The geometry of mixed-Euclidean metrics on symmetric positive definite matrices

[1]  I. Dryden,et al.  Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging , 2009, 0910.1656.

[2]  Xavier Pennec,et al.  A Riemannian Framework for Tensor Computing , 2005, International Journal of Computer Vision.

[3]  P. Thomas Fletcher,et al.  Riemannian geometry for the statistical analysis of diffusion tensor data , 2007, Signal Process..

[4]  R. Bhatia,et al.  On the Bures–Wasserstein distance between positive definite matrices , 2017, Expositiones Mathematicae.

[5]  F. Hiai,et al.  Riemannian metrics on positive definite matrices related to means , 2008, 0809.4974.

[6]  Andrea Fuster,et al.  Adjugate Diffusion Tensors for Geodesic Tractography in White Matter , 2015, Journal of Mathematical Imaging and Vision.

[7]  이화영.  X , 1960, Chinese Plants Names Index 2000-2009.

[8]  Shun-ichi Amari,et al.  Methods of information geometry , 2000 .

[9]  H. Shima,et al.  Geometry of Hessian manifolds , 1997 .

[10]  Sergio Cruces,et al.  Generalized Alpha-Beta Divergences and Their Application to Robust Nonnegative Matrix Factorization , 2011, Entropy.

[11]  P. Michor,et al.  THE CURVATURE OF THE BOGOLIUBOV-KUBO-MORI SCALAR PRODUCT ON MATRICES , 2008 .

[12]  Xavier Pennec,et al.  Riemannian Geometric Statistics in Medical Image Analysis , 2020 .

[13]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[14]  Frank Nielsen,et al.  Sided and Symmetrized Bregman Centroids , 2009, IEEE Transactions on Information Theory.

[15]  Shun-ichi Amari.  Information Geometry of Positive Measures and Positive-Definite Matrices: Decomposable Dually Flat Structure , 2014, Entropy.

[16]  Xavier Pennec,et al.  Exploration of Balanced Metrics on Symmetric Positive Definite Matrices , 2019, GSI.

[17]  Hà Quang Minh.  A Unified Formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt Distances between Positive Definite Operators , 2019, GSI.

[18]  Andrzej Cichocki,et al.  Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities , 2010, Entropy.

[19]  F. Opitz.  Information geometry and its applications , 2012, 2012 9th European Radar Conference.

[20]  Xavier Pennec,et al.  Power Euclidean metrics for covariance matrices with application to diffusion tensor imaging , 2010, 1009.3045.

[21]  Rachid Deriche,et al.  Inferring White Matter Geometry from Di.usion Tensor MRI: Application to Connectivity Mapping , 2004, ECCV.

[22]  Dénes Petz,et al.  The Bogoliubov inner product in quantum statistics , 1993 .

[23]  Rachid Deriche,et al.  Statistics on the Manifold of Multivariate Normal Distributions: Theory and Application to Diffusion Tensor MRI Processing , 2006, Journal of Mathematical Imaging and Vision.

[24]  I. Olkin,et al.  The distance between two random vectors with given dispersion matrices , 1982 .

[25]  Xavier Pennec,et al.  O(n)-invariant Riemannian metrics on SPD matrices , 2021, Linear Algebra and its Applications.

[26]  Xavier Pennec,et al.  Is Affine-Invariance Well Defined on SPD Matrices? A Principled Continuum of Metrics , 2019, GSI.

[27]  Zhenhua Lin,et al.  Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition , 2019, SIAM J. Matrix Anal. Appl..

[28]  N. Ayache,et al.  Log‐Euclidean metrics for fast and simple calculus on diffusion tensors , 2006, Magnetic resonance in medicine.

[29]  Asuka Takatsu.  Wasserstein geometry of Gaussian measures , 2011 .

[30]  L. Skovgaard.  A Riemannian geometry of the multivariate normal model , 1984 .

[31]  D. Dowson,et al.  The Fréchet distance between multivariate normal distributions , 1982 .

[32]  Maher Moakher,et al.  A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices , 2005, SIAM J. Matrix Anal. Appl..

[33]  P. Alam.  ‘N’ , 2021, Composites Engineering: An A–Z Guide.

[34]  S. Amari,et al.  Curvature of Hessian manifolds , 2014 .

[35]  Inderjit S. Dhillon,et al.  Clustering with Bregman Divergences , 2005, J. Mach. Learn. Res..