Efficient and Generalizable Archetypal Analysis for Discrete Data
Abstract
Archetypal Analysis (AA) represents observations as convex combinations of extremal data-driven profiles, yielding interpretable low-dimensional descriptions of complex datasets. Classical AA relies on a least-squares objective, which is poorly suited to discrete observations such as binary, count, and categorical data. We introduce an efficient likelihood-based framework for AA supporting Bernoulli, Poisson, and multinomial observation models. Our optimization scheme employs local quadratic approximations of the negative log-likelihood, enabling constrained updates through sequential minimal optimization (SMO) and an active-set method. Scalability is improved by bounding the active set while preserving simplex feasibility. We further introduce a cross-validated predictive likelihood criterion for selecting the number of archetypes, providing a principled alternative to reconstruction-error heuristics and stability-based diagnostics. Synthetic experiments demonstrate computational efficiency and accurate recovery of model complexity. Applications to single-cell RNA sequencing, microbiome composition, and somatic mutation data show that the learned archetypes capture interpretable domain-specific structures while achieving competitive likelihood fits and stable solutions. Overall, the proposed framework enables efficient likelihood-based archetypal analysis of discrete data, complemented by predictive likelihood-based model selection.
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BibTeX
@misc{wedenborg2026efficient,
title = {{Efficient and Generalizable Archetypal Analysis for Discrete Data}},
author = {A. Emilie J. Wedenborg and Jesper Løve Hinrich and Morten Mørup},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12035},
eprint = {2610.12035},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12035},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Efficient and Generalizable Archetypal Analysis for Discrete Data
AU - A. Emilie J. Wedenborg
AU - Jesper Løve Hinrich
AU - Morten Mørup
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12035
UR - https://arxiv.org/abs/2610.12035
AB - Archetypal Analysis (AA) represents observations as convex combinations of extremal data-driven profiles, yielding interpretable low-dimensional descriptions of complex datasets. Classical AA relies on a least-squares objective, which is poorly suited to discrete observations such as binary, count, and categorical data. We introduce an efficient likelihood-based framework for AA supporting Bernoulli, Poisson, and multinomial observation models. Our optimization scheme employs local quadratic approximations of the negative log-likelihood, enabling constrained updates through sequential minimal optimization (SMO) and an active-set method. Scalability is improved by bounding the active set while preserving simplex feasibility. We further introduce a cross-validated predictive likelihood criterion for selecting the number of archetypes, providing a principled alternative to reconstruction-error heuristics and stability-based diagnostics. Synthetic experiments demonstrate computational efficiency and accurate recovery of model complexity. Applications to single-cell RNA sequencing, microbiome composition, and somatic mutation data show that the learned archetypes capture interpretable domain-specific structures while achieving competitive likelihood fits and stable solutions. Overall, the proposed framework enables efficient likelihood-based archetypal analysis of discrete data, complemented by predictive likelihood-based model selection.
ER -