This paper provides a core-set construction for the problem of Archetypal Analysis, in which a dataset must be described as a convex combination of prototypes which represent vertices approximating the convex hull of the data. Their core-set construction extends from that for the k-means problem. In addition to their approximation algorithm to perform archetypal analysis, which can run on large data sets, they provide theoretical analysis. The reviewers were unanimous in their vote to accept. Authors are encouraged to revise with respect to reviewer comments.