Enhanced fractional probabilistic self-organizing maps with genetic algorithm optimization (EF-PRSOM)

The Fractional derivatives offer an effective method for incorporating memory into systems, increasing efficiency for tasks that require long-term memory processes. They provide considerable advantages over classical derivatives, enabling deeper analysis of complex processes through effective access to underlying aspects. Leveraging these benefits, this paper introduces a new clustering approach, Enhanced Fractional Probabilistic Self-Organizing Map and Genetic Algorithm optimization. This approach addresses the problem of kernel locality and the challenges associated with selecting the parameter alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}. To determine the appropriate order of alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}, we implemented an efficient method using Genetic Algorithm optimization, enhancing clustering quality by considering model complexity, goodness of fit, and cluster separation. Furthermore, the optimized EF-PRSOM was compared to several clustering methods across multiple datasets using the Dunn index. Remarkably, EF-PRSOM consistently outperformed its counterparts across all metrics. Additionally, the optimized EF-PRSOM has the potential to be applied to various tasks, including image compression, where its effectiveness could be assessed using performance measures such as Peak Signal-to-Noise Ratio and Structural Similarity Index. This highlights the versatility of the proposed EF-PRSOM method across different applications.