<p>Clustering ensemble improves clustering quality by integrating multiple base clustering results; however, existing methods suffer from inadequate handling of boundary uncertainty and lack a unified probabilistic-to-decision framework. This paper proposes GMM-3WD-CE, which integrates Gaussian Mixture Model (GMM) with three-way decision (3WD) theory to construct a multi-level uncertainty modelling framework. The method generates <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(M=50\)</EquationSource> </InlineEquation> diverse base clusterings via a multi-algorithm strategy, constructs a weighted co-association matrix using quality scores derived from the silhouette coefficient, the Caliński–Harabasz index, and the Davies–Bouldin index, employs the ICL criterion for optimal GMM model selection, and adaptively calculates three-way decision thresholds through the Otsu algorithm to partition samples into core, boundary, and trivial domains. Differentiated label-assignment strategies for each region yield the final consensus clustering. Comparative experiments on eight benchmark datasets with nine comparison methods show that GMM-3WD-CE achieves statistically significant average improvements of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(3.2\%\)</EquationSource> </InlineEquation> in NMI and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(3.9\%\)</EquationSource> </InlineEquation> in ARI over PCPA and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(8.8\%\)</EquationSource> </InlineEquation> in NMI and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(10.4\%\)</EquationSource> </InlineEquation> in ARI over classical MCLA, while remaining competitive with the strongest recent baseline, SDGCA (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(1.2\%\)</EquationSource> </InlineEquation> average NMI advantage; Wilcoxon <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(p=0.089\)</EquationSource> </InlineEquation>, medium effect size <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(d=0.41\)</EquationSource> </InlineEquation>). Ablation experiments verify the contribution of each component; Wilcoxon and Friedman tests with Cohen’s <i>d</i> effect sizes confirm statistical significance against all other baselines; and runtime/scalability analyses characterise the computational trade-offs.</p>

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Clustering ensemble method integrating Gaussian mixture model and three-way decision (GMM-3WD-CE)

  • Yunpeng Ma,
  • Zhicong Li

摘要

Clustering ensemble improves clustering quality by integrating multiple base clustering results; however, existing methods suffer from inadequate handling of boundary uncertainty and lack a unified probabilistic-to-decision framework. This paper proposes GMM-3WD-CE, which integrates Gaussian Mixture Model (GMM) with three-way decision (3WD) theory to construct a multi-level uncertainty modelling framework. The method generates \(M=50\) diverse base clusterings via a multi-algorithm strategy, constructs a weighted co-association matrix using quality scores derived from the silhouette coefficient, the Caliński–Harabasz index, and the Davies–Bouldin index, employs the ICL criterion for optimal GMM model selection, and adaptively calculates three-way decision thresholds through the Otsu algorithm to partition samples into core, boundary, and trivial domains. Differentiated label-assignment strategies for each region yield the final consensus clustering. Comparative experiments on eight benchmark datasets with nine comparison methods show that GMM-3WD-CE achieves statistically significant average improvements of \(3.2\%\) in NMI and \(3.9\%\) in ARI over PCPA and \(8.8\%\) in NMI and \(10.4\%\) in ARI over classical MCLA, while remaining competitive with the strongest recent baseline, SDGCA ( \(1.2\%\) average NMI advantage; Wilcoxon \(p=0.089\) , medium effect size \(d=0.41\) ). Ablation experiments verify the contribution of each component; Wilcoxon and Friedman tests with Cohen’s d effect sizes confirm statistical significance against all other baselines; and runtime/scalability analyses characterise the computational trade-offs.