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We briefly review the basic ideas behind archetypal analysis for matrixfactorization and discuss its behavior in approximating the convex hull of adata sample. We then ask how good such approximations can be and considerdifferent cases. Understanding archetypal analysis as the problem of computinga convexity constrained low-rank approximation of the identity matrix providesestimates for archetypal analysis and the SiVM heuristic.

A Note on Archetypal Analysis and the Approximation of Convex Hulls