Near Neighbor Distribution in Fractal and Finite Sets

Authors: Marcel Jiřina
Publication year: 2011
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Proceedings of the 2011 International Conference of Soft Computing and Pattern Recognition SocPaR
Projects: Centre for Applied Cybernetics
Bibliographic citation: JIŘINA, Marcel. Near Neighbor Distribution in Fractal and Finite Sets. In: ABRAHAM, A., LIU, H., SUN, F., GUO, C., MCLOONE, S., CORCHADO, E., eds. Proceedings of the 2011 International Conference of Soft Computing and Pattern Recognition SocPaR. Piscataway: IEEE, 2011, S. 452-457. ISBN 978-1-4577-1195-4
Dostupné z: doi:10.1109/SoCPaR.2011.6089286
DOI: 10.1109/SoCPaR.2011.6089286
ID: 365540

Abstract

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.