Near Neighbor Distribution in Fractal and Finite Sets

0365540 - ÚI 2012 RIV US eng C - Conference Paper (international conference)
Jiřina, Marcel
Near Neighbor Distribution in Fractal and Finite Sets.
Proceedings of the 2011 International Conference of Soft Computing and Pattern Recognition SocPaR. Piscataway: IEEE, 2011 - (Abraham, A.; Liu, H.; Sun, F.; Guo, C.; McLoone, S.; Corchado, E.), s. 452-457. ISBN 978-1-4577-1195-4.
[SoCPaR 2011. International Conference on Soft Computing and Pattern Recognition. Dalian (CN), 14.10.2011-16.10.2011]
R&D Projects: GA MŠMT(CZ) 1M0567
Institutional research plan: CEZ:AV0Z10300504
Keywords : nearest neighbor * fractal set * multifractal * Erlang distribution
Subject RIV: BB - Applied Statistics, Operational Research

Distances of several nearest neighbors of a given point in a multidimensional space play important role in some tasks of data mining. Here we analyze these distances analyzed 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 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/11104/0200763