arXiv Machine Learning By Aleix Alcacer, Irene Epifanio, Sebastian Mair, Morten M{\o}rup

A Survey on Archetypal Analysis

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A Survey on Archetypal Analysis reviews the method introduced by Cutler and Breiman in 1994 for extracting archetypes—distinct aspects—from data, where each observation is expressed as a convex combination of these archetypes. The survey covers AA’s role in feature extraction, dimensionality reduction, and its interpretability, discusses its nonconvex optimization challenges, and surveys applications across various scientific fields. It also outlines best practices, limitations, and future research directions for AA.

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arXiv Statistics ML
Sep 3

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

The paper extends the h‑plot multidimensional scaling technique to handle three‑way asymmetric dissimilarities, enabling the extraction of archetypal profiles and clustering in a unified Euclidean space. It provides an explicit eigenvector‑based solution that avoids local minima, is scale‑invariant, computationally efficient, and includes a straightforward goodness‑of‑fit assessment. The method is benchmarked against existing models and demonstrated on a financial dataset, with all data and code made publicly available for reproducibility.

By Mireia Mollar-Gumbau, Aleix Alcacer, Rafael Benitez, Vicente J. Bolos, Irene Epifanio