Online Dictionary Learning for Approximate Archetypal Analysis

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.