Package elki.distance.probabilistic

Class FisherRaoDistance

java.lang.Object

elki.distance.AbstractNumberVectorDistance

elki.distance.probabilistic.FisherRaoDistance

All Implemented Interfaces:

Distance<NumberVector>, NumberVectorDistance<NumberVector>, PrimitiveDistance<NumberVector>, SpatialPrimitiveDistance<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({"rao","fisher-rao","fisher"})
public class FisherRaoDistance
extends AbstractNumberVectorDistance
implements SpatialPrimitiveDistance<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	Description
static class	FisherRaoDistance.Par	Parameterization class.

Field Summary

Fields

Modifier and Type	Field	Description
static FisherRaoDistance	STATIC	Static instance.

Constructor Summary

Constructors

Constructor	Description
FisherRaoDistance()	Deprecated.

Method Summary

Modifier and Type	Method	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 elki.distance.AbstractNumberVectorDistance

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 elki.distance.Distance

isSquared, isSymmetric

Methods inherited from interface elki.distance.SpatialPrimitiveDistance

instantiate

Field Detail

STATIC

public static final FisherRaoDistance STATIC

Static instance.

Constructor Detail

FisherRaoDistance

@Deprecated
public FisherRaoDistance()

Deprecated.

Rao distance. Use static instance STATIC!

Method Detail

distance

public double distance(NumberVector fv1,
                       NumberVector fv2)

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:

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: 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

isMetric

public boolean isMetric()

Description copied from interface: Distance

Is this distance function metric (satisfy the triangle inequality)

Specified by:

isMetric in interface Distance<NumberVector>

Returns:

true when metric.

getInputTypeRestriction

public SimpleTypeInformation<? super NumberVector> getInputTypeRestriction()

Description copied from interface: Distance

Get the input data type of the function.

Specified by:

getInputTypeRestriction in interface Distance<NumberVector>

Specified by:

getInputTypeRestriction in interface PrimitiveDistance<NumberVector>

Overrides:

getInputTypeRestriction in class AbstractNumberVectorDistance

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