Near Neighbor Distribution in Sets of Fractal Nature

0420987 - ÚI 2014 RIV US eng J - Journal Article
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
R&D Projects: GA MŠMT(CZ) LG12020
Institutional support: RVO:67985807
Keywords : nearest neighbor * fractal set * multifractal * Erlang distribution
Subject RIV: BB - Applied Statistics, Operational Research
http://www.mirlabs.org/ijcisim/regular_papers_2013/Paper91.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0227434