Partitional clustering via successive transportation problems

We propose to extend the spherical separation approach, amply used in supervised classification, to clustering problems by assigning each datum to a suitable sphere. Our idea consists in designing a heuristic approach based on solving successive transportation problems aimed at providing the radii of the clustering spheres, whose centers are fixed in advance as the barycenters of each current cluster, similarly to the well known K-Means algorithm. Numerical results show the effectiveness of our proposal.