Package elki.distance.histogram
Class HistogramMatchDistance
- java.lang.Object
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- elki.distance.AbstractNumberVectorDistance
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- elki.distance.histogram.HistogramMatchDistance
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- All Implemented Interfaces:
Distance<NumberVector>
,NumberVectorDistance<NumberVector>
,PrimitiveDistance<NumberVector>
,SpatialPrimitiveDistance<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 HistogramMatchDistance extends AbstractNumberVectorDistance implements SpatialPrimitiveDistance<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
ManhattanDistance
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
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Nested Class Summary
Nested Classes Modifier and Type Class Description static class
HistogramMatchDistance.Par
Parameterization class, using the static instance.
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Field Summary
Fields Modifier and Type Field Description static HistogramMatchDistance
STATIC
Static instance.
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Constructor Summary
Constructors Constructor Description HistogramMatchDistance()
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.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()
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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
isSquared, 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 HistogramMatchDistance 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>
- 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>
- 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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isMetric
public boolean isMetric()
Description copied from interface:Distance
Is this distance function metric (satisfy the triangle inequality)- Specified by:
isMetric
in interfaceDistance<NumberVector>
- Returns:
true
when metric.
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toString
public java.lang.String toString()
- Overrides:
toString
in classjava.lang.Object
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equals
public boolean equals(java.lang.Object obj)
- Overrides:
equals
in classjava.lang.Object
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hashCode
public int hashCode()
- Overrides:
hashCode
in classjava.lang.Object
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