190
F. Nielsen
2. Amari, S.: Information geometry of positive measures and positive-definite matrices: decomposable dually flat structure. Entropy 16(4), 2131–2145 (2014)
3. Amari, S.-I.: Information Geometry and its Applications, vol. 194. Springer, Berlin (2016)
4. Banerjee, A., Merugu, S., Dhillon, I.S., Ghosh, J.: Clustering with Bregman divergences. J.
Mach. Learn. Res. 6, 1705–1749 (2005)
5. Boissonnat, J.-D., Nielsen, F., Nock, R.: Bregman Voronoi diagrams. Discret. Comput. Geom.
44(2), 281–307 (2010)
6. Crouzeix, J.-P.: A relationship between the second derivatives of a convex function and of its
conjugate. Math. Program. 13(1), 364–365 (1977)
7. Edelsbrunner, H., Wagner, H.: Topological data analysis with Bregman divergences. In:
33rd International Symposium on Computational Geometry (SoCG 2017). Schloss DagstuhlLeibniz-Zentrum fuer Informatik (2017)
8. Eguchi, S., et al.: Geometry of minimum contrast. Hiroshima Math. J. 22(3), 631–647 (1992)
9. Eisenhart, L.P.: Riemannian Geometry. Princeton University Press, Princeton (1997)
10. Kurose, T.: Dual connections and affine geometry. Math. Z. 203(1), 115–121 (1990)
11. Lauritzen, S.L.: Statistical manifolds. Differ. Geom. Stat. Inference 10, 163–216 (1987)
12. Mahalanobis, P.C.: On the generalized distance in statistics. Proc. Natl. Inst. Sci. (Calcutta) 2,
49–55 (1936)
13. Nielsen, F.: Legendre transformation and information geometry (2010)
14. Nielsen, F.: Cramér-Rao lower bound and information geometry. In: Connected at Infinity II,
pp. 18–37. Springer, Berlin (2013)
15. Nielsen, F.: An elementary introduction to information geometry (2018). arXiv:1808.08271
16. Nielsen, F., Boltz, S.: The Burbea-Rao and Bhattacharyya centroids. IEEE Trans. Inf. Theory
57(8), 5455–5466 (2011)
17. Nielsen, F., Bhatia, R.: Matrix Information Geometry. Springer, Berlin (2013)
18. Nielsen, F., Garcia, V. Statistical exponential families: a digest with flash cards (2009).
arXiv:0911.4863
19. Nielsen, F., Hadjeres, G.: Monte Carlo information geometry: the dually flat case (2018).
arXiv:1803.07225
20. Nielsen, F., Nock, R.: Sided and symmetrized Bregman centroids. IEEE Trans. Inf. Theory
55(6), 2882–2904 (2009)
21. Nielsen, F., Nock, R. Skew Jensen-Bregman Voronoi diagrams. In: Transactions on Computational Science, vol. XIV, pp. 102–128. Springer, Berlin (2011)
22. Nielsen, F., Nock, R.: On the geometry of mixtures of prescribed distributions. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 2861–2865.
IEEE (2018)
23. Nielsen, F., Muzellec, B., Nock, R.: Classification with mixtures of curved Mahalanobis metrics. In: 2016 IEEE International Conference on Image Processing (ICIP), pp. 241–245. IEEE
(2016)
24. Nock, R., Magdalou, B., Briys, E., Nielsen, F.: Mining matrix data with Bregman matrix
divergences for portfolio selection. In: Matrix Information Geometry, pp. 373–402. Springer,
Berlin (2013)
25. Norden, A.P.: On pairs of conjugate parallel displacements in multidimensional spaces. Dokl.
Akad. Nauk SSSR 49(9), 1345–1347 (1945)
26. Pietra, S.F., Pietra, V.D., Lafferty, J.: Inducing features of random fields. IEEE Trans. Pattern
Anal. Mach. Intell. 19(4), 380–393 (1997)
27. Rosenfeld, B.A.: A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space, vol. 12. Springer Science & Business Media (2012)
28. Sen, R.N.: Parallel displacement and scalar product of vectors. In: Proceedings of the National
Institute of Sciences of India, vol. 14, p. 45. National Institute of Sciences of India (1948)
29. Shima, H.: The Geometry of Hessian Structures. World Scientific (2007)
30. Sturmfels, B.: Solving Systems of Polynomial Equations, vol. 97. American Mathematical
Society (2002)
