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<p>Probabilistic models have become one of the most powerful statistical methods for modeling random phenomena, particularly the Probabilistic Self-Organizing Map (PrSOM), which is a probabilistic interpretation of the classical Kohonen model (SOM). This algorithm approximates the distribution of data density using a mixture of normal distributions. However, the likelihood function of the normal mixture is unbounded and exhibits some local maxima (degeneracy). In this context, this paper aims to solve this problem. For this purpose, we apply specific constraints to the PrSOM model based on Ingrassia’s approach as well as directly integrate them into each step of the PrSOM algorithm during the phase of updating the covariance matrices. Indeed, this approach gives rise to a new algorithm called a constrained probabilistic self-organizing map (CPrSOM). We give the implementation of our proposed (CPrSOM) method. We then evaluate its effectiveness by comparing its performance with that of other classification methods through numerical simulations and by applying it to a real dataset.</p>

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Constrained Probabilistic Self-Organizing Map: Enhanced Approach for Degeneracy Prevention

  • 期刊论文

  • 发表日期：

    2026年6月25日

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  • Zakariya Abibi,
  • Zakariae En-Naimani,
  • Khalid Haddouch

摘要

Probabilistic models have become one of the most powerful statistical methods for modeling random phenomena, particularly the Probabilistic Self-Organizing Map (PrSOM), which is a probabilistic interpretation of the classical Kohonen model (SOM). This algorithm approximates the distribution of data density using a mixture of normal distributions. However, the likelihood function of the normal mixture is unbounded and exhibits some local maxima (degeneracy). In this context, this paper aims to solve this problem. For this purpose, we apply specific constraints to the PrSOM model based on Ingrassia’s approach as well as directly integrate them into each step of the PrSOM algorithm during the phase of updating the covariance matrices. Indeed, this approach gives rise to a new algorithm called a constrained probabilistic self-organizing map (CPrSOM). We give the implementation of our proposed (CPrSOM) method. We then evaluate its effectiveness by comparing its performance with that of other classification methods through numerical simulations and by applying it to a real dataset.