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

arXiv: https://arxiv.org/abs/2511.15813 · HTML: https://mlsanity.com/paper/2511.15813/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 54 references that are in the map.
- First posted on arXiv 19 Nov 2025.

## Builds on (most cited first, 2 of 2)

- [A Survey on Archetypal Analysis](https://mlsanity.com/paper/2504.12392/) (2025)
- [Biarchetype analysis: simultaneous learning of observations and features based on extremes](https://mlsanity.com/paper/2311.11153/) (2023)

## Abstract (arXiv)

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.