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

Class PWM2Estimator

java.lang.Object

de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.PWM2Estimator

All Implemented Interfaces:

IntrinsicDimensionalityEstimator

@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 PWM2Estimator
extends java.lang.Object
implements IntrinsicDimensionalityEstimator

Probability weighted moments based estimator, using the second moment.

It can be shown theoretically that this estimator is expected to have a higher variance than the one using the first moment only, it is included for completeness only.

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 two additional data points 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 lower PWMs, 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:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	PWM2Estimator.Parameterizer Parameterization class.

Field Summary

Fields

Modifier and Type	Field and Description
static PWM2Estimator	STATIC Static instance.

Constructor Summary

Constructors

Constructor and Description
PWM2Estimator()

Method Summary

Modifier and Type	Method and 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 de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.IntrinsicDimensionalityEstimator

countLeadingZeros, estimate, estimate, estimate, estimate, estimate

Field Detail

STATIC

public static final PWM2Estimator STATIC

Static instance.

Constructor Detail

PWM2Estimator

public PWM2Estimator()

Method Detail

estimate

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

Description copied from interface: IntrinsicDimensionalityEstimator

Estimate from a distance list.

Specified by:

estimate in interface IntrinsicDimensionalityEstimator

Type Parameters:

A - array type

Parameters:

data - Data

adapter - Array adapter

end - Length

Returns:

Estimated intrinsic dimensionality