Publications of Yann Thanwerdas

1. Yann Thanwerdas. Riemannian and stratified geometries on covariance and correlation matrices. Theses, Université Côte d'Azur, May 2022. Keyword(s): Riemannian geometry, Covariance matrices, Correlation matrices, Families of metrics, Geodesics, Stratified spaces, Géométrie riemannienne, Matrices de covariance, Matrices de corrélation, Familles de métriques, Géodésiques, Espaces stratifiés. [bibtex-entry]

1. Yann Thanwerdas and Xavier Pennec. Bures-Wasserstein minimizing geodesics between covariance matrices of different ranks. SIAM Journal on Matrix Analysis and Applications, 44(3):1447-1476, September 2023. Keyword(s): Covariance matrices, PSD matrices, Bures-Wasserstein, Orbit space, Geodesics, Injection domain, 15B48, 15A63, 53B20, 53C22, 58D17, 53-08, 53A04, 54E50, 58A35. [bibtex-entry]



2. Yann Thanwerdas and Xavier Pennec. O(n)-invariant Riemannian metrics on SPD matrices. Linear Algebra and its Applications, 661:163-201, March 2023. Keyword(s): 53B20, Symmetric Positive Definite matrices, Riemannian geometry, Invariance under orthogonal transformations, Families of metrics, Log-Euclidean metric, Affine-invariant metric, Bures-Wasserstein metric, Kernel metrics. [bibtex-entry]



3. Yann Thanwerdas and Xavier Pennec. The geometry of mixed-Euclidean metrics on symmetric positive definite matrices. Differential Geometry and its Applications, 81(101867), April 2022. Keyword(s): Symmetric Positive Definite matrices, Riemannian geometry, information geometry, families of metrics, kernel metrics, alpha-Procrustes, mixed-power-Euclidean, mixed-Euclidean, (u, v)-divergence, ($\alpha$, $\beta$)-divergence, 15B48, 53B12, 15A63, 53B20. [bibtex-entry]



4. Yann Thanwerdas and Xavier Pennec. Theoretically and computationally convenient geometries on full-rank correlation matrices. SIAM Journal on Matrix Analysis and Applications, 43(4):1851-1872, December 2022. Keyword(s): SPD matrices, Correlation matrices, Lie group, Lie group actions, Quotient-affine metric, Lie-Cholesky metrics, Poly-hyperbolic-Cholesky metrics, Euclidean-Cholesky metrics, Log-Euclidean-Cholesky metrics. [bibtex-entry]



5. Nina Miolane, Nicolas Guigui, Alice Le Brigant, Johan Mathe, Benjamin Hou, Yann Thanwerdas, Stefan Heyder, Olivier Peltre, Niklas Koep, Hadi Zaatiti, Hatem Hajri, Yann Cabanes, Thomas Gerald, Paul Chauchat, Christian Shewmake, Daniel Brooks, Bernhard Kainz, Claire Donnat, Susan Holmes, and Xavier Pennec. Geomstats: A Python Package for Riemannian Geometry in Machine Learning. Journal of Machine Learning Research, 21(223):1-9, December 2020. Keyword(s): differential geometry, Riemannian geometry, statistics, machine learning, manifold. [bibtex-entry]

1. Yann Thanwerdas and Xavier Pennec. Characterization of Invariant Inner Products. In GSI 2023 - International Conference on Geometric Science of Information, volume LNCS-14071 of Geometric Science of Information: 6th International Conference, GSI 2023, St. Malo, France, August 30 -- September 1, 2023, Proceedings, Part I, Saint Malo, France, France, pages 384-391, August 2023. Springer Nature Switzerland. Keyword(s): Invariant inner product Invariant Riemannian metric Group action Representation theory, Invariant inner product, Invariant Riemannian metric, Group action, Representation theory. [bibtex-entry]



2. Yann Thanwerdas and Xavier Pennec. Geodesics and Curvature of the Quotient-Affine Metrics on Full-Rank Correlation Matrices. In GSI 2021 - 5th conference on Geometric Science of Information, volume 12829 of Proceedings of Geometric Science of Information, Paris, France, pages 93-102, July 2021. Springer, Cham. Keyword(s): Correlation matrices, SPD matrices, Quotient manifold, Quotient-affine metric, Riemannian geometry. [bibtex-entry]



3. Nina Miolane, Nicolas Guigui, Hadi Zaatiti, Christian Shewmake, Hatem Hajri, Daniel Brooks, Alice Le Brigant, Johan Mathe, Benjamin Hou, Yann Thanwerdas, Stefan Heyder, Olivier Peltre, Niklas Koep, Yann Cabanes, Thomas Gerald, Paul Chauchat, Bernhard Kainz, Claire Donnat, Susan Holmes, and Xavier Pennec. Introduction to Geometric Learning in Python with Geomstats. In Meghann Agarwal, Chris Calloway, Dillon Niederhut, and David Shupe, editors, SciPy 2020 - 19th Python in Science Conference, Austin, Texas, United States, pages 48-57, July 2020. Keyword(s): Index Terms-differential geometry, statistics, manifold, machine learning. [bibtex-entry]



4. Yann Thanwerdas and Xavier Pennec. Exploration of Balanced Metrics on Symmetric Positive Definite Matrices. In GSI 2019 - 4th conference on Geometric Science of Information, volume Lecture Notes in Computer Science 11712 of Proceedings of Geometric Science of Information, Toulouse, France, pages 484-493, August 2019. Springer. Keyword(s): Dually flat connections, SPD matrices, Information geometry. [bibtex-entry]



5. Yann Thanwerdas and Xavier Pennec. Is affine invariance well defined on SPD matrices? A principled continuum of metrics. In GSI 2019 - 4th conference on Geometric Science of Information, volume Lecture Notes in Computer Science 11712 of Proceedings of Geometric Science of Information, Toulouse, France, pages 502-510, August 2019. Springer. Keyword(s): SPD matrices, Riemannian symmetric spaces. [bibtex-entry]

1. Yann Thanwerdas. Permutation-invariant log-Euclidean geometries on full-rank correlation matrices. Note: Working paper or preprint, November 2023. Keyword(s): SPD matrices, elliptope, correlation matrices, log-Euclidean metric, permutationinvariant, cor-inversion, off-log metric, log-scaled metric, quotient-affine metric AMS subject classifications.. [bibtex-entry]

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