THE CHORD GAP DIVERGENCE AND A GENERALIZATION OF THE BHATTACHARYYA DISTANCE

We introduce a novel family of distances, called the chord gap divergences, that generalizes the Jensen/Burbea-Rao distances and study its properties. It follows a generalization of the statistical Bhattacharyya distance that is frequently met in applications. We then report an iterative concave-convex procedure for computing centroids, and analyze the performance of the k-means++ clustering with respect to that new dissimilarity measure by introducing the Taylor-Lagrange remainder form of skew Jensen divergences.