Conference publications

Abstracts

XVI conference

On a Number of Gaussian Mixture Modes

Aprausheva N.N., Sorokin S.V.

Institution of the Russian Academy of Sciences Dorodnicyn Computing Centre RAS, Russia, 119333, Moscow, Vavilov str. 40. 8 (499) 135-40-98, plat@ccas.ru 8 (499) 135-14-98, www2008@ccas.ru

A wide use of normal distributions mixture as a universal approximator of unknown probability density stimulates the development of methods of the definition of the number of its modes. Research of the probability density properties k of normal distributions f(X) with the equal covariant matrixes and with various vectors of expectation values Σ and with various vectors of expectation values µi, i=1, 2, ..., k 2≤k<∞, allows to draw the following conclusions [1, 2].

1. The number m of the modes of the function f(X) satisfies the inequalities 1≤m≤k.

2. For the fixed value k he number of modes m depends on aprioristic probabilities of a component of the mixture πi, i=1, 2, ..., k and on the Mahalanobis distance between them ρis, i

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