S. Amari and H. Nagaoka, Methods of Information Geometry, 2000.

A. Ben-hur, D. Horn, H. T. Siegelmann, and V. , Vapnik Support Vector Clustering, Journal of Machine Learning Research, issue.2, pp.125-137, 2001.

F. Aurenhammer, Power Diagrams: Properties, Algorithms and Applications, SIAM Journal on Computing, vol.16, issue.1, pp.78-96, 1987.
DOI : 10.1137/0216006

F. Aurenhammer and H. Imai, Geometric relations among voronoi diagrams, 4th Annual Symposium on Theoretical Aspects of Computer Sciences (STACS), pp.53-65, 1987.

F. Aurenhammer and R. Klein, Voronoi Diagrams, Handbook of Computational Geometry, Chapter, pp.201-290, 2000.

A. Banerjee, S. Merugu, I. S. Dhillon, and J. Ghosh, Clustering with Bregman Divergences, Journal of Machine Learning Research (JMLR), vol.6, pp.1705-1749, 2005.
DOI : 10.1137/1.9781611972740.22

M. De-berg, M. Katz, F. Van-der-stappen, and J. Vleugels, Realistic Input Models for Geometric Algorithms, Algorithmica, vol.34, issue.1, pp.81-97, 2002.
DOI : 10.1007/s00453-002-0961-x

J. Boissonnat and M. Karavelas, On the combinatorial complexity of Euclidean Voronoi cells and convex hulls of d-dimensional spheres, Proc. 14th ACM-SIAM Sympos. Discrete Algorithms (SODA), pp.305-312, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00072084

J. Boissonnat, C. Wormser, and M. Yvinec, Anisotropic diagrams: Labelle Shewchuk approach revisited, 17th Canadian Conference on Computational Geometry (CCCG), pp.266-269, 2005.
DOI : 10.1016/j.tcs.2008.08.006
URL : https://hal.archives-ouvertes.fr/inria-00070277

J. Boissonnat and M. Yvinec, Algorithmic Geometry, 1998.
DOI : 10.1017/CBO9781139172998

J. Boissonnat, C. Wormser, and M. Yvinec, Curved Voronoi Diagrams, Effective Computational Geometry for Curves and Surfaces, pp.67-116, 2007.
DOI : 10.1007/978-3-540-33259-6_2
URL : https://hal.archives-ouvertes.fr/hal-00488446

L. M. Bregman, The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming, USSR Computational Mathematics and Mathematical Physics, vol.7, issue.3, pp.200-217, 1967.
DOI : 10.1016/0041-5553(67)90040-7

H. Brönnimann and M. T. Goodrich, Almost optimal set covers in finite VC-dimension, Discrete & Computational Geometry, vol.16, issue.2, pp.463-479, 1995.
DOI : 10.1007/BF02570718

B. Chazelle, An optimal convex hull algorithm in any fixed dimension, Discrete & Computational Geometry, vol.16, issue.4, pp.377-409, 1993.
DOI : 10.1007/BF02573985

B. Chazelle, The Discrepancy Method, 2000.

I. Csiszár, Why Least Squares and Maximum Entropy? An Axiomatic Approach to Inference for Linear Inverse Problems, The Annals of Statistics, vol.19, issue.4, pp.2032-2066, 1991.
DOI : 10.1214/aos/1176348385

L. Devroye, L. Györfi, and G. Lugosi, A Probabilistic Theory of Pattern Recognition, 1996.
DOI : 10.1007/978-1-4612-0711-5

Q. Du, V. Faber, and M. Gunzburger, Centroidal Voronoi Tessellations: Applications and Algorithms, SIAM Review, vol.41, issue.4, pp.637-676, 1999.
DOI : 10.1137/S0036144599352836

A. Efrat, M. J. Katz, F. Nielsen, and M. Sharir, Dynamic data structures for fat objects and their applications, Computational Geometry, vol.15, issue.4, pp.215-227, 2000.
DOI : 10.1016/S0925-7721(99)00059-0

Y. Eldar, M. Lindenbaum, M. Porat, and Y. Y. Zeevi, The farthest point strategy for progressive image sampling, IEEE Transactions on Image Processing, vol.6, issue.9, pp.1305-1315, 1997.
DOI : 10.1109/83.623193

G. Even, D. Rawitz, and S. Shahar, Hitting sets when the VC-dimension is small, Information Processing Letters, vol.95, issue.2, pp.358-362, 2005.
DOI : 10.1016/j.ipl.2005.03.010

E. Fix and J. L. Hodges, Discrimatory analysis, nonparametric discrimination, 1951.

P. Goldberg and M. Jerrum, Bounding the Vapnik-Chervonenkis dimension of concept classes parameterized by real numbers, Machine Learning, pp.131-148, 1995.

