# Finding Archetypal Spaces Using Neural Networks

## TL;DR

This paper introduces AAnet, a neural network framework that learns non-linear archetypal representations of data, enabling better recovery of archetypes in complex, non-linear domains like biology and images.

## Contribution

The paper proposes a novel deep learning approach for archetypal analysis that handles non-linear data transformations, extending the applicability of archetypal analysis to complex systems.

## Key findings

- Achieves state-of-the-art recovery of ground-truth archetypes in non-linear data.
- Can generate data based on geometry rather than density.
- Identifies biologically meaningful archetypes in gene expression data.

## Abstract

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.