# Finding Archetypal Spaces Using Neural Networks

arXiv: https://arxiv.org/abs/1901.09078 · HTML: https://mlsanity.com/paper/1901.09078/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jan 2019.

## Built on by (most cited first, 6 of 6)

- [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)
- [Finding Belief Geometries with Sparse Autoencoders](https://mlsanity.com/paper/2604.02685/) (2026)
- [Riemannian Archetypal Analysis: Interpretable non-linear data analysis on deformed star distributions](https://mlsanity.com/paper/2605.24113/) (2026)
- [The Polytopal Neural Network](https://mlsanity.com/paper/2610.12004/) (2026)

## Abstract (arXiv)

Archetypal analysis is a data decomposition method that describes each observation in a dataset as a convex combination of "pure types" or archetypes. These archetypes represent extrema of a data space in which there is a trade-off between features, such as in biology where different combinations of traits provide optimal fitness for different environments. Existing methods for archetypal analysis work well when a linear relationship exists between the feature space and the archetypal space. However, such methods are not applicable to systems where the feature space is generated non-linearly from the combination of archetypes, such as in biological systems or image transformations. Here, we propose a reformulation of the problem such that the goal is to learn a non-linear transformation of the data into a latent archetypal space. To solve this problem, we introduce Archetypal Analysis network (AAnet), which is a deep neural network framework for learning and generating from a latent archetypal representation of data. We demonstrate state-of-the-art recovery of ground-truth archetypes in non-linear data domains, show AAnet can generate from data geometry rather than from data density, and use AAnet to identify biologically meaningful archetypes in single-cell gene expression data.