Package elki.math.statistics.intrinsicdimensionality

Class PWMEstimator

java.lang.Object

elki.math.statistics.intrinsicdimensionality.PWMEstimator

All Implemented Interfaces:

DistanceBasedIntrinsicDimensionalityEstimator, IntrinsicDimensionalityEstimator<java.lang.Object>

@Reference(authors="L. Amsaleg, O. Chelly, T. Furon, S. Girard, M. E. Houle, K. Kawarabayashi, M. Nett",title="Estimating Local Intrinsic Dimensionality",booktitle="Proc. SIGKDD International Conference on Knowledge Discovery and Data Mining 2015",url="https://doi.org/10.1145/2783258.2783405",bibkey="DBLP:conf/kdd/AmsalegCFGHKN15") @Reference(authors="J. Maciunas Landwehr, N. C. Matalas, J. R. Wallis",title="Probability weighted moments compared with some traditional techniques in estimating Gumbel parameters and quantiles",booktitle="Water Resources Research 15(5)",url="https://doi.org/10.1029/WR015i005p01055",bibkey="doi:10.1029/WR015i005p01055")
public class PWMEstimator
extends java.lang.Object
implements DistanceBasedIntrinsicDimensionalityEstimator

Probability weighted moments based estimator.

Reference:

L. Amsaleg, O. Chelly, T. Furon, S. Girard, M. E. Houle, K. Kawarabayashi, M. Nett
Estimating Local Intrinsic Dimensionality
Proc. SIGKDD Int. Conf. on Knowledge Discovery and Data Mining

We use the unbiased weights of Maciunas Landwehr et al.:

J. Maciunas Landwehr, N. C. Matalas, J. R. Wallis
Probability weighted moments compared with some traditional techniques in estimating Gumbel parameters and quantiles
Water Resources Research 15(5)

but we pretend we had one additional data point at 0, to not lose valuable data. When implemented exactly, we would have to assign a weight of 0 to the first point. But since we are not using the mean, we don't want to do this. This hack causes this estimator to have a bias to underestimate the ID.

Since:

0.7.0

Author:

Jonathan von Brünken, Erich Schubert

Nested Class Summary

Nested Classes

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

Field Summary

Fields

Modifier and Type	Field	Description
static PWMEstimator	STATIC	Static instance.

Constructor Summary

Constructors

Constructor	Description
PWMEstimator()

Method Summary

Modifier and Type	Method	Description
<A> double	estimate(A data, NumberArrayAdapter<?,? super A> adapter, int end)	Estimate from a distance list.

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.intrinsicdimensionality.DistanceBasedIntrinsicDimensionalityEstimator

estimate, estimate, estimate, estimate, estimate

Field Detail

STATIC

public static final PWMEstimator STATIC

Static instance.

Constructor Detail

PWMEstimator

public PWMEstimator()

Method Detail

estimate

public <A> double estimate(A data,
                           NumberArrayAdapter<?,? super A> adapter,
                           int end)

Description copied from interface: DistanceBasedIntrinsicDimensionalityEstimator

Estimate from a distance list.

Specified by:

estimate in interface DistanceBasedIntrinsicDimensionalityEstimator

Type Parameters:

A - array type

Parameters:

data - Data

adapter - Array adapter

end - Length

Returns:

Estimated intrinsic dimensionality