2013/04/25 by Elisabeth M. Werner, Werner, Elisabeth M., Deping Ye +1 · 2 citations
Computer Science · Mathematics · #94A15 #94A17 #Combinatorics #Computer science #Convex function #Divergence (linguistics) #FOS: Computer and information sciences #FOS: Mathematics #Geometry #Information Theory (cs.IT) #Isoperimetric inequality #Mathematical Inequalities and Applications #Mathematics #Measure (data warehouse) #Metric Geometry (math.MG) #Permutation (music) #Physics #Point processes and geometric inequalities #Pure mathematics #Regular polygon #Symmetry (geometry) #cs.IT #math.IT #math.MG #msc:94A15 #msc:94A17
paper · pdf · doi:10.48550/arxiv.1304.6792
published in arXiv (Cornell University) (Cornell University)
arxiv created 2013/04/25 · openalex publication_date 2013/04/25 · arxiv updated 2013/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
In this paper, the concept of the classical f-divergence (for a pair of measures) is extended to the mixed f-divergence (for multiple pairs of measures). The mixed f-divergence provides a way to measure the difference between multiple pairs of (probability) measures. Properties for the mixed f-divergence are established, such as permutation invariance and symmetry in distributions. An Alexandrov-Fenchel type inequality and an isoperimetric type inequality for the mixed f-divergence will be proved and applications in the theory of convex bodies are given.