Class PWM2Estimator

  • 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 PWM2Estimator
    extends java.lang.Object
    implements DistanceBasedIntrinsicDimensionalityEstimator
    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