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

Class HoeffdingsDDependenceMeasure

java.lang.Object

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

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

All Implemented Interfaces:

DependenceMeasure

@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 HoeffdingsDDependenceMeasure
extends AbstractDependenceMeasure

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 and Description
static class	HoeffdingsDDependenceMeasure.Parameterizer Parameterization class.

Field Summary

Fields

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

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	HoeffdingsDDependenceMeasure() Constructor - use STATIC instance.

Method Summary

Modifier and Type	Method and 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 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, dependence

Field Detail

STATIC

public static final HoeffdingsDDependenceMeasure STATIC

Static instance.

TABVAL

private static final double[] TABVAL

TABPOS

private static final double[] TABPOS

Constructor Detail

HoeffdingsDDependenceMeasure

protected HoeffdingsDDependenceMeasure()

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: 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

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