Architecture Optimization Model for the Probabilistic Self-Organizing Maps and Speech Compression

The probabilistic self-organizing map (PRSOM) is an improved version of the Kohonen classical model (SOM) that appeared in the late 1990's. In the last years, the interest of probabilistic methods, especially in the fields of clustering and classification has increased, and the PRSOM has been successfully employed in many technological uses, such as: pattern recognition, speech recognition, data compression, medical diagnosis, etc. Mathematically, the PRSOM gives an estimation of the density probability function of a set of samples. And this estimation depends on the 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 and the initialization parameters). 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 nonlinear optimization model under linear constraints, resolved by the genetic algorithm. Then to prove the efficiency of the proposed model, we chose to apply it on a speech compression technique based on the determination of the optimal codebook, and finally, we give an implementation and an evaluation of the proposed method that we compare with the results of the classical model.