Package elki.math.statistics.dependence

Class HoeffdingsD

java.lang.Object

elki.math.statistics.dependence.HoeffdingsD

All Implemented Interfaces:

Dependence

@Reference(authors="W. Hoeffding",
           title="A non-parametric test of independence",
           booktitle="The Annals of Mathematical Statistics 19",
           url="http://www.jstor.org/stable/2236021",
           bibkey="journals/mathstat/Hoeffding48")
public class HoeffdingsD
extends java.lang.Object
implements Dependence

Calculate Hoeffding's D as a measure of dependence.

References:

W. Hoeffding:
A non-parametric test of independence
The Annals of Mathematical Statistics 19:546–57

The resulting value is scaled by 30, so it is in the range [-.5;1].

Since:

0.7.0

Author:

Yinchong Yang, Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	HoeffdingsD.Par	Parameterization class.

Nested classes/interfaces inherited from interface elki.math.statistics.dependence.Dependence

Dependence.Utils

Field Summary

Fields

Modifier and Type	Field	Description
static HoeffdingsD	STATIC	Static instance.
private static double[]	TABPOS
private static double[]	TABVAL

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	HoeffdingsD()	Constructor - use STATIC instance.

Method Summary

Modifier and Type	Method	Description
protected static <A,B> double[]	computeBivariateRanks(NumberArrayAdapter<?,A> adapter1, A data1, NumberArrayAdapter<?,B> adapter2, B data2, int len)	Compute bivariate ranks.
<A,B> double	dependence(NumberArrayAdapter<?,A> adapter1, A data1, NumberArrayAdapter<?,B> adapter2, B data2)	Measure the dependence of two variables.
double	toPValue(double d, int n)	Convert Hoeffding D value to a p-value.

Methods inherited from class java.lang.Object

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

Methods inherited from interface elki.math.statistics.dependence.Dependence

dependence, dependence, dependence

Field Detail

STATIC

public static final HoeffdingsD STATIC

Static instance.

TABVAL

private static final double[] TABVAL

TABPOS

private static final double[] TABPOS

Constructor Detail

HoeffdingsD

protected HoeffdingsD()

Constructor - use STATIC instance.

Method Detail

dependence

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

Description copied from interface: Dependence

Measure the dependence of two variables.

This is the more flexible API, which allows using different internal data representations.

Specified by:

dependence in interface Dependence

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

computeBivariateRanks

protected static <A,B> double[] computeBivariateRanks(NumberArrayAdapter<?,A> adapter1,
                                                            A data1,
                                                            NumberArrayAdapter<?,B> adapter2,
                                                            B data2,
                                                            int len)

Compute bivariate ranks.

q[i] is the number of objects such that x[j] < x[i] and y[j] < y[i]

Parameters:

adapter1 - First adapter

data1 - First data set

adapter2 - Second adapter

data2 - Second data set

len - Length

Returns:

Bivariate rank statistics.

toPValue

public double toPValue(double d,
                       int n)

Convert Hoeffding D value to a p-value.

Parameters:

d - D value

n - Data set size

Returns:

p-value