Using continuous Hopfield neural network for solving a new optimization architecture model of probabilistic self organizing map

Abstract

Probabilistic models have proven their strength to model many natural phenomena as close as possible to reality, in particular, the probabilistic self organizing map (PRSOM) that belongs to the unsupervised learning models. It allows to provide an estimation of the probability density function through the likelihood maximization. This latter function depends on several parameters given by the model architecture. In this context, the aim of this paper is to deal with the architecture choice problem that consists in determining the optimal number of components needed for a better performance. In this paper, we propose a new optimization model that describes the problem above. We present the architecture of PRSOM in a mathematical system of a non linear objective function with mixed variables under linear and quadratic constraints. Due to the complexity of the resolution, we suggest the continuous Hopfield neural network (CHN) that we support by a deep stability analysis. Performance of the proposed model is demonstrated through the dataset clustering.