Exact equation of the boundary of unimodal and bimodal domains of a two-component Gaussian mixture

Authors:
N. N. Aprausheva;S. V. Sorokin
Affiliations:
Dorodnicyn Computing Centre, Russian Academy of Sciences, Moscow, Russia;Dorodnicyn Computing Centre, Russian Academy of Sciences, Moscow, Russia
Venue:
Pattern Recognition and Image Analysis
Year:
2013

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Mode-Finding for Mixtures of Gaussian Distributions

IEEE Transactions on Pattern Analysis and Machine Intelligence

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Abstract

Common necessary and sufficient conditions of unimodality and bimodality of a two-component Gaussian mixture with equal variances of components are obtained. An exact equation for the boundary of unimodal and bimodal domains is presented. The boundary is proved to be a set of degenerated critical inflection points of the probability density.