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

• URL: http://arxiv.org/abs/2511.15813v1
• Date: Wed, 19 Nov 2025 19:10:23 GMT
• Title: Multidimensional scaling of two-mode three-way asymmetric dissimilarities: finding archetypal profiles and clustering
• Authors: Aleix Alcacer, Rafael Benitez, Vicente J. Bolos, Irene Epifanio,
• Abstract summary: Multidimensional scaling visualizes dissimilarities among objects and reduces data dimensionality.<n>Recent developments, such as the h-plot, enable the analysis of asymmetric and non-reflexive relationships.<n>This work extends the h-plot methodology to three-way proximity data under both symmetric and asymmetric, conditional and unconditional frameworks.
• Score: 4.43316916502814
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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. Recent developments, such as the h-plot, enable 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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