Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Voronoi diagram in statistical parametric space by Kullback-Leibler divergence
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Voronoi diagrams by divergences with additive weights
Proceedings of the fourteenth annual symposium on Computational geometry
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
Algorithmic geometry
Delaunay triangulations and Voronoi diagrams for Riemannian manifolds
Proceedings of the sixteenth annual symposium on Computational geometry
On the combinatorial complexity of euclidean Voronoi cells and convex hulls of d-dimensional spheres
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Clustering with Bregman Divergences
The Journal of Machine Learning Research
Fitting the smallest enclosing bregman ball
ECML'05 Proceedings of the 16th European conference on Machine Learning
The farthest point strategy for progressive image sampling
IEEE Transactions on Image Processing
Visualizing bregman voronoi diagrams
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Fast nearest neighbor retrieval for bregman divergences
Proceedings of the 25th international conference on Machine learning
Mixed Bregman Clustering with Approximation Guarantees
ECML PKDD '08 Proceedings of the European conference on Machine Learning and Knowledge Discovery in Databases - Part II
Bregman Divergences and the Self Organising Map
IDEAL '08 Proceedings of the 9th International Conference on Intelligent Data Engineering and Automated Learning
Coresets and approximate clustering for Bregman divergences
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Computational Geometry from the Viewpoint of Affine Differential Geometry
Emerging Trends in Visual Computing
Clustering Multivariate Normal Distributions
Emerging Trends in Visual Computing
Intrinsic Geometries in Learning
Emerging Trends in Visual Computing
Sparse Multiscale Patches for Image Processing
Emerging Trends in Visual Computing
Bregman vantage point trees for efficient nearest neighbor queries
ICME'09 Proceedings of the 2009 IEEE international conference on Multimedia and Expo
Algorithms and theory of computation handbook
Independent component analysis using bregman divergences
IEA/AIE'10 Proceedings of the 23rd international conference on Industrial engineering and other applications of applied intelligent systems - Volume Part II
Channel capacity restoration of noisy optical quantum channels
NEHIPISIC'11 Proceeding of 10th WSEAS international conference on electronics, hardware, wireless and optical communications, and 10th WSEAS international conference on signal processing, robotics and automation, and 3rd WSEAS international conference on nanotechnology, and 2nd WSEAS international conference on Plasma-fusion-nuclear physics
Constructing two-dimensional Voronoi diagrams via divide-and-conquer of envelopes in space
Transactions on computational science IX
Constructing two-dimensional Voronoi diagrams via divide-and-conquer of envelopes in space
Transactions on computational science IX
Transactions on Computational Science XIV
Levels of details for gaussian mixture models
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part II
Algorithmic superactivation of asymptotic quantum capacity of zero-capacity quantum channels
Information Sciences: an International Journal
Pattern learning and recognition on statistical manifolds: an information-geometric review
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
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The Voronoi diagram of a point set is a fundamental geometric structure that partitions the space into elementary regions of influence defining a discrete proximity graph and dually a well-shaped Delaunay triangulation. In this paper, we investigate a framework for defining and building the Voronoi diagrams for a broad class of distortion measures called Bregman divergences, that includes not only the traditional (squared) Euclidean distance, but also various divergence measures based on entropic functions. As a by-product, Bregman Voronoi diagrams allow one to define information-theoretic Voronoi diagrams in statistical parametric spaces based on the relative entropy of distributions. We show that for a given Bregman divergence, one can define several types of Voronoi diagrams related to each other by convex duality or embedding. Moreover, we can always compute them indirectly as power diagrams in primal or dual spaces, or directly after linearization in an extra-dimensional space as the projection of a Euclidean polytope. Finally, our paper proposes to generalize Bregman divergences to higher-order terms, called κ-jet Bregman divergences, and touch upon their Voronoi diagrams.