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arXiv · 2511.15813

Multidimensional scaling of two-mode three-way asymmetric dissimilarities: finding archetypal profiles and clustering

Mireia Mollar-Gumbau·Aleix Alcacer·Rafael Benitez·Vicente J. Bolos·Irene Epifanio
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Abstract

Multidimensional scaling visualizes dissimilarities among objects and reduces data dimensionality. While many methods address symmetric proximity data, asymmetric and especially three-way proximity data (capturing relationships across multiple occasions) remain underexplored. The h-plot enables the analysis of asymmetric and non-reflexive relationships by embedding dissimilarities in a Euclidean space, allowing further techniques like archetypoid analysis to identify representative extreme profiles. However, no existing methods extract archetypal profiles from three-way asymmetric proximity data. This work extends the h-plot methodology to three-way proximity data under both symmetric and asymmetric, conditional and unconditional frameworks. The proposed approach offers several advantages: intuitive interpretability through a unified Euclidean representation; an explicit, eigenvector-based analytical solution free from local minima; scale invariance under linear transformations; computational efficiency for large matrices; and a straightforward goodness-of-fit evaluation. Furthermore, it enables the identification of archetypal profiles and clustering structures for three-way asymmetric proximities. Its performance is compared with existing models for multidimensional scaling and clustering, and illustrated through a financial application. All data and code are provided to facilitate reproducibility.

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Mireia Mollar-Gumbau, Aleix Alcacer, Rafael Benitez, Vicente J. Bolos, Irene Epifanio. 2025-11-19. Multidimensional scaling of two-mode three-way asymmetric dissimilarities: finding archetypal profiles and clustering. https://arxiv.org/abs/2511.15813

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