Foundations of Geometric Statistics and Their Application in the Life Sciences

Advances in Geometric Statistics for Manifold Dimension Reduction

Autori: Xavier Pennec
Pubblicato in: Handbook of Variational Methods for Nonlinear Geometric Data, 2020, Pagina/e 339-359, ISBN 978-3-030-31350-0
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-31351-7_11

Beyond Riemannian geometry: The affine connection setting for transformation groups

Autori: Pennec, Xavier; Lorenzi, Marco
Pubblicato in: Riemannian Geometric Statistics in Medical Image Analysis, 2021, Pagina/e pp.169-229, ISBN 978-0-12-814725-2
Editore: Academic Press
DOI: 10.1016/b978-0-12-814725-2.00012-1

Manifold-valued image processing with SPD matrices

Autori: Xavier Pennec
Pubblicato in: Riemannian Geometric Statistics in Medical Image Analysis, 2020, Pagina/e 75-134, ISBN 9780-128147252
Editore: Academic Press
DOI: 10.1016/B978-0-12-814725-2.00010-8

Parallel transport, a central tool in geometric statistics for computational anatomy: Application to cardiac motion modeling

Autori: Nicolas Guigui; Xavier Pennec
Pubblicato in: Handbook of Statistics, volume 46: Geometry and Statistics; Editors: Frank Nielsen; Arni S.R. Srinivasa Rao; C.R. Rao., Numero 46, 2022, Pagina/e 285-326, ISBN 978-0-323-91345-4
Editore: Elsevier - Academic Press
DOI: 10.1016/bs.host.2022.03.006

Statistical Analysis of Organs’ Shapes and Deformations: The Riemannian and the Affine Settings in Computational Anatomy

Autori: Xavier Pennec
Pubblicato in: Digital Anatomy - Applications of Virtual, Mixed and Augmented Reality, 2021, Pagina/e 159-183, ISBN 978-3-030-61904-6
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-61905-3_9

Bias on estimation in quotient space and correction methods

Autori: Nina Miolane, Loic Devilliers, Xavier Pennec
Pubblicato in: Riemannian Geometric Statistics in Medical Image Analysis, 2024, Pagina/e 343-376, ISBN 978-0-12-814725-2
Editore: Academic Press
DOI: 10.1016/b978-0-12-814725-2.00017-0

Barycentric embeddings for geometric manifold learning : with application to shapes and graphs

Autori: Elodie Maignant
Pubblicato in: Numero 06-12-2023, 2023
Editore: Université Côte d’Azur

Riemannian and stratified geometries on covariance and correlation matrices

Autori: Thanwerdas, Yann
Pubblicato in: Numero 2022-05-22, 2022
Editore: Universite Côte d'Azur

Riemannian and sub-riemannian methods for dimension reduction

Autori: Morten Akhøj Pedersen
Pubblicato in: Numero 23-11-2023, 2023
Editore: Université Côte d’Azur, France & University of Copenhagen, Denmark

Computational methods for statistical estimation on Riemannian manifolds and application to the study of cardiac deformations

Autori: Guigui, Nicolas
Pubblicato in: Numero 2023-11-18, 2021
Editore: Univresité Côte d'Azur

A Bi-Invariant Statistical Model Parametrized by Mean and Covariance on Rigid Motions

Autori: Emmanuel Chevallier, Nicolas Guigui
Pubblicato in: Entropy, Numero 22/4, 2020, Pagina/e 432, ISSN 1099-4300
Editore: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/e22040432

O(n)-invariant Riemannian metrics on SPD matrices

Autori: Yann Thanwerdas; Xavier Pennec
Pubblicato in: Linear Algebra and its Applications, Numero Vol. 661, 2023, Pagina/e 163-201, ISSN 0024-3795
Editore: Elsevier BV
DOI: 10.1016/j.laa.2022.12.009

Theoretically and computationally convenient geometries on full-rank correlation matrices

Autori: Yann Thanwerdas; Xavier Pennec
Pubblicato in: SIAM Journal on Matrix Analysis and Applications, Numero Vol. 43, no 4, 2022, Pagina/e 1851 - 1872, ISSN 1095-7162
Editore: SIAM
DOI: 10.48550/arxiv.2201.06282

The Measurement and Analysis of Shapes

Autori: Benn, James; Marsland, Stephen
Pubblicato in: Annals of Global Analysis and Geometry, inPress, 62, pp.47-70., Numero 62, 2022, Pagina/e 47–70, ISSN 0232-704X
Editore: Kluwer Academic Publishers
DOI: 10.1007/s10455-022-09839-z

Permutation-Invariant Log-Euclidean Geometries on Full-Rank Correlation Matrices

Autori: Yann Thanwerdas
Pubblicato in: SIAM Journal on Matrix Analysis and Applications, Numero 45, 2024, Pagina/e 930-953, ISSN 0895-4798
Editore: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m1538144

Bures–Wasserstein Minimizing Geodesics between Covariance Matrices of Different Ranks

Autori: Yann Thanwerdas, Xavier Pennec
Pubblicato in: SIAM Journal on Matrix Analysis and Applications, Numero 44, 2023, Pagina/e 1447-1476, ISSN 0895-4798
Editore: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m149168x

Numerical Accuracy of Ladder Schemes for Parallel Transport on Manifolds

Autori: Nicolas Guigui, Xavier Pennec
Pubblicato in: Foundations of Computational Mathematics, 2021, ISSN 1615-3375
Editore: Springer Verlag
DOI: 10.1007/s10208-021-09515-x

