Finding Archetypal Spaces Using Neural Networks
This addresses the limitation of existing linear methods for data decomposition in fields like biology and image analysis, though it is an incremental improvement by extending to non-linear cases.
The authors tackled the problem of archetypal analysis in non-linear data domains by proposing AAnet, a deep neural network framework that learns a latent archetypal space, achieving state-of-the-art recovery of ground-truth archetypes and identifying biologically meaningful archetypes in single-cell gene expression data.
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.