Class JensenShannonDivergenceDistance
- java.lang.Object
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- elki.distance.AbstractNumberVectorDistance
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- elki.distance.probabilistic.JeffreyDivergenceDistance
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- elki.distance.probabilistic.JensenShannonDivergenceDistance
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- All Implemented Interfaces:
Distance<NumberVector>
,NumberVectorDistance<NumberVector>
,PrimitiveDistance<NumberVector>
,SpatialPrimitiveDistance<NumberVector>
- Direct Known Subclasses:
SqrtJensenShannonDivergenceDistance
@Reference(authors="J. Lin",title="Divergence measures based on the Shannon entropy",booktitle="IEEE Transactions on Information Theory 37(1)",url="https://doi.org/10.1109/18.61115",bibkey="DBLP:journals/tit/Lin91") @Reference(authors="D. M. Endres, J. E. Schindelin",title="A new metric for probability distributions",booktitle="IEEE Transactions on Information Theory 49(7)",url="https://doi.org/10.1109/TIT.2003.813506",bibkey="DBLP:journals/tit/EndresS03") @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") public class JensenShannonDivergenceDistance extends JeffreyDivergenceDistance
Jensen-Shannon Divergence forNumberVector
s is a symmetric, smoothened version of theKullbackLeiblerDivergenceAsymmetricDistance
.It essentially is the same as
JeffreyDivergenceDistance
, only scaled by half. For completeness, we include both.\[JS(\vec{x},\vec{y}):=\tfrac12\sum\nolimits_i x_i\log\tfrac{2x_i}{x_i+y_i}+y_i\log\tfrac{2y_i}{x_i+y_i} = \tfrac12 KL(\vec{x},\tfrac12(\vec{x}+\vec{y})) + \tfrac12 KL(\vec{y},\tfrac12(\vec{x}+\vec{y}))\]
There exists a variable definition where the two vectors are weighted with \(\beta\) and \(1-\beta\), which for the common choice of \(\beta=\tfrac12\) yields this version.
Reference:
J. Lin
Divergence measures based on the Shannon entropy
IEEE Transactions on Information Theory 37(1)D. M. Endres, J. E. Schindelin
A new metric for probability distributions
IEEE Transactions on Information Theory 49(7)M.-M. Deza, E. Deza
Dictionary of distances- Since:
- 0.6.0
- Author:
- Erich Schubert
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Nested Class Summary
Nested Classes Modifier and Type Class Description static class
JensenShannonDivergenceDistance.Par
Parameterization class, using the static instance.
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Field Summary
Fields Modifier and Type Field Description static JensenShannonDivergenceDistance
STATIC
Static instance.
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Constructor Summary
Constructors Constructor Description JensenShannonDivergenceDistance()
Deprecated.Use static instance!
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description double
distance(NumberVector v1, NumberVector v2)
Computes the distance between two given DatabaseObjects according to this distance function.double
minDist(SpatialComparable mbr1, SpatialComparable mbr2)
Computes the distance between the two given MBRs according to this distance function.java.lang.String
toString()
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Methods inherited from class elki.distance.probabilistic.JeffreyDivergenceDistance
equals, hashCode, isSquared
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Methods inherited from class elki.distance.AbstractNumberVectorDistance
dimensionality, dimensionality, dimensionality, dimensionality, dimensionality, dimensionality, dimensionality, dimensionality, getInputTypeRestriction
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Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait
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Methods inherited from interface elki.distance.Distance
isMetric, isSymmetric
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Methods inherited from interface elki.distance.PrimitiveDistance
getInputTypeRestriction
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Methods inherited from interface elki.distance.SpatialPrimitiveDistance
instantiate
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Field Detail
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STATIC
public static final JensenShannonDivergenceDistance STATIC
Static instance. Use this!
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Method Detail
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distance
public double distance(NumberVector v1, NumberVector v2)
Description copied from interface:PrimitiveDistance
Computes the distance between two given DatabaseObjects according to this distance function.- Specified by:
distance
in interfaceNumberVectorDistance<NumberVector>
- Specified by:
distance
in interfacePrimitiveDistance<NumberVector>
- Overrides:
distance
in classJeffreyDivergenceDistance
- Parameters:
v1
- first DatabaseObjectv2
- second DatabaseObject- Returns:
- the distance between two given DatabaseObjects according to this distance function
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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 interfaceSpatialPrimitiveDistance<NumberVector>
- Overrides:
minDist
in classJeffreyDivergenceDistance
- Parameters:
mbr1
- the first MBR objectmbr2
- the second MBR object- Returns:
- the distance between the two given MBRs according to this distance function
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toString
public java.lang.String toString()
- Overrides:
toString
in classJeffreyDivergenceDistance
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