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Features of Neighbors Spaces
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SYSNO ASEP 0103283 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Features of Neighbors Spaces Title Vlastnosti prostoru sousedů Author(s) Jiřina, Marcel (UIVT-O) SAI, RID
Jiřina jr., M. (CZ)Source Title SOFSEM 2004: Theory and Practice of Computer Science. - Berlin : SpringerVerlag, 2004 / Van Emde Boa P. ; Pokorný J. ; Bieliková M. ; Štuller J. - ISBN 3-540-20779-1 Pages s. 241-248 Number of pages 8 s. Action SOFSEM 2004. Conference on Current Trends in Theory and Practice of Computer Science /30./ Event date 24.01.2004-30.01.2004 VEvent location Měřín Country CZ - Czech Republic Event type WRD Language eng - English Country DE - Germany Keywords distribution mapping function ; power application ; nearest neighbor ; boundary effect Subject RIV BA - General Mathematics R&D Projects LN00B096 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) UT WOS 000189212700020 EID SCOPUS 35048814461 DOI https://doi.org/10.1007/978-3-540-24618-3_20 Annotation Distances of the nearest neighbor or several nearest neighbors are essential in probability density estimate by the method of k nearest neighbors or in problems of searching in large databases. A typical task of the probability density estimate using several nearest neighbors is the Bayes s classifier. The task of searching in large databases is looking for other nearest neighbor queries. In this paper it is shown that for a uniform distribution of points in an n-dimensional Euclidean space the distribution of the distance of the i-th nearest neighbor to the n-power has Erlang distribution. The power approximation of the newly introduced probability distribution mapping function of distances of nearest neighbors in the form of suitable power of the distance is presented. A way to state distribution mapping exponent q for a probability density estimation including boundary effect in high dimensions is shown. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2005
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