Application of Bayesian Methods to SOM

G. A. Valverde Castilla, J. M. Mira McWilliams, B. González Pérez

The purpose of this paper is to formulate a stochastic model for self organizing maps (SOM) within the bayesian framework. SOMs were developed by Kohonen (1980) as a tool to represent stuctures such as cortical layers in the brain as two or three dimensional maps. Even so, the first algorithm has been derived from heuristic ideas without underlying statistical motivations. The idea of proposing a SOM map that can represent the probabilistic distribution underlying a data sample has led to the development of different probabilistic alternatives. PRSOM was developed by Anouar (1998). PrSOMs was presented by Lebbah (2015). Yin proposed BSOM (Bayesian SOM). We propose a new bayesian alternative focusing on the advantages of establishing a priori distributions, a formal comparison with BSOM, SOM and EM algorithm is also presented. Finally, we showed the feasibility and accuracy of our approach over a simulated mixture of Gaussian distribution.

Keywords: Self Organizing Maps; bayesian methodology; simulations; dimensionality reduction; Gaussian mixture; Expectation-Maximization; prior.

GT8-1 Bayesian Inference
September 4, 2019  10:40 AM
I2L7. Georgina Blanes building

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