Algorithmic validation shows superior clustering accuracy using three-way semi-perimeter distances in simulated and census data, highlighting improvements over standard fuzzy c-medoids.
In this paper, we propose a novel clustering method based on three-way distances. We define a fuzzy c -medoid algorithm based on the semi-perimeter three-way distance, which can be derived from any classical (two-way) distance. This algorithm minimizes an objective function defined as a linear combination of the three-way distances between the medoid of each cluster and call couples of members of the cluster, and an entropic regularization term. We test its effectiveness, applying it both to simulated data and data from the Italian census, showing how it outperforms the standard fuzzy c -medoids algorithm.
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D’Urso et al. (2026) studied this question.
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