Package elki.distance
Class MahalanobisDistance
- java.lang.Object
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- elki.distance.AbstractNumberVectorDistance
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- elki.distance.MatrixWeightedQuadraticDistance
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- elki.distance.MahalanobisDistance
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- All Implemented Interfaces:
Distance<NumberVector>
,Norm<NumberVector>
,NumberVectorDistance<NumberVector>
,PrimitiveDistance<NumberVector>
@Reference(authors="P. C. Mahalanobis", title="On the generalized distance in statistics", booktitle="Proceedings of the National Institute of Sciences of India. 2 (1)", bibkey="journals/misc/Mahalanobis36") public class MahalanobisDistance extends MatrixWeightedQuadraticDistance
Mahalanobis quadratic form distance for feature vectors.For a weight matrix M, this distance is defined as \[ \text{Mahalanobis}_M(\vec{x},\vec{y}) := \sqrt{(\vec{x}-\vec{y})^T \cdot M \cdot (\vec{x}-\vec{y})} \]
Reference:
P. C. Mahalanobis
On the generalized distance in statistics
Proceedings of the National Institute of Sciences of India. 2 (1)This is the implementation as quadratic form distance function. In many cases it will be more convenient to use the static function
VMath.mahalanobisDistance(double[][], double[], double[])
instead.TODO: Add a factory with parameterizable weight matrix! Right now, this can only be used from Java and from subclasses, not from command line or MiniGUI.
- Since:
- 0.7.5
- Author:
- Erich Schubert
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Field Summary
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Fields inherited from class elki.distance.MatrixWeightedQuadraticDistance
weightMatrix
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Constructor Summary
Constructors Constructor Description MahalanobisDistance(double[][] weightMatrix)
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description double
distance(NumberVector o1, NumberVector o2)
Computes the distance between two given DatabaseObjects according to this distance function.boolean
isMetric()
Is this distance function metric (satisfy the triangle inequality)boolean
isSquared()
Squared distances, that would become metric after square root.double
norm(NumberVector obj)
Compute the norm of object obj.-
Methods inherited from class elki.distance.MatrixWeightedQuadraticDistance
equals, getInputTypeRestriction, hashCode
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Methods inherited from class elki.distance.AbstractNumberVectorDistance
dimensionality, dimensionality, dimensionality, dimensionality, dimensionality, dimensionality, dimensionality, dimensionality
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Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, toString, 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
instantiate
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Method Detail
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distance
public double distance(NumberVector o1, NumberVector o2)
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 classMatrixWeightedQuadraticDistance
- Parameters:
o1
- first DatabaseObjecto2
- second DatabaseObject- Returns:
- the distance between two given DatabaseObjects according to this distance function
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norm
public double norm(NumberVector obj)
Description copied from interface:Norm
Compute the norm of object obj.- Specified by:
norm
in interfaceNorm<NumberVector>
- Overrides:
norm
in classMatrixWeightedQuadraticDistance
- Parameters:
obj
- Object- Returns:
- Norm
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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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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 classMatrixWeightedQuadraticDistance
- Returns:
true
when squared.
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