OSPA Barycenters for Clustering Set-Valued Data

We consider the problem of clustering set-valued observations, i.e., each observation is a set that consists of a finite number of real vectors. For this purpose, we develop a $k$-means algorithm that employs the OSPA distance for measuring the distance between sets. In particular, we introduce a novel alternating optimization algorithm for the OSPA barycenter of sets with varying cardinalities that is required for calculating cluster centroids efficiently. The benefits of clustering set-valued data with respect to the OSPA distance are illustrated by means of simulated experiments in the context of target tracking and recognition.