%0 Journal Article %1 nielsen2017generalization %A Nielsen, Frank %D 2017 %K divergences %T A generalization of the Jensen divergence: The chord gap divergence %U http://arxiv.org/abs/1709.10498 %X 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.

@article{nielsen2017generalization, abstract = {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.}, added-at = {2019-12-11T14:25:41.000+0100}, author = {Nielsen, Frank}, biburl = {https://www.bibsonomy.org/bibtex/22d3a9ee6b85195910bfd8314af7a25a2/kirk86}, description = {[1709.10498] A generalization of the Jensen divergence: The chord gap divergence}, interhash = {377992837a178a7b96d9948f9953a7ec}, intrahash = {2d3a9ee6b85195910bfd8314af7a25a2}, keywords = {divergences}, note = {cite arxiv:1709.10498Comment: 13 pages, 2 figures}, timestamp = {2019-12-11T14:25:41.000+0100}, title = {A generalization of the Jensen divergence: The chord gap divergence}, url = {http://arxiv.org/abs/1709.10498}, year = 2017 }