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pro vyhledávání: '"Thanwerdas, Yann"'
Autor:
Thanwerdas, Yann, Pennec, Xavier
The set of covariance matrices equipped with the Bures-Wasserstein distance is the orbit space of the smooth, proper and isometric action of the orthogonal group on the Euclidean space of square matrices. This construction induces a natural orbit str
Externí odkaz:
http://arxiv.org/abs/2204.09928
Autor:
Thanwerdas, Yann, Pennec, Xavier
In contrast to SPD matrices, few tools exist to perform Riemannian statistics on the open elliptope of full-rank correlation matrices. The quotient-affine metric was recently built as the quotient of the affine-invariant metric by the congruence acti
Externí odkaz:
http://arxiv.org/abs/2201.06282
Autor:
Thanwerdas, Yann, Pennec, Xavier
Several Riemannian metrics and families of Riemannian metrics were defined on the manifold of Symmetric Positive Definite (SPD) matrices. Firstly, we formalize a common general process to define families of metrics: the principle of deformed metrics.
Externí odkaz:
http://arxiv.org/abs/2111.02990
Autor:
Thanwerdas, Yann, Pennec, Xavier
Symmetric Positive Definite (SPD) matrices are ubiquitous in data analysis under the form of covariance matrices or correlation matrices. Several O(n)-invariant Riemannian metrics were defined on the SPD cone, in particular the kernel metrics introdu
Externí odkaz:
http://arxiv.org/abs/2109.05768
Autor:
Thanwerdas, Yann, Pennec, Xavier
Publikováno v:
GSI 2021 - 5th conference on Geometric Science of Information, Jul 2021, Paris, France
Correlation matrices are used in many domains of neurosciences such as fMRI, EEG, MEG. However, statistical analyses often rely on embeddings into a Euclidean space or into Symmetric Positive Definite matrices which do not provide intrinsic tools. Th
Externí odkaz:
http://arxiv.org/abs/2103.04621
Autor:
Miolane, Nina, Brigant, Alice Le, Mathe, Johan, Hou, Benjamin, Guigui, Nicolas, Thanwerdas, Yann, Heyder, Stefan, Peltre, Olivier, Koep, Niklas, Zaatiti, Hadi, Hajri, Hatem, Cabanes, Yann, Gerald, Thomas, Chauchat, Paul, Shewmake, Christian, Kainz, Bernhard, Donnat, Claire, Holmes, Susan, Pennec, Xavier
We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more. We provide object-o
Externí odkaz:
http://arxiv.org/abs/2004.04667
Autor:
Thanwerdas, Yann, Pennec, Xavier
Publikováno v:
Geometric Science of Information, Aug 2019, Toulouse, France
Symmetric Positive Definite (SPD) matrices have been used in many fields of medical data analysis. Many Riemannian metrics have been defined on this manifold but the choice of the Riemannian structure lacks a set of principles that could lead one to
Externí odkaz:
http://arxiv.org/abs/1909.03852
Autor:
Thanwerdas, Yann, Pennec, Xavier
Publikováno v:
Geometric Science of Information, Aug 2019, Toulouse, France
Symmetric Positive Definite (SPD) matrices have been widely used in medical data analysis and a number of different Riemannian met-rics were proposed to compute with them. However, there are very few methodological principles guiding the choice of on
Externí odkaz:
http://arxiv.org/abs/1906.01349
Autor:
Thanwerdas, Yann, Pennec, Xavier
Publikováno v:
In Linear Algebra and Its Applications 15 March 2023 661:163-201
Autor:
Thanwerdas, Yann, Pennec, Xavier
Publikováno v:
In Differential Geometry and its Applications April 2022 81