-
1
-
-
85041123735
-
Divergence function, duality, and convex analysis
-
J. Zhang, Divergence function, duality, and convex analysis, Neural Comput. 16 (1) (2004) 159-195.
-
(2004)
Neural Comput.
, vol.16
, Issue.1
, pp. 159-195
-
-
Zhang, J.1
-
2
-
-
49949144765
-
The relaxation method of finding the common point of convex sets and its application to the solutions of problems in convex programming
-
L.M. Bregman, The relaxation method of finding the common point of convex sets and its application to the solutions of problems in convex programming, USSR Comput. Math. Math. Phys. 7 (3) (1967) 200-217.
-
(1967)
USSR Comput. Math. Math. Phys.
, vol.7
, Issue.3
, pp. 200-217
-
-
Bregman, L.M.1
-
3
-
-
77955693545
-
Jensen-Bregman Voronoi diagrams and centroidal tessellations
-
F. Nielsen, R. Nock, Jensen-Bregman Voronoi diagrams and centroidal tessellations, in: 2010 International Symposium on Voronoi Diagrams in Science and Engineering ISVD'10 , IEEE, 2010, pp. 56-65.
-
(2010)
2010 International Symposium on Voronoi Diagrams in Science and Engineering ISVD'10), IEEE
, pp. 56-65
-
-
Nielsen, F.1
Nock, R.2
-
5
-
-
10044238894
-
F-Information measures inmedical image registration
-
J.P.W. Pluim, J.B.A.Maintz, M.A. Viergever, f-Information measures inmedical image registration, IEEE Trans. Med. Imaging 23 (12) (2004) 1508-1516.
-
(2004)
IEEE Trans. Med. Imaging
, vol.23
, Issue.12
, pp. 1508-1516
-
-
Pluim, J.P.W.1
Maintz, J.B.A.2
Viergever, M.A.3
-
6
-
-
0346093810
-
Uses of entropy and divergence measures for evaluating econometric approximations and inference
-
A. Ullah, Uses of entropy and divergence measures for evaluating econometric approximations and inference, J. Economet. 107 (1-2) (2002) 313-326.
-
(2002)
J. Economet.
, vol.107
, Issue.1-2
, pp. 313-326
-
-
Ullah, A.1
-
7
-
-
77951472664
-
The dual Voronoi diagrams with respect to representational Bregman divergences
-
F. Nielsen, R. Nock, The dual Voronoi diagrams with respect to representational Bregman divergences, in: Sixth International Symposium on Voronoi Diagrams ISVD'09), IEEE, 2009, pp. 71-78.
-
(2009)
Sixth International Symposium on Voronoi Diagrams (ISVD' 09), IEEE
, pp. 71-78
-
-
Nielsen, F.1
Nock, R.2
-
8
-
-
70349085755
-
Coresets and approximate clustering for Bregman divergences
-
Philadelphia, PA, New York
-
M.R. Ackermann, J. Blömer, Coresets and approximate clustering for Bregman divergences, in: Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, PA, New York, 2009, pp. 1088-1097.
-
(2009)
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM
, pp. 1088-1097
-
-
Ackermann, M.R.1
Blömer, J.2
-
9
-
-
26244461684
-
Clustering with Bregman divergences
-
A. Banerjee, S. Merugu, I. Dhillon, J. Ghosh, Clustering with Bregman divergences, J. Mach Learn. Res. 6 (2005) 1705-1749.
-
(2005)
J. Mach Learn. Res.
, vol.6
, pp. 1705-1749
-
-
Banerjee, A.1
Merugu, S.2
Dhillon, I.3
Ghosh, J.4
-
10
-
-
38349053625
-
Matrix nearness problems with Bregmandivergences
-
I.S. Dhillon, J.A. Tropp, Matrix nearness problems with Bregmandivergences, SIAM J.MatrixAnal. Appl. 29 (4) (2007) 1120-1146.
-
(2007)
SIAM J.MatrixAnal. Appl.
