Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Elements of information theory
Elements of information theory
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Two-Dimensional Voronoi Diagrams in the Lp-Metric
Journal of the ACM (JACM)
Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
A tight bound for the complexity of voroni diagrams under polyhedral convex distance functions in 3D
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Neural Computation
Matrix Exponentiated Gradient Updates for On-line Learning and Bregman Projection
The Journal of Machine Learning Research
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Capacity-constrained point distributions: a variant of Lloyd's method
ACM SIGGRAPH 2009 papers
Davenport-Schinzel Sequences and their Geometric Applications
Davenport-Schinzel Sequences and their Geometric Applications
Jensen-Bregman Voronoi Diagrams and Centroidal Tessellations
ISVD '10 Proceedings of the 2010 International Symposium on Voronoi Diagrams in Science and Engineering
Discrete & Computational Geometry
Statistical analysis of tensor fields
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part I
On the Information Geometry of Audio Streams With Applications to Similarity Computing
IEEE Transactions on Audio, Speech, and Language Processing
The Burbea-Rao and Bhattacharyya Centroids
IEEE Transactions on Information Theory
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A Jensen-Bregman divergence is a distortion measure defined by a Jensen convexity gap induced by a strictly convex functional generator. Jensen-Bregman divergences unify the squared Euclidean and Mahalanobis distances with the celebrated information-theoretic Jensen-Shannon divergence, and can further be skewed to include Bregman divergences in limit cases. We study the geometric properties and combinatorial complexities of both the Voronoi diagrams and the centroidal Voronoi diagrams induced by such as class of divergences. We show that Jensen-Bregman divergences occur in two contexts: (1) when symmetrizing Bregman divergences, and (2) when computing the Bhattacharyya distances of statistical distributions. Since the Bhattacharyya distance of popular parametric exponential family distributions in statistics can be computed equivalently as Jensen-Bregman divergences, these skew Jensen-Bregman Voronoi diagrams allow one to define a novel family of statistical Voronoi diagrams.