06004529

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06004529 Avros, R. Granichin, O. Shalymov, D. Volkovich, Z. Weber, G.-W. Randomized algorithm of finding the true number of clusters based on Chebychev polynomial approximation. Holmes, Dawn E (ed.). et al., Data mining: foundations and intelligent paradigms. Volume 1: Clustering, association and classification. Berlin: Springer (ISBN 978-3-642-23165-0/hbk; 978-3-642-23166-7/ebook). Intelligent Systems Reference Library 23, 131-155 (2012). 2012 Berlin: Springer EN cluster analysis clustering cluster stability randomized algorithms

doi:10.1007/978-3-642-23166-7_6

Summary: One of the important problems arising in cluster analysis is the estimation of the appropriate number of clusters. In the case when the expected number of clusters is sufficiently large, the majority of the existing methods involve high complexity computations. This difficulty can be avoided by using a suitable confidence interval to estimate the number of clusters. Such a method is proposed in the current chapter. The main idea is to allocate the jump position of the within-cluster dispersion function using Chebyshev polynomial approximations. The confidence interval for the true number of clusters can be obtained in this way by means of a comparatively small number of the distortion calculations. A significant computational complexity decreasing is proven. Several examples are given to demonstrate the high ability of the proposed methodology.