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<p>This paper proposes a novel fuzzy clustering algorithm for probability density functions (PDFs) utilizing an improved Kullback–Leibler divergence (FCP). The proposed algorithm not only determines the optimal number of clusters and assigns PDFs to these clusters but also defines the fuzzy membership degrees between the PDFs and the identified clusters based on the improved divergence measure. The convergence and stability of the FCP algorithm are theoretically guaranteed through two theorems: Theorem 1 proves the convergence of cluster centers as iterations proceed, while Theorem 2 establishes the optimal update formulas for cluster centers and membership matrix by minimizing the clustering objective function via derivative and Lagrangian methods. The effectiveness of the FCP algorithm is demonstrated through a numerical example, where the improved Kullback–Leibler divergence is compared with both <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10618_2025_1136_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^1\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10618_2025_1136_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^2\)</EquationSource> </InlineEquation> distances. Additionally, the algorithm is applied to cluster an image dataset based on features extracted using the Inception Resnet-v2 architecture. The experimental results show that the FCP algorithm outperforms existing models, achieving both accuracy and F1-Score of over 99%, along with a statistically significant improvement according to one-way ANOVA testing.</p>

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A enhanced fuzzy clustering algorithm for probability density functions and image clustering using Inception Resnet-v2 features

  • 期刊论文

  • 发表日期：

    2025年7月29日

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  • Dinh PhamToan

摘要

This paper proposes a novel fuzzy clustering algorithm for probability density functions (PDFs) utilizing an improved Kullback–Leibler divergence (FCP). The proposed algorithm not only determines the optimal number of clusters and assigns PDFs to these clusters but also defines the fuzzy membership degrees between the PDFs and the identified clusters based on the improved divergence measure. The convergence and stability of the FCP algorithm are theoretically guaranteed through two theorems: Theorem 1 proves the convergence of cluster centers as iterations proceed, while Theorem 2 establishes the optimal update formulas for cluster centers and membership matrix by minimizing the clustering objective function via derivative and Lagrangian methods. The effectiveness of the FCP algorithm is demonstrated through a numerical example, where the improved Kullback–Leibler divergence is compared with both \(L^1\) and \(L^2\) distances. Additionally, the algorithm is applied to cluster an image dataset based on features extracted using the Inception Resnet-v2 architecture. The experimental results show that the FCP algorithm outperforms existing models, achieving both accuracy and F1-Score of over 99%, along with a statistically significant improvement according to one-way ANOVA testing.