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Correlation Dimension-Based Classifier
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SYSNO ASEP 0421968 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Correlation Dimension-Based Classifier Tvůrce(i) Jiřina, Marcel (UIVT-O) SAI, RID
Jiřina jr., M. (CZ)Zdroj.dok. IEEE Transactions on Cybernetics - ISSN 2168-2267
Roč. 44, č. 12 (2014), s. 2253-2263Poč.str. 11 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova classifier ; multidimensional data ; correlation dimension ; scaling exponent ; polynomial expansion Vědní obor RIV BB - Aplikovaná statistika, operační výzkum CEP LG12020 GA MŠMT - Ministerstvo školství, mládeže a tělovýchovy Institucionální podpora UIVT-O - RVO:67985807 UT WOS 000345629000002 EID SCOPUS 84911928407 DOI 10.1109/TCYB.2014.2305697 Anotace Correlation dimension, singularity exponents, also scaling exponents are widely used in multifractal chaotic series analysis. Correlation dimension and other measures of effective dimensionality are used for characterization of data in applications. A direct use of correlation dimension to multidimensional data classification has not been hitherto presented. There are observations that the correlation integral is a distribution function of distances between all pairs of data points, and that by using polynomial expansion of distance with exponent equal to the correlation dimension this distribution is transformed into locally uniform. The classifier is based on consideration that the "influence" of neighbor points of some class on the probability that the query point belongs to this class is inversely proportional to its distance to the correlation dimension - power. New classification approach is based on summing up all these influences for each class. We prove that a resulting formula gives an estimate of probability of class - not a measure of membership to a class only - to which the query point belongs. For this assertion to be valid it is necessary that exponent of the polynomial transformation must be the correlation dimension. We also propose an "averaging approach" that speeds up computation of the correlation dimension especially for large data sets. It is demonstrated that the correlation dimension based classifier can outperform more sophisticated classifiers. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2015
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