Weighted and robust archetypal analysis

Authors

Friedrich Leisch, University of WollongongFollow
Manuel Eugster

RIS ID

35491

Publication Details

Eugster, M. J.A. & Leisch, F. (2011). Weighted and robust archetypal analysis. Computational Statistics and Data Analysis, 55 (3), 1215-1225.

Abstract

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. The original algorithm is adapted to be a robust M-estimator and an iteratively reweighted least squares fitting algorithm is presented. As a required first step, the weighted archetypal problem is formulated and solved. The algorithm is demonstrated using an artificial example, a real world example and a detailed simulation study.