31. Wolf, J.A.: Spaces of Constant Curvature, vol. 372. American Mathematical Society (1972)
32. Wong, T.-K.L.: Logarithmic divergences from optimal transport and Rényi geometry. Inf.
Geom. 1(1), 39–78 (2018)
F. Nielsen
2. Amari, S.: Information geometry of positive measures and positive-definite matrices: decomposable dually flat structure. Entropy 16(4), 2131–2145 (2014)
3. Amari, S.-I.: Information Geometry and its Applications, vol. 194. Springer, Berlin (2016)
4. Banerjee, A., Merugu, S., Dhillon, I.S., Ghosh, J.: Clustering with Bregman divergences. J.
Mach. Learn. Res. 6, 1705–1749 (2005)
5. Boissonnat, J.-D., Nielsen, F., Nock, R.: Bregman Voronoi diagrams. Discret. Comput. Geom.
44(2), 281–307 (2010)
6. Crouzeix, J.-P.: A relationship between the second derivatives of a convex function and of its
conjugate. Math. Program. 13(1), 364–365 (1977)
7. Edelsbrunner, H., Wagner, H.: Topological data analysis with Bregman divergences. In:
33rd International Symposium on Computational Geometry (SoCG 2017). Schloss DagstuhlLeibniz-Zentrum fuer Informatik (2017)
8. Eguchi, S., et al.: Geometry of minimum contrast. Hiroshima Math. J. 22(3), 631–647 (1992)
9. Eisenhart, L.P.: Riemannian Geometry. Princeton University Press, Princeton (1997)
10. Kurose, T.: Dual connections and affine geometry. Math. Z. 203(1), 115–121 (1990)
11. Lauritzen, S.L.: Statistical manifolds. Differ. Geom. Stat. Inference 10, 163–216 (1987)
12. Mahalanobis, P.C.: On the generalized distance in statistics. Proc. Natl. Inst. Sci. (Calcutta) 2,
49–55 (1936)
13. Nielsen, F.: Legendre transformation and information geometry (2010)
14. Nielsen, F.: Cramér-Rao lower bound and information geometry. In: Connected at Infinity II,
pp. 18–37. Springer, Berlin (2013)
15. Nielsen, F.: An elementary introduction to information geometry (2018). arXiv:1808.08271
16. Nielsen, F., Boltz, S.: The Burbea-Rao and Bhattacharyya centroids. IEEE Trans. Inf. Theory
57(8), 5455–5466 (2011)
17. Nielsen, F., Bhatia, R.: Matrix Information Geometry. Springer, Berlin (2013)
18. Nielsen, F., Garcia, V. Statistical exponential families: a digest with flash cards (2009).
arXiv:0911.4863
19. Nielsen, F., Hadjeres, G.: Monte Carlo information geometry: the dually flat case (2018).
arXiv:1803.07225
20. Nielsen, F., Nock, R.: Sided and symmetrized Bregman centroids. IEEE Trans. Inf. Theory
55(6), 2882–2904 (2009)
21. Nielsen, F., Nock, R. Skew Jensen-Bregman Voronoi diagrams. In: Transactions on Computational Science, vol. XIV, pp. 102–128. Springer, Berlin (2011)
22. Nielsen, F., Nock, R.: On the geometry of mixtures of prescribed distributions. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 2861–2865.
IEEE (2018)
23. Nielsen, F., Muzellec, B., Nock, R.: Classification with mixtures of curved Mahalanobis metrics. In: 2016 IEEE International Conference on Image Processing (ICIP), pp. 241–245. IEEE
(2016)
24. Nock, R., Magdalou, B., Briys, E., Nielsen, F.: Mining matrix data with Bregman matrix
divergences for portfolio selection. In: Matrix Information Geometry, pp. 373–402. Springer,
Berlin (2013)
25. Norden, A.P.: On pairs of conjugate parallel displacements in multidimensional spaces. Dokl.
Akad. Nauk SSSR 49(9), 1345–1347 (1945)
26. Pietra, S.F., Pietra, V.D., Lafferty, J.: Inducing features of random fields. IEEE Trans. Pattern
Anal. Mach. Intell. 19(4), 380–393 (1997)
27. Rosenfeld, B.A.: A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space, vol. 12. Springer Science & Business Media (2012)
28. Sen, R.N.: Parallel displacement and scalar product of vectors. In: Proceedings of the National
Institute of Sciences of India, vol. 14, p. 45. National Institute of Sciences of India (1948)
29. Shima, H.: The Geometry of Hessian Structures. World Scientific (2007)
30. Sturmfels, B.: Solving Systems of Polynomial Equations, vol. 97. American Mathematical
Society (2002)
31. Wolf, J.A.: Spaces of Constant Curvature, vol. 372. American Mathematical Society (1972)
32. Wong, T.-K.L.: Logarithmic divergences from optimal transport and Rényi geometry. Inf.
Geom. 1(1), 39–78 (2018)