de.lmu.ifi.dbs.elki.math.statistics.dependence

Class DistanceCorrelationDependenceMeasure

java.lang.Object

de.lmu.ifi.dbs.elki.math.statistics.dependence.AbstractDependenceMeasure

de.lmu.ifi.dbs.elki.math.statistics.dependence.DistanceCorrelationDependenceMeasure

All Implemented Interfaces:

DependenceMeasure

@Reference(authors="G. J. Sz\u00e9kely, M. L. Rizzo, N. K. Bakirov",
           title="Measuring and testing dependence by correlation of distances",
           booktitle="The Annals of Statistics, 35(6), 2769-2794",
           url="https://doi.org/10.1214/009053607000000505",
           bibkey="doi:10.1214/009053607000000505")
public class DistanceCorrelationDependenceMeasure
extends AbstractDependenceMeasure

Distance correlation.

The value returned is the square root of the dCor² value. This matches the R implementation by the original authors.

Reference:

G. J. Székely, M. L. Rizzo, N. K. Bakirov
Measuring and testing dependence by correlation of distances
The Annals of Statistics, 35(6), 2769-2794

Implementation notice: we exploit symmetry, and thus use diagonal matrixes. While initially the diagonal is zero, after double-centering the matrix these values can become non-zero!

Since:

0.7.0

Author:

Marie Kiermeier, Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	DistanceCorrelationDependenceMeasure.Parameterizer Parameterization class

Field Summary

Fields

Modifier and Type	Field and Description
static DistanceCorrelationDependenceMeasure	STATIC Static instance.

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	DistanceCorrelationDependenceMeasure() Constructor - use STATIC instance instead!

Method Summary

Modifier and Type	Method and Description
protected double	computeDCovar(double[] dVarMatrixA, double[] dVarMatrixB, int n) Computes the distance covariance for two axis.
protected static <A> double[]	computeDistances(NumberArrayAdapter<?,A> adapter, A data) Compute the double-centered delta matrix.
<A,B> double	dependence(NumberArrayAdapter<?,A> adapter1, A data1, NumberArrayAdapter<?,B> adapter2, B data2) Measure the dependence of two variables.
<A> double[]	dependence(NumberArrayAdapter<?,A> adapter, java.util.List<? extends A> data) Measure the dependence of two variables.
static void	doubleCenterMatrix(double[] dMatrix, int size) Computes the distance variance matrix of one axis.

Methods inherited from class de.lmu.ifi.dbs.elki.math.statistics.dependence.AbstractDependenceMeasure

clamp, computeNormalizedRanks, discretize, index, ranks, ranks, size, size, sortedIndex

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface de.lmu.ifi.dbs.elki.math.statistics.dependence.DependenceMeasure

dependence, dependence

Field Detail

STATIC

public static final DistanceCorrelationDependenceMeasure STATIC

Static instance.

Constructor Detail

DistanceCorrelationDependenceMeasure

protected DistanceCorrelationDependenceMeasure()

Constructor - use STATIC instance instead!

Method Detail

dependence

public <A,B> double dependence(NumberArrayAdapter<?,A> adapter1,
                               A data1,
                               NumberArrayAdapter<?,B> adapter2,
                               B data2)

Description copied from interface: DependenceMeasure

Measure the dependence of two variables. This is the more flexible API, which allows using different internal data representations.

Type Parameters:

A - First array type

B - Second array type

Parameters:

adapter1 - First data adapter

data1 - First data set

adapter2 - Second data adapter

data2 - Second data set

Returns:

Dependence measure

dependence

public <A> double[] dependence(NumberArrayAdapter<?,A> adapter,
                               java.util.List<? extends A> data)

Description copied from interface: DependenceMeasure

Measure the dependence of two variables. This is the more flexible API, which allows using different internal data representations. The resulting data is a serialized lower triangular matrix:

  X  S  S  S  S  S
  0  X  S  S  S  S
  1  2  X  S  S  S
  3  4  5  X  S  S
  6  7  8  9  X  S
 10 11 12 13 14  X
 

Type Parameters:

A - Array type

Parameters:

adapter - Data adapter

data - Data sets. Must have fast random access!

Returns:

Lower triangular serialized matrix

computeDistances

protected static <A> double[] computeDistances(NumberArrayAdapter<?,A> adapter,
                                               A data)

Compute the double-centered delta matrix.

Parameters:

adapter - Data adapter

data - Input data

Returns:

Double-centered delta matrix.

doubleCenterMatrix

public static void doubleCenterMatrix(double[] dMatrix,
                                      int size)

Computes the distance variance matrix of one axis.

Parameters:

dMatrix - distance matrix of the axis

size - Dimensionality

computeDCovar

protected double computeDCovar(double[] dVarMatrixA,
                               double[] dVarMatrixB,
                               int n)

Computes the distance covariance for two axis. Can also be used to compute the distance variance of one axis (dVarMatrixA = dVarMatrixB).

Parameters:

dVarMatrixA - distance variance matrix of the first axis

dVarMatrixB - distance variance matrix of the second axis

n - number of points

Returns:

distance covariance