN002166941")
@Alias(value={"hellinger","bhattacharyya"})
public class HellingerDistanceFunction
extends AbstractNumberVectorDistanceFunction
implements PrimitiveSimilarityFunction<NumberVector>

Hellinger kernel / Hellinger distance are used with SIFT vectors, and also known as Bhattacharyya distance / coefficient. This distance is appropriate for histograms, and is equal to A) L1 normalizing the vectors and then B) using Euclidean distance. As this is usually much faster, this is the recommended way of handling such data. Reference:

E. Hellinger
Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen
Journal für die reine und angewandte Mathematik

TODO: support acceleration for sparse vectors

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	HellingerDistanceFunction.Parameterizer Parameterization class.

Field Summary

Fields

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

Constructor Summary

Constructors

Constructor and Description
HellingerDistanceFunction() Deprecated.

Method Summary

Methods

Modifier and Type	Method and Description
double	distance(NumberVector fv1, NumberVector fv2) Computes the distance between two given DatabaseObjects according to this distance function.
SimpleTypeInformation<? super NumberVector>	getInputTypeRestriction() Get the input data type of the function.
<T extends NumberVector> DistanceSimilarityQuery<T>	instantiate(Relation<T> database) Instantiate with a database to get the actual distance query.
boolean	isMetric() Is this distance function metric (in particular, does it satisfy the triangle equation?)
double	similarity(NumberVector o1, NumberVector o2) Computes the similarity between two given DatabaseObjects according to this similarity function.

Methods inherited from class de.lmu.ifi.dbs.elki.distance.distancefunction.AbstractNumberVectorDistanceFunction

dimensionality, dimensionality, dimensionality, dimensionality

Methods inherited from class de.lmu.ifi.dbs.elki.distance.distancefunction.AbstractPrimitiveDistanceFunction

isSymmetric

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface de.lmu.ifi.dbs.elki.distance.similarityfunction.SimilarityFunction

isSymmetric

Methods inherited from interface de.lmu.ifi.dbs.elki.distance.distancefunction.DistanceFunction

isSymmetric

Field Detail

STATIC

public static final HellingerDistanceFunction STATIC

Static instance.

Constructor Detail

HellingerDistanceFunction

@Deprecated
public HellingerDistanceFunction()

Deprecated.

Hellinger kernel. Use static instance STATIC!

Method Detail

distance

public double distance(NumberVector fv1,
              NumberVector fv2)

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>

Specified by:

distance in class AbstractPrimitiveDistanceFunction<NumberVector>

Parameters:

fv1 - first DatabaseObject

fv2 - second DatabaseObject

Returns:

the distance between two given DatabaseObjects according to this distance function

similarity

public double similarity(NumberVector o1,
                NumberVector o2)

Description copied from interface: PrimitiveSimilarityFunction

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

Specified by:

similarity in interface PrimitiveSimilarityFunction<NumberVector>

Parameters:

o1 - first DatabaseObject

o2 - second DatabaseObject

Returns:

the similarity between two given DatabaseObjects according to this similarity function

isMetric

public boolean isMetric()

Description copied from interface: DistanceFunction

Is this distance function metric (in particular, does it satisfy the triangle equation?)

Specified by:

isMetric in interface DistanceFunction<NumberVector>

Overrides:

isMetric in class AbstractPrimitiveDistanceFunction<NumberVector>

Returns:

true when metric.

instantiate

public <T extends NumberVector> DistanceSimilarityQuery<T> instantiate(Relation<T> database)

Description copied from class: AbstractPrimitiveDistanceFunction

Instantiate with a database to get the actual distance query.

Specified by:

instantiate in interface DistanceFunction<NumberVector>

Specified by:

instantiate in interface SimilarityFunction<NumberVector>

Overrides:

instantiate in class AbstractPrimitiveDistanceFunction<NumberVector>

Parameters:

database - Representation

Returns:

Actual distance query.

getInputTypeRestriction

public SimpleTypeInformation<? super NumberVector> getInputTypeRestriction()

Description copied from interface: DistanceFunction

Get the input data type of the function.

Specified by:

getInputTypeRestriction in interface DistanceFunction<NumberVector>

Specified by:

getInputTypeRestriction in interface PrimitiveDistanceFunction<NumberVector>

Specified by:

getInputTypeRestriction in interface PrimitiveSimilarityFunction<NumberVector>

Specified by:

getInputTypeRestriction in interface SimilarityFunction<NumberVector>

Overrides:

getInputTypeRestriction in class AbstractNumberVectorDistanceFunction

Returns:

Type restriction