A generalization of the Jensen divergence: The chord gap divergence
This work provides a theoretical extension of divergence measures for statistical and clustering applications, but appears incremental as it builds on existing Jensen and Bhattacharyya distances.
The authors introduced the chord gap divergence, a new family of distances that generalizes Jensen divergences and extends the Bhattacharyya distance, and analyzed its properties including an iterative concave-convex procedure for centroid computation and performance in k-means++ clustering using Taylor-Lagrange remainders.
We introduce a novel family of distances, called the chord gap divergences, that generalizes the Jensen divergences (also called the Burbea-Rao distances), and study its properties. It follows a generalization of the celebrated statistical Bhattacharyya distance that is frequently met in applications. We 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 the skew Jensen divergences.