Package elki.algorithm.statistics

Class HopkinsStatisticClusteringTendency

java.lang.Object

elki.algorithm.statistics.HopkinsStatisticClusteringTendency

All Implemented Interfaces:

Algorithm

@Reference(authors="B. Hopkins, J. G. Skellam",
           title="A new method for determining the type of distribution of plant individuals",
           booktitle="Annals of Botany, 18(2), 213-227",
           url="https://doi.org/10.1093/oxfordjournals.aob.a083391",
           bibkey="doi:10.1093/oxfordjournals.aob.a083391")
public class HopkinsStatisticClusteringTendency
extends java.lang.Object
implements Algorithm

The Hopkins Statistic of Clustering Tendency measures the probability that a data set is generated by a uniform data distribution.

The statistic compares the ratio of the 1NN distance for objects from the data set compared to the 1NN distances of uniform distributed objects.

Reference:

B. Hopkins, J. G. Skellam
A new method for determining the type of distribution of plant individuals
Annals of Botany, 18(2), 213-227.

Since:

0.7.0

Author:

Lisa Reichert, Erich Schubert

Nested Class Summary

Nested Classes

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

Nested classes/interfaces inherited from interface elki.Algorithm

Algorithm.Utils

Field Summary

Fields

Modifier and Type	Field	Description
protected NumberVectorDistance<? super NumberVector>	distance	Distance function used.
protected int	k	Nearest neighbor to use.
private static Logging	LOG	The logger for this class.
private double[]	maxima	Stores the maximum in each dimension.
private double[]	minima	Stores the minimum in each dimension.
protected RandomFactory	random	Random generator seeding.
protected int	rep	Number of repetitions
protected int	sampleSize	The parameter sampleSizes

Constructor Summary

Constructors

Constructor	Description
HopkinsStatisticClusteringTendency(NumberVectorDistance<? super NumberVector> distance, int samplesize, RandomFactory random, int rep, int k, double[] minima, double[] maxima)	Constructor.

Method Summary

Modifier and Type	Method	Description
protected double	computeNNForRealData(KNNSearcher<DBIDRef> knnQuery, Relation<NumberVector> relation, int dim)	Search nearest neighbors for real data members.
protected double	computeNNForUniformData(KNNSearcher<NumberVector> knnQuery, double[] min, double[] extend)	Search nearest neighbors for artificial, uniform data.
TypeInformation[]	getInputTypeRestriction()	Get the input type restriction used for negotiating the data query.
protected void	initializeDataExtends(Relation<NumberVector> relation, int dim, double[] min, double[] extend)	Initialize the uniform sampling area.
java.lang.Double	run(Relation<NumberVector> relation)	Compute the Hopkins statistic for a vector relation.

Methods inherited from class java.lang.Object

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

Methods inherited from interface elki.Algorithm

autorun

Field Detail

LOG

private static final Logging LOG

The logger for this class.

sampleSize

protected int sampleSize

The parameter sampleSizes

rep

protected int rep

Number of repetitions

k

protected int k

Nearest neighbor to use.

random

protected RandomFactory random

Random generator seeding.

maxima

private double[] maxima

Stores the maximum in each dimension.

minima

private double[] minima

Stores the minimum in each dimension.

distance

protected NumberVectorDistance<? super NumberVector> distance

Distance function used.

Constructor Detail

HopkinsStatisticClusteringTendency

public HopkinsStatisticClusteringTendency(NumberVectorDistance<? super NumberVector> distance,
                                          int samplesize,
                                          RandomFactory random,
                                          int rep,
                                          int k,
                                          double[] minima,
                                          double[] maxima)

Constructor.

Parameters:

distance - Distance function

samplesize - Sample size

random - Random generator

rep - Number of repetitions

k - Nearest neighbors to use

minima - Data space minima, may be null (get from data).

maxima - Data space minima, may be null (get from data).

Method Detail

getInputTypeRestriction

public TypeInformation[] getInputTypeRestriction()

Description copied from interface: Algorithm

Get the input type restriction used for negotiating the data query.

Specified by:

getInputTypeRestriction in interface Algorithm

Returns:

Type restriction

run

public java.lang.Double run(Relation<NumberVector> relation)

Compute the Hopkins statistic for a vector relation.

Parameters:

relation - Relation

Returns:

Hopkins statistic

computeNNForRealData

protected double computeNNForRealData(KNNSearcher<DBIDRef> knnQuery,
                                      Relation<NumberVector> relation,
                                      int dim)

Search nearest neighbors for real data members.

Parameters:

knnQuery - KNN query

relation - Data relation

Returns:

Aggregated 1NN distances

computeNNForUniformData

protected double computeNNForUniformData(KNNSearcher<NumberVector> knnQuery,
                                         double[] min,
                                         double[] extend)

Search nearest neighbors for artificial, uniform data.

Parameters:

knnQuery - KNN query

min - Data minima

extend - Data extend

Returns:

Aggregated 1NN distances

initializeDataExtends

protected void initializeDataExtends(Relation<NumberVector> relation,
                                     int dim,
                                     double[] min,
                                     double[] extend)

Initialize the uniform sampling area.

Parameters:

relation - Data relation

dim - Dimensionality

min - Minima output array (preallocated!)

extend - Data extend output array (preallocated!)