{"ID":2839703,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.15813","arxiv_id":"2511.15813","title":"Multidimensional scaling of two-mode three-way asymmetric dissimilarities: finding archetypal profiles and clustering","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.","short_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, en...","url_abs":"https://arxiv.org/abs/2511.15813","url_pdf":"https://arxiv.org/pdf/2511.15813v1","authors":"[\"Aleix Alcacer\",\"Rafael Benitez\",\"Vicente J. Bolos\",\"Irene Epifanio\"]","published":"2025-11-19T19:10:23Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"stat.AP\",\"stat.ML\"]","methods":"[]","has_code":false}