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Near Neighbor Distribution in Sets of Fractal Nature
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SYSNO ASEP 0420987 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Ostatní články Title Near Neighbor Distribution in Sets of Fractal Nature Author(s) Jiřina, Marcel (UIVT-O) SAI, RID Source Title International Journal of Computer Information Systems and Industrial Management Applications - ISSN 2150-7988
Roč. 5, č. 1 (2013), s. 159-166Number of pages 8 s. Language eng - English Country US - United States Keywords nearest neighbor ; fractal set ; multifractal ; Erlang distribution Subject RIV BB - Applied Statistics, Operational Research R&D Projects LG12020 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Institutional support UIVT-O - RVO:67985807 Annotation 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. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2014 Electronic address http://www.mirlabs.org/ijcisim/regular_papers_2013/Paper91.pdf
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