Fixing Convergence, Robustness, and Scalability Gaps in Centroid-free Fuzzy K-means Clustering

Abu Bakkar

Fixing Convergence, Robustness, and Scalability Gaps in Centroid-free Fuzzy K-means Clustering

Author(s)	Mr. Abu Bakkar
Country	India
Abstract	Distance-based fuzzy k-means clustering without cluster centroids (FKMWC) is a fuzzy clustering method published in 2024 that reformulates classical fuzzy clustering to remove cluster centroids entirely, solving directly from a pairwise distance matrix through a multiplicative update rule. This paper reproduces that method from its original equations, verifies it with an independent unit test suite, and reports six issues found through direct experimentation rather than re-reading the mathematics: a genuine convergence failure in the published update rule for a broad range of the method's regularization parameter, an unsupported robustness-to-outliers claim, a silent cluster-count validity failure, a scalability bottleneck inherent to a dense pairwise distance matrix, a terminology gap in what the method is claimed to be equivalent to, and an undocumented dependence of the regularization parameter on the absolute scale of the input data. For four of these issues, a concrete fix is proposed and evaluated against the original behaviour: a backtracking line search that eliminates all observed divergence, a distance-capping step that raises outlier-contaminated clustering agreement from 59.3 percent to 92.7 percent, a win-count-based reseeding rule that restores validity at a previously invalid cluster count, and an exact order-Nk reformulation of the method's own k-nearest-neighbour distance option that removes its dependence on a dense N-by-N matrix while producing identical clustering output. All findings are validated on three public benchmark datasets, with clustering accuracy differences confirmed through a paired significance test rather than reported as single-run numbers. The scale-dependence issue is reported honestly as only partially resolved, since a proposed automatic calibration rule did not reduce cross-dataset variance in the tested setting.
Keywords	fuzzy clustering, fuzzy k-means, cluster validity, convergence analysis, distance matrix, clustering robustness
Field	Computer > Artificial Intelligence / Simulation / Virtual Reality
Published In	Volume 8, Issue 4, July-August 2026
Published On	2026-08-31

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Fixing Convergence, Robustness, and Scalability Gaps in Centroid-free Fuzzy K-means Clustering

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