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Geometry and Fixed-Rate Quantization in Riemannian Metric Spaces Induced by Separable Bregman Divergences

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Geometric Science of Information (GSI 2019)

Abstract

Dual separable Bregman divergences induce dual Riemannian metric spaces which are isometric to the Euclidean space after non-linear monotone embeddings. We investigate fixed-rate quantization and the induced Voronoi diagrams in those metric spaces.

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References

  1. Amari, S.-i., Nagaoka, H.: Methods of Information Geometry. Translations of Mathematical Monographs, vol. 191. Oxford University Press, New York (2000)

    Google Scholar 

  2. Nielsen, F, Boissonnat, J-D., Nock, F.: On Bregman Voronoi diagrams. In: ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 746–755 (2007)

    Google Scholar 

  3. Boissonnat, J.-D., Nielsen, F., Nock, F.: Bregman Voronoi diagrams. Discret. Comput. Geom. 44, 281–307 (2010)

    Article  MathSciNet  Google Scholar 

  4. Nielsen, F., Nock, R.: Skew Jensen-Bregman Voronoi diagrams. In: Gavrilova, M.L., Tan, C.J.K., Mostafavi, M.A. (eds.) Transactions on Computational Science XIV. LNCS, vol. 6970, pp. 102–128. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25249-5_4

    Chapter  Google Scholar 

  5. Calin, O., Urdiste, C.: Geometric Modeling in Probability and Statistics. Springer Internl. Pub, Switzerland (2010)

    Google Scholar 

  6. Gzyl, H.: Prediction in Riemannian metrics derived from divergence functions (2018). http://arxiv.org/abs/1808.01638

  7. Linder, T.: Learning-theoretic methods in vector quantization. In: Györfi, L. (ed.) Principles of Nonparametric Learning. CISM, vol. 434, pp. 163–210. Springer, Vienna (2002). https://doi.org/10.1007/978-3-7091-2568-7_4

    Chapter  Google Scholar 

  8. Nielsen, F., Nock, R.: Sided and symmetrized Bregman centroids. IEEE Trans. Inf. Theory 55(6), 2882–2904 (2009)

    Article  MathSciNet  Google Scholar 

  9. Nielsen, F.: An elementary introduction to information geometry (2018). https://arxiv.org/abs/1808.08271

  10. Pollard, D.: A User’s Guide to Measure Theoretic Probability. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

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Correspondence to Frank Nielsen.

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Gomes-Gonçalves, E., Gzyl, H., Nielsen, F. (2019). Geometry and Fixed-Rate Quantization in Riemannian Metric Spaces Induced by Separable Bregman Divergences. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2019. Lecture Notes in Computer Science(), vol 11712. Springer, Cham. https://doi.org/10.1007/978-3-030-26980-7_36

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