, vol.29
, Issue.4
, pp. 1120-1146
-
-
Dhillon, I.S.1
Tropp, J.A.2
-
12
-
-
22944439423
-
A differential-geometric approach to the geometric mean of symmetric positive-definite matrices
-
M. Moakher, A differential-geometric approach to the geometric mean of symmetric positive-definite matrices, SIAM J.Matrix Anal. Appl. 26 (3) (2005) 735-747.
-
(2005)
SIAM J.Matrix Anal. Appl.
, vol.26
, Issue.3
, pp. 735-747
-
-
Moakher, M.1
-
13
-
-
31444440896
-
Riemannian geometry and matrix geometric means
-
R. Bhatia, J. Holbrook, Riemannian geometry and matrix geometric means, Linear Algebra Appl. 413 (2-3) (2006) 594-618.
-
(2006)
Linear Algebra Appl.
, vol.413
, Issue.2-3
, pp. 594-618
-
-
Bhatia, R.1
Holbrook, J.2
-
14
-
-
85032187592
-
The symmetric space of positive definite tensors: From geometry to applications and visualization
-
J.Weickert, H. Hagen (Eds.), Springer, Berlin chapter 17
-
M. Moakher, P.G. Batchelor, The symmetric space of positive definite tensors: from geometry to applications and visualization, in: J.Weickert, H. Hagen (Eds.), Visualization and Processing of Tensor Fields, Springer, Berlin, 2006, pp. 285-298. (chapter 17).
-
Visualization and Processing of Tensor Fields
, vol.2006
, pp. 285-298
-
-
Moakher, M.1
Batchelor, P.G.2
-
15
-
-
33645812768
-
On the averaging of symmetric positive-definite tensors
-
M. Moakher, On the averaging of symmetric positive-definite tensors, J. Elasticity 83 (3) (2006) 273-296.
-
(2006)
J. Elasticity
, vol.83
, Issue.3
, pp. 273-296
-
-
Moakher, M.1
-
16
-
-
34547871974
-
Means of positive matrices: Geometry and a conjecture
-
D. Petz, Means of positive matrices: geometry and a conjecture, Ann. Math. Informat. 32 129-139
-
(2005)
Ann. Math. Informat.
, vol.32
, Issue.2005
, pp. 129-139
-
-
Petz, D.1
-
17
-
-
2542467065
-
Geometric means
-
T. Ando, C.K. Li, R. Mathias, Geometric means, Linear Algebra Appl. 385 (1) (2004) 305-334.
-
(2004)
Linear Algebra Appl.
, vol.385
, Issue.1
, pp. 305-334
-
-
Ando, T.1
Li, C.K.2
Mathias, R.3
-
18
-
-
77952792929
-
An effective matrix geometric mean satisfying the Ando-Li-Mathias properties
-
D.A. Bini, B. Meini, F. Poloni, An effective matrix geometric mean satisfying the Ando-Li-Mathias properties, Math. Comp. 79 (2010) 437-452.
-
(2010)
Math. Comp.
, vol.79
, pp. 437-452
-
-
Bini, D.A.1
Meini, B.2
Poloni, F.3
-
19
-
-
64649091240
-
Riemannian geometry on positive definitematrices related to means
-
F. Hiai,D. Petz, Riemannian geometry on positive definitematrices related to means, Linear AlgebraAppl. 430 (2009) 3105-3130.
-
(2009)
Linear Algebra Appl.
, vol.430
, pp. 3105-3130
-
-
Hiai, F.1
Petz, D.2
-
20
-
-
72449176330
-
Geometric distance and mean for positive semi-definite matrices of fixed rank
-
S. Bonnabel, R. Sepulchre, Geometric distance and mean for positive semi-definite matrices of fixed rank, SIAM J. Matrix Anal. Appl. 31 (2009) 1055-1070.
-
(2009)
SIAM J. Matrix Anal. Appl.
