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Foundations of Computational Intelligence
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SYSNO ASEP 0342904 Document Type M - Monograph Chapter R&D Document Type Monograph Chapter Title Classification by the Use of Decomposition of Correlation Integral Author(s) Jiřina, Marcel (UIVT-O) SAI, RID
Jiřina jr., M. (CZ)Source Title Foundations of Computational Intelligence, Function Approximation and Classification, 5. - Berlin : Springer, 2009 / Abraham A. ; Hassanien A.E. ; Snášel V. - ISSN 1860-949X - ISBN 978-3-642-01535-9 Pages s. 39-55 Number of pages 17 s. Number of pages 378 Language eng - English Country DE - Germany Keywords classification ; multifractal ; correlation dimension ; distribution mapping exponent Subject RIV IN - Informatics, Computer Science R&D Projects 1M0567 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000268010900002 EID SCOPUS 67949108239 DOI 10.1007/978-3-642-01536-6_2 Annotation For estimating the value of the correlation dimension, a polynomial approximation of correlation integral is often used and then linear regression for logarithms of variables is applied. In this Chapter, we show that the correlation integral can be decomposed into functions each related to a particular point of data space. The essential difference is that the value of the exponent, which would correspond to the correlation dimension, differs in accordance to the position of the point in question. Moreover, we show that the multiplicative constant represents the probability density estimation at that point. This finding is used to construct a classifier. Tests with some data sets from the Machine Learning Repository show that this classifier can be very effective. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2011
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