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

Class FisherRaoDistanceFunction

java.lang.Object

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

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

All Implemented Interfaces:

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

@Reference(authors="C. R. Rao",title="Information and the Accuracy Attainable in the Estimation of Statistical Parameters",booktitle="Bulletin of the Calcutta Mathematical Society 37(3)",bibkey="journals/bcalms/Rao45") @Reference(authors="M.-M. Deza, E. Deza",title="Dictionary of distances",booktitle="Dictionary of distances",url="https://doi.org/10.1007/978-3-642-00234-2",bibkey="doi:10.1007/978-3-642-00234-2")
 @Alias(value={"rao","fisher-rao","fisher"})
public class FisherRaoDistanceFunction
extends AbstractNumberVectorDistanceFunction
implements SpatialPrimitiveDistanceFunction<NumberVector>

Fisher-Rao riemannian metric for (discrete) probability distributions.

\[ \text{Fisher-Rao}(\vec{x},\vec{y}) := 2 \arccos \sum\nolimits_i \sqrt{p_iq_i} \]

References:

The metric was theoretically introduced by Rao in 1945:

C. R. Rao
Information and the Accuracy Attainable in the Estimation of Statistical Parameters
Bulletin of the Calcutta Mathematical Society 37(3)

here, we use a version for discrete distributions, from:

M.-M. Deza, E. Deza
Dictionary of distances

Since:

0.7.5

Author:

Erich Schubert

Nested Class Summary

Nested Classes

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

Field Summary

Fields

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

Constructor Summary

Constructors

Constructor and Description
FisherRaoDistanceFunction() Deprecated.

Method Summary

Modifier and Type	Method and Description
double	distance(NumberVector fv1, NumberVector fv2) Computes the distance between two given DatabaseObjects according to this distance function.
boolean	equals(java.lang.Object obj)
SimpleTypeInformation<? super NumberVector>	getInputTypeRestriction() Get the input data type of the function.
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.

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

dimensionality, dimensionality, dimensionality, dimensionality, dimensionality, dimensionality, dimensionality, dimensionality

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, toString, 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.DistanceFunction

isSquared, isSymmetric

Field Detail

STATIC

public static final FisherRaoDistanceFunction STATIC

Static instance.

Constructor Detail

FisherRaoDistanceFunction

@Deprecated
public FisherRaoDistanceFunction()

Deprecated.

Rao distance. 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>

Parameters:

fv1 - first DatabaseObject

fv2 - 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.

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>

Overrides:

getInputTypeRestriction in class AbstractNumberVectorDistanceFunction

Returns:

Type restriction

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