# Probabilistic Archetypal Analysis

arXiv: https://arxiv.org/abs/1312.7604 · HTML: https://mlsanity.com/paper/1312.7604/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2013.

## Built on by (most cited first, 11 of 11)

- [Archetypal SAE: Adaptive and Stable Dictionary Learning for Concept Extraction in Large Vision Models](https://mlsanity.com/paper/2502.12892/) (2025)
- [Linear Representations of Political Perspective Emerge in Large Language Models](https://mlsanity.com/paper/2503.02080/) (2025)
- [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)
- [Archetypal Analysis++: Rethinking the Initialization Strategy](https://mlsanity.com/paper/2301.13748/) (2023)
- [Archetypal Analysis for Binary Data](https://mlsanity.com/paper/2502.04172/) (2025)
- [Wasserstein Archetypal Analysis](https://mlsanity.com/paper/2210.14298/) (2022)
- [Injective flows for star-like manifolds](https://mlsanity.com/paper/2406.09116/) (2024)
- [Modeling Human Responses by Ordinal Archetypal Analysis](https://mlsanity.com/paper/2409.07934/) (2024)
- [BenchMake: Turn any scientific data set into a reproducible benchmark](https://mlsanity.com/paper/2506.23419/) (2025)
- [Archetypal cases for questionnaires with nominal multiple choice questions](https://mlsanity.com/paper/2601.05392/) (2026)

## Abstract (arXiv)

Archetypal analysis represents a set of observations as convex combinations of pure patterns, or archetypes. The original geometric formulation of finding archetypes by approximating the convex hull of the observations assumes them to be real valued. This, unfortunately, is not compatible with many practical situations. In this paper we revisit archetypal analysis from the basic principles, and propose a probabilistic framework that accommodates other observation types such as integers, binary, and probability vectors. We corroborate the proposed methodology with convincing real-world applications on finding archetypal winter tourists based on binary survey data, archetypal disaster-affected countries based on disaster count data, and document archetypes based on term-frequency data. We also present an appropriate visualization tool to summarize archetypal analysis solution better.