2017/09/29 by Frank Nielsen, Nielsen, Frank
Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Mathematical Inequalities and Applications #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1709.10498
openalex publication_date 2017/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.