, vol.31
, pp. 1055-1070
-
-
Bonnabel, S.1
Sepulchre, R.2
-
22
-
-
0028398052
-
Estimation of the effective self-diffusion tensor from the NMR spin-echo
-
P.J. Basser, J. Mattiello, D.L. Bihan, Estimation of the effective self-diffusion tensor from the NMR spin-echo, J. Magn. Reson. Ser. B 103 (3) (1994) 247-254.
-
(1994)
J. Magn. Reson. Ser. B
, vol.103
, Issue.3
, pp. 247-254
-
-
Basser, P.J.1
Mattiello, J.2
Bihan, D.L.3
-
23
-
-
70349684897
-
Consistency clustering: A robust algorithm for group-wise registration, segmentation and automatic atlas construction in diffusion MRI
-
U. Ziyan, M.R. Sabuncu, W.E.L. Grimson, C.F. Westin, Consistency clustering: a robust algorithm for group-wise registration, segmentation and automatic atlas construction in diffusion MRI, Int. J. Comput. Vis. 85 (2009) 279-290.
-
(2009)
Int. J. Comput. Vis.
, vol.85
, pp. 279-290
-
-
Ziyan, U.1
Sabuncu, M.R.2
Grimson, W.E.L.3
Westin, C.F.4
-
24
-
-
0006623358
-
On a theorem ofWeyl concerning eigenvalues of linear transformations II
-
K. Fan, On a theorem ofWeyl concerning eigenvalues of linear transformations II, Proc. Natl. Acad. Sci. USA 36 (1950) 31-35.
-
(1950)
Proc. Natl. Acad. Sci. USA
, vol.36
, pp. 31-35
-
-
Fan, K.1
-
25
-
-
0003643027
-
-
Springer, New York
-
C. Berg, J.P.R. Christensen, P. Ressel, Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions, Springer, New York, 1984.
-
(1984)
Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions
-
-
Berg, C.1
Christensen, J.P.R.2
Ressel, P.3
-
26
-
-
66049090714
-
Properties of classical and quantum Jensen-Shannon divergence
-
J. Briët, P. Harremoës, Properties of classical and quantum Jensen-Shannon divergence, Phys. Rev. A 79 (5) (2009) 052311
-
(2009)
Phys. Rev. A
, vol.79
, Issue.5
, pp. 052311
-
-
Briët, J.1
Harremoës, P.2
-
27
-
-
0038105161
-
A new metric for probability distributions
-
D.M. Endres, J.E. Schindelin, A new metric for probability distributions, IEEE Trans. Inform. Theory 49 (7) (2003) 1858-1860.
-
(2003)
IEEE Trans. Inform. Theory
, vol.49
, Issue.7
, pp. 1858-1860
-
-
Endres, D.M.1
Schindelin, J.E.2
-
29
-
-
0003372875
-
Methods of Information Geometry
-
OxfordUniversity Press, New York
-
S. Amari, H.Nagaoka,Methods of Information Geometry, Translations ofMathematical Monographs, vol. 191, OxfordUniversity Press, New York, 2000.
-
(2000)
Translations of Mathematical Monographs
, vol.191
-
-
Amari, S.1
Nagaoka, H.2
-
31
-
-
0009967509
-
Siegel's Modular Forms and Dirichlet Series
-
Springer-Verlag
-
H. Maass, Siegel's Modular Forms and Dirichlet Series, No. 216 in Lecture Notes in Math., Springer-Verlag, 1971.
-
(1971)
No. 216 in Lecture Notes in Math.
-
-
Maass, H.1
-
32
-
-
79953208930
-
The Riemannian geometry of the space of positive-definite matrices and its application to the regularization of positive-definite matrix-valued data
-
M. Moakher, M. Zerai, The Riemannian geometry of the space of positive-definite matrices and its application to the regularization of positive-definite matrix-valued data, J. Math. Imaging Vis. 40 (2) (2011) 171-187.
