# Efficient and Generalizable Archetypal Analysis for Discrete Data

arXiv: https://arxiv.org/abs/2610.12035 · HTML: https://mlsanity.com/paper/2610.12035/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 29 references that are in the map.
- First posted on arXiv 8 Oct 2026.

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

- [Unsupervised Learning of Artistic Styles with Archetypal Style Analysis](https://mlsanity.com/paper/1805.11155/) (2018)
- [A Survey on Archetypal Analysis](https://mlsanity.com/paper/2504.12392/) (2025)

## Abstract (arXiv)

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.