Constrained Probabilistic Self-Organizing Maps

Zakariya Abibi, Zakariae En-Naimani, Khalid Haddouch

Abstract: Probabilistic self-organizing maps and Gaussian mixture models represent flexible and interpretable probabilistic models that address various machine learning needs, such as speech processing and compression. In this context, the probabilistic self-organization map (PRSOM), as an extension of the classical Kohonen self-organization map (SOM), estimates the density distributions of the data using a combination of normal distributions. However, the likelihood function in the normal mixture may exhibit unbounded features and spurious local maxima (degeneracy). To tackle this problem, we introduce specific constraints to the PRSOM model, based on Ingrassia’s approach. Finally, we provide an implementation of the proposed method and give a comparative evaluation of its performance through numerical experiments.