О выборе параметров ЕМ-алгоритма для разделения смеси распределений
Journal Title: Математичне моделювання - Year 2017, Vol 1, Issue 1
Abstract
ON THE CHOICE OF THE PARAMETERS OF THE EM ALGORITHM FOR THE SEPARATION OF THE MIXTURE OF DISTRIBUTIONS. Shumeiko A.A, Iskandarova-Mala A. Abstract The paper considers one of the types of non-hierarchical clustering - the EM-algorithm. This methd is traditionally the most used tool for separating a mixture of distributions with a known number of components. Determining the number of components (clusters) is a non-trivial problem. As a rule, this parameter is chosen by the researcher from some a priori assumptions. Nevertheless, the problem of the automatic choice of this parameter was investigated in many papers. Existing approaches, as a rule, differ in the complexity of implementation, intuitive approaches or approximate methods for solving complex analytical problems, it is often not clear how they are generally related to this task. The EM-algorithm for separating the mixture of normal distributions is in fact a reconstruction of the existing histogram by a linear combination of Gaussian functions, so, naturally, having the value of the specified error of reconstruction, describe the available histogram by a depleted histogram with free nodes, which is best (ie, with a minimum number nodes). The resulting number of nodes is an estimate of the number of components of the mixture, which is reconstructed by a linear combination of Gaussian functions with a given error. Moreover, the values of free nodes make it possible to obtain a starting estimate of the remaining parameters of the mixture. References [1]. McLachlan G.J. The EM algorithm and extensions / G. J. McLachlan, T. Krishnan.-New York: John Wiley & Sons, Inc., 1997 .– 288 p. [2]. Korolev V.Yu. EM-algorithm, its modifications and their application to the problem of separation of mixtures of probability distributions. / V.Yu.Korolev; Theoretical review .– M: IPI RAS, 2007 .– 94 p. [3]. Shumeiko A.A. Intelligent Data Analysis (Introduction to Data Mining) / A.A. Shumeiko, S.L.Sotnik .– Dnepropetrovsk: Belaya EA, 2012.– 212 pp. [4]. Optimal Histograms with Quality Guarantees / H.Jagadish, N.Koudas, S.Multhukrishan та ін. .– Access mode: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.36.769&rep=rep1&type=ps [5]. Vetrov, D.P. Automatic determination of the number of components in the EM-algorithm for recovering a mixture of normal distributions / D.P.Vetrov, D.A.Kropotov, A.A.Asokin // Zh. Vychisl. Math. and Math. fiz. .– 2010 .– No. 4 (50).–P.770–783. [6]. Ligun AA Asymptotic methods for reconstructing curves / AA Ligun, AA Shumeiko .– K .: Naukova dumka, 1997 .– 358 pp.
Authors and Affiliations
А. А. Шумейко, А. О. Искандарова-Мала
Keywords
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