  "Deep Archetypal Analysis" generates latent representations of
high-dimensional datasets in terms of fractions of intuitively understandable
basic entities called archetypes. The proposed method is an extension of linear
"Archetypal Analysis" (AA), an unsupervised method to represent multivariate
data points as sparse convex combinations of extremal elements of the dataset.
Unlike the original formulation of AA, "Deep AA" can also handle side
information and provides the ability for data-driven representation learning
which reduces the dependence on expert knowledge. Our method is motivated by
studies of evolutionary trade-offs in biology where archetypes are species
highly adapted to a single task. Along these lines, we demonstrate that "Deep
AA" also lends itself to the supervised exploration of chemical space, marking
a distinct starting point for de novo molecular design. In the unsupervised
setting we show how "Deep AA" is used on CelebA to identify archetypal faces.
These can then be superimposed in order to generate new faces which inherit
dominant traits of the archetypes they are based on.