-
(2011)
J. Math. Imaging Vis.
, vol.40
, Issue.2
, pp. 171-187
-
-
Moakher, M.1
Zéraï, M.2
-
34
-
-
0000625873
-
On tests and measures of group divergence
-
P.C. Mahalanobis, On tests and measures of group divergence, J. Asiatic Soc. Bengal 26 (4) (1930) 541-588.
-
(1930)
J. Asiatic Soc. Bengal
, vol.26
, Issue.4
, pp. 541-588
-
-
Mahalanobis, P.C.1
-
36
-
-
0002215069
-
On a measure of divergence between two statistical populations defined by their probability distributions
-
A. Bhattacharyya, On a measure of divergence between two statistical populations defined by their probability distributions, Bull. Calcutta Math. Soc. 35 1943 99-109.
-
(1943)
Bull. Calcutta Math. Soc.
, vol.35
, pp. 99-109
-
-
Bhattacharyya, A.1
-
38
-
-
35549004167
-
Integration of stochastic models by minimizing ?-divergence
-
S.i. Amari, Integration of stochastic models by minimizing ?-divergence, Neural Comput. 19 (10) (2007) 2780-2796.
-
(2007)
Neural Comput.
, vol.19
, Issue.10
, pp. 2780-2796
-
-
I. Amari, S.1
-
41
-
-
84966219504
-
On certain contraction mappings in a partially ordered vector space
-
A.C. Thompson, On certain contraction mappings in a partially ordered vector space, Proc. Amer. Math. Soc. 14 (1963) 438-443.
-
(1963)
Proc. Amer. Math. Soc.
, vol.14
, pp. 438-443
-
-
Thompson, A.C.1
-
42
-
-
58049195551
-
i via a contraction principle
-
i via a contraction principle, Linear Algebra Appl. 430 (2009) 1380-1383.
-
(2009)
Linear Algebra Appl.
, vol.430
, pp. 1380-1383
-
-
Lim, Y.1
-
43
-
-
0027626240
-
Kalman filtering with random coefficients and contractions
-
P. Bougerol, Kalman filtering with random coefficients and contractions, SIAM J. Control Optim. 31 1993 942-959.
-
(1993)
SIAM J. Control Optim.
, vol.31
, pp. 942-959
-
-
Bougerol, P.1
-
44
-
-
0001338184
-
Hilbert's Projective Metric and Iterated Nonlinear Maps
-
R.D. Nussbaum, Hilbert's Projective Metric and Iterated Nonlinear Maps, vol. 391, Mem. Amer. Math. Soc., 1988.
-
(1988)
Mem. Amer. Math. Soc.
, vol.391
-
-
Nussbaum, R.D.1
-
45
-
-
0037686659
-
The concave-convex procedure
-
A.L. Yuille, A. Rangarajan, The concave-convex procedure, Neural Comput. 15 (4) (2003) 915-936.
-
(2003)
Neural Comput.
, vol.15
, Issue.4
, pp. 915-936
-
-
Yuille, A.L.1
Rangarajan, A.2
-
46
-
-
0020126872
-
On the convexity of some divergence measures based on entropy functions
-
J. Burbea, C. Rao, On the convexity of some divergence measures based on entropy functions, IEEE Trans. Inform. Theory 28 (3) (1982) 489-495.
-
(1982)
IEEE Trans. Inform. Theory
, vol.28
, Issue.3
, pp. 489-495
-
-
Burbea, J.1
Rao, C.2
-
47
-
-
0028539993
-
Recursive algorithms for solving a class of nonlinear matrix equations with applications to certain sensitivity optimization problems
-
W.Y. Yan, J.B. Moore, U. Helmke, Recursive algorithms for solving a class of nonlinear matrix equations with applications to certain sensitivity optimization problems, SIAM J. Control Optim. 32 1994 1559-1576.
-
(1994)
SIAM J. Control Optim.
, vol.32
, pp. 1559-1576
-
-
Yan, W.Y.1
Moore, J.B.2
Helmke, U.3
|