Title: Finding Archetypal Spaces for Data Using Neural Networks,
Abstract: Archetypal analysis is a type of factor analysis where data is fit by a
convex polytope whose corners are "archetypes" of the data, with the data
represented as a convex combination of these archetypal points. While
archetypal analysis has been used on biological data, it has not achieved
widespread adoption because most data are not well fit by a convex polytope in
either the ambient space or after standard data transformations. We propose a
new approach to archetypal analysis. Instead of fitting a convex polytope
directly on data or after a specific data transformation, we train a neural
network (AAnet) to learn a transformation under which the data can best fit
into a polytope. We validate this approach on synthetic data where we add
nonlinearity. Here, AAnet is the only method that correctly identifies the
archetypes. We also demonstrate AAnet on two biological datasets. In a T cell
dataset measured with single cell RNA-sequencing, AAnet identifies several
archetypal states corresponding to naive, memory, and cytotoxic T cells. In a
dataset of gut microbiome profiles, AAnet recovers both previously described
microbiome states and identifies novel extrema in the data. Finally, we show
that AAnet has generative properties allowing us to uniformly sample from the
data geometry even when the input data is not uniformly distributed.