A REMARK ON L2 DISTANCE FUNCTION AND NON-IDENTIFIABILITY PROBLEM OF FINITE MIXTURE DISTRIBUTION MODELS IN MODEL-BASED CLASSIFICATION

Yüksel ÖNER¹ , Fikriye KABAKÇI² , Mehmet GÜRCAN³

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 (pdfs) of the finite mixture distribution models for two different populations by L2 distance. We propose the componentwise L2 distance function to compare the pdfs 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 pdfs of finite mixture distribution models for two different populations.

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