Weighted and robust archetypal analysis

Archetypal analysis represents observations in a multivariate data set as convex combinations of a few extremal points lying on the boundary of the convex hull. Data points which vary from the majority have great influence on the solution; in fact one outlier can break down the archetype solution. This paper adapts the original algorithm to be a robust M-estimator and presents an iteratively reweighted least squares fitting algorithm. As required first step, the weighted archetypal problem is formulated and solved. The algorithm is demonstrated using both an artificial and a real world example.