Comparison of Methods for Hyperspherical Data Averaging and Parameter Estimation

Averaging is an important concept which has found numerous applications in general and in pattern recognition and computer vision in particular. In this paper we consider averaging directional vectors of arbitrary dimensions. Given a set of vectors, we intend to compute an average vector which optimally represents the input vectors according to some formal criterion. Several optimisation criteria are formulated. In particular, we present a class of robust estimators of up to 50% outlier tolerance. Furthermore, we propose a technique to estimate another distribution parameter. Experimental results on spherical data are presented to demonstrate the usefulness of the proposed methods