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Near Neighbor Distribution in Sets of Fractal Nature

  1. 1.
    0420987 - UIVT-O 2014 RIV US eng J - Článek v odborném periodiku
    Jiřina, Marcel
    Near Neighbor Distribution in Sets of Fractal Nature.
    International Journal of Computer Information Systems and Industrial Management Applications. Roč. 5, č. 1 (2013), s. 159-166. ISSN 2150-7988
    Grant CEP: GA MŠk(CZ) LG12020
    Institucionální podpora: RVO:67985807
    Klíčová slova: nearest neighbor * fractal set * multifractal * Erlang distribution
    Kód oboru RIV: BB - Aplikovaná statistika, operační výzkum

    Distances of several nearest neighbors of a given point in a multidimensional space play an important role in some tasks of data mining. Here we analyze these distances as random variables defined to be functions of a given point and its k-th nearest neighbor. We prove that if there is a constant q such that the mean k-th neighbor distance to this constant power is proportional to the near neighbor index k then its distance to this constant power converges to the Erlang distribution of order k. We also show that constant q is the scaling exponent known from the theory of multifractals.
    Trvalý link: http://hdl.handle.net/11104/0227434