Package elki.distance.probabilistic
Class TriangularDistance
- java.lang.Object
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- elki.distance.AbstractNumberVectorDistance
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- elki.distance.probabilistic.TriangularDiscriminationDistance
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- elki.distance.probabilistic.TriangularDistance
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- All Implemented Interfaces:
Distance<NumberVector>
,NumberVectorDistance<NumberVector>
,PrimitiveDistance<NumberVector>
,SpatialPrimitiveDistance<NumberVector>
@Reference(authors="R. Connor, F. A. Cardillo, L. Vadicamo, F. Rabitti", title="Hilbert Exclusion: Improved Metric Search through Finite Isometric Embeddings", booktitle="arXiv preprint arXiv:1604.08640", url="http://arxiv.org/abs/1604.08640", bibkey="DBLP:journals/corr/ConnorCVR16") public class TriangularDistance extends TriangularDiscriminationDistance
Triangular Distance has relatively tight upper and lower bounds to the (square root of the) Jensen-Shannon divergence, but is much less expensive.\[\text{Triangular-Distance}(\vec{x},\vec{y}):=\sqrt{ \sum\nolimits_i \tfrac{|x_i-y_i|^2}{x_i+y_i}}\]
This distance function is meant for distribution vectors that sum to 1, and does not work on negative values.
This differs from
TriangularDistance
simply by the square root, which makes it a proper metric and a good approximation for the much more expensiveSqrtJensenShannonDivergenceDistance
.Reference:
R. Connor, F. A. Cardillo, L. Vadicamo, F. Rabitti
Hilbert Exclusion: Improved Metric Search through Finite Isometric Embeddings
arXiv preprint arXiv:1604.08640TODO: support sparse vectors, varying length
- Since:
- 0.7.5
- Author:
- Erich Schubert
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Nested Class Summary
Nested Classes Modifier and Type Class Description static class
TriangularDistance.Par
Parameterization class, using the static instance.
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Field Summary
Fields Modifier and Type Field Description static TriangularDistance
STATIC
Static instance.
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Constructor Summary
Constructors Modifier Constructor Description private
TriangularDistance()
Deprecated.
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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)boolean
isSquared()
Squared distances, that would become metric after square root.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
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 TriangularDistance STATIC
Static instance. Use this!
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Constructor Detail
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TriangularDistance
@Deprecated private TriangularDistance()
Deprecated.Deprecated constructor: use the static instanceSTATIC
instead.
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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 classTriangularDiscriminationDistance
- 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 classTriangularDiscriminationDistance
- 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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isSquared
public boolean isSquared()
Description copied from interface:Distance
Squared distances, that would become metric after square root.E.g. squared Euclidean.
- Specified by:
isSquared
in interfaceDistance<NumberVector>
- Overrides:
isSquared
in classTriangularDiscriminationDistance
- Returns:
true
when squared.
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isMetric
public boolean isMetric()
Description copied from interface:Distance
Is this distance function metric (satisfy the triangle inequality)- Returns:
true
when metric.
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toString
public java.lang.String toString()
- Overrides:
toString
in classTriangularDiscriminationDistance
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equals
public boolean equals(java.lang.Object obj)
- Overrides:
equals
in classTriangularDiscriminationDistance
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hashCode
public int hashCode()
- Overrides:
hashCode
in classTriangularDiscriminationDistance
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