Approximation of n-dimensional data using spherical and ellipsoidal primitives

This paper discusses the problem of approximating data points in -dimensional Euclidean space using spherical and ellipsoidal surfaces. A closed form solution is provided for spherical approximation, while an efficient, globally optimal solution for the ellipsoidal problem is proposed in terms of semidefinite programming (SDP). In addition, the paper presents a result for robust fitting in presence of outliers, and illustrates the theory with several numerical examples. A brief survey is also presented on the solutions to other relevant geometric approximation problems, such as ellipsoidal covering of convex hulls and pattern separation.