Multidimensional scaling of two-mode three-way asymmetric dissimilarities: finding archetypal profiles and clustering
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| Format: | Preprint |
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2025
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| author | Alcacer, Aleix Benitez, Rafael Bolos, Vicente J. Epifanio, Irene |
| author_facet | Alcacer, Aleix Benitez, Rafael Bolos, Vicente J. Epifanio, Irene |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_15813 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multidimensional scaling of two-mode three-way asymmetric dissimilarities: finding archetypal profiles and clustering Alcacer, Aleix Benitez, Rafael Bolos, Vicente J. Epifanio, Irene Methodology Applications Machine Learning 62H30, 62H99 G.3 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. |
| title | Multidimensional scaling of two-mode three-way asymmetric dissimilarities: finding archetypal profiles and clustering |
| topic | Methodology Applications Machine Learning 62H30, 62H99 G.3 |
| url | https://arxiv.org/abs/2511.15813 |