Algorithms for the spatial median

Abstract

The spatial median can be defined as the unique minimum of a strictly convex objective function. Hence, its computation through an iterative algorithm ought to be straightforward. The simplest algorithm is the steepest descent Weiszfeld algorithm, as modified by Ostresh and by Vardi and Zhang. Another natural algorithm is Newton-Raphson. Unfortunately, all these algorithms can have problems near data points; indeed, Newton-Raphson can converge to a nonoptimal data point, even if a line search is included! However, by combining these algorithms, a reliable and efficient “hybrid” algorithm can be developed