Weighted and Robust Archetypal Analysis

Eugster, Manuel J. A. and Leisch, Friedrich (2010): Weighted and Robust Archetypal Analysis. Department of Statistics: Technical Reports, No.82

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. 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.

• Item Type: Paper (Technical Report)
• Keywords: Robust Archetypal Analysis, M-estimator, Breakdown Point, Iteratively Reweighted Least Squares
• Subjects: Mathematics, Computer Science and Statistics > Statistics > Technical Reports
• Dewey Classification: 300 Social sciences > 310 General statistics
• Language: English