Measuring centrality and dispersion in directional datasets: the ellipsoidal cone covering approach

Consider a finite collection $$\{\xi _k\}_{k=1}^p$${ξk}k=1p of vectors in the space $$\mathbb {R}^n$$Rn. The $$\xi _k$$ξk’s are not to be seen as position points but as directions. This work addresses the problem of computing the ellipsoidal cone of minimal volume that contains all the $$\xi _k$$ξk’s. The volume of an ellipsoidal cone is defined as the usual n-dimensional volume of a certain truncation of the cone. The central axis of the ellipsoidal cone of minimal volume serves to define the central direction of the datapoints, whereas its volume can be used as measure of dispersion of the datapoints.