M. Inaba and H. Imai, Geometric clustering models for multimedia databases, Proceedings of the 10th Canadian Conference on Computational Geometry (CCCG'98, 1998.

M. Inaba and H. Imai, Geometric clustering for multiplicative mixtures of distributions in exponential families, Proceedings of the 12th Canadian Conference on Computational Geometry, 2000.

R. Klein, Concrete and Abstract Voronoi Diagrams, Lecture Notes in Computer Science, vol.400, 1989.
DOI : 10.1007/3-540-52055-4

F. Labelle and J. R. Shewchuk, Anisotropic voronoi diagrams and guaranteed-quality anisotropic mesh generation, Proceedings of the nineteenth conference on Computational geometry , SCG '03, pp.191-200, 2003.
DOI : 10.1145/777792.777822
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.13.376

J. Lafferty, Additive models, boosting, and inference for generalized divergences, Proceedings of the twelfth annual conference on Computational learning theory , COLT '99, pp.125-133, 1999.
DOI : 10.1145/307400.307422

D. Le and S. Satoh, Ent-Boost: Boosting using entropy measures for robust object detection, Proc. 18th International Conference on Pattern Recognition, pp.602-605, 2006.
DOI : 10.1016/j.patrec.2007.01.007

S. P. Lloyd, Least squares quantization in PCM, IEEE Transactions on Information Theory, vol.28, issue.2, pp.129-136, 1982.
DOI : 10.1109/TIT.1982.1056489

P. Mcmullen, The maximum numbers of faces of a convex polytope, Mathematika, vol.16, issue.02, pp.179-184, 1971.
DOI : 10.1007/BF02771542

F. Nielsen, Visual Computing: Geometry, Graphics, and Vision. Charles River Media, 2005.

M. Teillaud, O. Devillers, and S. Meiser, The space of spheres, a geometric tool to unify duality results on voronoi diagrams, 1992.
URL : https://hal.archives-ouvertes.fr/hal-01180157

K. Onishi and H. Imai, Voronoi diagram in statistical parametric space by Kullback-Leibler divergence, Proceedings of the thirteenth annual symposium on Computational geometry , SCG '97, pp.463-465, 1997.
DOI : 10.1145/262839.263084

K. Onishi and H. Imai, Voronoi diagrams for an exponential family of probability distributions in information geometry, Japan-Korea Joint Workshop on Algorithms and Computation, 1997.

S. Pion and M. Teillaud, 3d triangulation data structure, CGAL-3.2 User and Reference Manual, 2006.

V. T. Rajan, Optimality of the Delaunay triangulation in ??? d, Discrete & Computational Geometry, vol.80, issue.9, pp.189-202, 1994.
DOI : 10.1007/BF02574375

R. T. Rockafellar, Convex Analysis, 1970.
DOI : 10.1515/9781400873173

J. Ruppert, A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation, Journal of Algorithms, vol.18, issue.3, pp.548-585, 1995.
DOI : 10.1006/jagm.1995.1021

K. Sadakane, H. Imai, K. Onishi, M. Inaba, F. Takeuchi et al., Voronoi diagrams by divergences with additive weights, Proceedings of the fourteenth annual symposium on Computational geometry , SCG '98, pp.403-404, 1998.
DOI : 10.1145/276884.276929

M. Sharir, Almost tight upper bounds for lower envelopes in higher dimensions, Discrete & Computational Geometry, vol.6, issue.3, pp.327-345, 1994.
DOI : 10.1007/BF02574384

D. , R. Wilson, and T. R. Martinez, Improved heterogeneous distance functions, Journal of Artificial Intelligence Research, vol.1, pp.1-34, 1997.

.. Exponential, 11 2.4.1 Parametric statistical spaces and exponential families, 12 2.4.3 Dual parameterizations and dual divergences . . . . . . . . . . . . . . 14

I. Unité-de-recherche-inria-sophia and . Antipolis, route des Lucioles -BP 93 -06902 Sophia Antipolis Cedex (France) Unité de recherche INRIA Futurs : Parc Club Orsay Université -ZAC des Vignes 4, 2004.

I. Unité-de-recherche and . Lorraine, Technopôle de Nancy-Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu -35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l'Europe -38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Rocquencourt, Domaine de Voluceau -Rocquencourt -BP 105 -78153 Le Chesnay Cedex

I. De-voluceau-rocquencourt, BP 105 -78153 Le Chesnay Cedex (France) http://www.inria.fr ISSN, pp.249-6399