A Remark on L2 Distance Function And Non-Identifiability Problem of Finite Mixture Distribution Models in Model-Based Classification

Year 2019, Volume: 14 Issue: 4, 139 - 146, 26.10.2019

Yüksel Öner , Fikriye Kabakcı Burçin Öner , Mehmet Gürcan

Abstract

          Finite
mixture models provide flexible method of modeling data obtained from
population consisting of finite number of homogeneous subpopulations. One of
the main areas in which the finite mixture model structures is practically used
in statistics is model based classification. However, the result of non
identifiability problem arising from the structure of the finite mixture models
may cause unreliable results on classification. In this paper we compare the
probability density functions () of
the finite mixture distribution models for two different populations by L2
distance. We propose the componentwise L2 distance function to compare the  of finite mixture distribution models for two
different populations in the presence of non identifiability problem. Besides,
a condition is proposed to control whether the L2 distance function gives
similar results with the componentwise L2 distance function to compare the  of finite mixture distribution models for two
different populations. 

Keywords

Finite Mixture Distribution, L2 Distance Function, Model Based Classification, Mixture Model, Non-identifiability

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