Using Continuous Hopfield Neural Network for Choice Architecture of Probabilistic Self-Organizing Map

Abstract

The probabilistic self-organizing map (PRSOM) is an improved version of the Kohonen classical model (SOM) that appeared in the late 1990’s. Mathematically, PRSOM gives an estimation of the density probability function of a set of samples. And this estimation depends on parameters given by the architecture of the model. Therefore, the main problem of this model, that we try to approach in this paper, is the architecture choice (the number of neurons). In summary, in the present paper, we describe a recent approach of PRSOM trying to find a solution to the problem below. For that, we propose an architecture optimization model that is a mixed integer non-linear optimization model under linear and quadratic constraints. Resolution of suggested model is carried out by continuous Hopfield neural network (CHN). The performance of the technique is supported by the use of the proposed model in data analysis, notably, classification of iris dataset.