Foundations of Computational Intelligence

0342904 - ÚI 2011 RIV DE eng M - Monography Chapter
Jiřina, Marcel - Jiřina jr., M.
Classification by the Use of Decomposition of Correlation Integral.
Foundations of Computational Intelligence. Vol. 5. Berlin: Springer, 2009 - (Abraham, A.; Hassanien, A.; Snášel, V.), s. 39-55. Studies in Computational Intelligence, 205. ISBN 978-3-642-01535-9
R&D Projects: GA MŠMT(CZ) 1M0567
Institutional research plan: CEZ:AV0Z10300504
Keywords : classification * multifractal * correlation dimension * distribution mapping exponent
Subject RIV: IN - Informatics, Computer Science

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.
Permanent Link: http://hdl.handle.net/11104/0185512