Abstract. Archetypal analysis is an unsupervised learning approach
which represents data by convex combinations of a set of archetypes. The
archetypes generally correspond to the extremal points in the dataset and
are learned by requiring them to be convex combinations of the training
data. In spite of its nice property of interpretability, the method is slow.
We propose a variant of archetypal analysis which scales gracefully to
large datasets. The core idea is to decouple the binding between data
and archetypes and require them to be unit normalized. Geometrically,
the method learns a convex hull inside the unit sphere and represents
the data by their projections on the closest surfaces of the convex hull.
By minimizing the representation error, the method pushes the convex
hull surfaces close to the regions of the sphere where the data reside.
The vertices of the convex hull are the learned archetypes. We apply
the method to human faces and poses to validate its effectiveness in the
context of reconstructions and classifications