Geometry of sample spaces

Autori: Philipp Harms, Peter W. Michor, Xavier Pennec, Stefan Sommer
Pubblicato in: Differential Geometry and its Applications, Numero 90, 2023, Pagina/e 102029, ISSN 0926-2245
Editore: Elsevier BV
DOI: 10.1016/j.difgeo.2023.102029

Introduction to Riemannian Geometry and Geometric Statistics: from basic theory to implementation with Geomstats

Autori: Nicolas Guigui; Nina Miolane; Xavier Pennec
Pubblicato in: Foundations and Trends® in Machine Learning, Numero Vol 16, Numero 3, 2023, Pagina/e 329-493, ISSN 1935-8237
Editore: Now Publishers Inc.
DOI: 10.1561/2200000098

Classifying histograms of medical data using information geometry of beta distributions

Autori: Alice Le Brigant, Nicolas Guigui, Sana Rebbah, Stéphane Puechmorel
Pubblicato in: IFAC-PapersOnLine, Numero 54, 2021, Pagina/e 514-520, ISSN 2405-8963
Editore: International Federation of Automatic Control.
DOI: 10.1016/j.ifacol.2021.06.110

Voxel-based assessments of treatment effects on longitudinal brain changes in the Multidomain Alzheimer Preventive Trial cohort

Autori: Raphaël Sivera, Nicolas Capet, Valeria Manera, Roxane Fabre, Marco Lorenzi, Hervé Delingette, Xavier Pennec, Nicholas Ayache, Philippe Robert
Pubblicato in: Neurobiology of Aging, Numero 94, 2020, Pagina/e 50-59, ISSN 0197-4580
Editore: Elsevier BV
DOI: 10.1016/j.neurobiolaging.2019.11.020

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

Autori: Yann Thanwerdas; Xavier Pennec
Pubblicato in: Differential Geometry and its Applications, Numero Vol.81, 2022, Pagina/e 101867, ISSN 0926-2245
Editore: Elsevier BV
DOI: 10.1016/j.difgeo.2022.101867

Graph alignment exploiting the spatial organization improves the similarity of brain networks

Autori: Anna Calissano, Theodore Papadopoulo, Xavier Pennec, Samuel Deslauriers‐Gauthier
Pubblicato in: Human Brain Mapping, Numero 45, 2024, Pagina/e e26554, ISSN 1065-9471
Editore: John Wiley & Sons Inc.
DOI: 10.1002/hbm.26554

Geomstats: A Python Package for Riemannian Geometry in Machine Learning

Autori: 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, Xavier Pennec
Pubblicato in: JMLR - Journal of Machine Learning Research, Numero 21, 2020, Pagina/e 19-027, ISSN 1533-7928
Editore: JMLR

Parallel Transport on Kendall Shape Spaces

Autori: Nicolas Guigui, Elodie Maignant, Alain Trouvé, Xavier Pennec
Pubblicato in: Geometric Science of Information - 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings, Numero 12829, 2021, Pagina/e 103-110, ISBN 978-3-030-80208-0
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-80209-7_12

Rethinking the Riemannian Logarithm on Flag Manifolds as an Orthogonal Alignment Problem

Autori: Tom Szwagier, Xavier Pennec
Pubblicato in: Lecture Notes in Computer Science, Geometric Science of Information, Numero Proc of Geometric Science of Information (GSI 2023) - LNCS 14071, 2023, Pagina/e 375-383
Editore: Springer Nature Switzerland
DOI: 10.1007/978-3-031-38271-0_37

Cardiac Motion Modeling With Parallel Transport And Shape Splines

Autori: Nicolas Guigui, Pamela Moceri, Maxime Sermesant, Xavier Pennec
Pubblicato in: 2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI), 2021, Pagina/e 1394-1397, ISBN 978-1-6654-1246-9
Editore: IEEE
DOI: 10.1109/isbi48211.2021.9433887

Towards Quotient Barycentric Subspaces

Autori: Anna Calissano, Elodie Maignant, Xavier Pennec
Pubblicato in: Lecture Notes in Computer Science, Geometric Science of Information, Numero LNCS 14071, 2023, Pagina/e 366-374
Editore: Springer Nature Switzerland
DOI: 10.1007/978-3-031-38271-0_36

Geodesics and Curvature of the Quotient-Affine Metrics on Full-Rank Correlation Matrices

Autori: Yann Thanwerdas, Xavier Pennec
Pubblicato in: Geometric Science of Information - 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings, Numero 12829, 2021, Pagina/e 93-102, ISBN 978-3-030-80208-0
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-80209-7_11

Riemannian Locally Linear Embedding with Application to Kendall Shape Spaces

Autori: Elodie Maignant, Alain Trouvé, Xavier Pennec
Pubblicato in: Lecture Notes in Computer Science, Geometric Science of Information, Numero LNCS 14071, 2023, Pagina/e 12-20
Editore: Springer Nature Switzerland
DOI: 10.1007/978-3-031-38271-0_2

Exploration of Balanced Metrics on Symmetric Positive Definite Matrices

Autori: Yann Thanwerdas, Xavier Pennec
Pubblicato in: Geometric Science of Information - 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings, Numero 11712, 2019, Pagina/e 484-493, ISBN 978-3-030-26979-1
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-26980-7_50

Symmetric Algorithmic Components for Shape Analysis with Diffeomorphisms

Autori: Nicolas Guigui, Shuman Jia, Maxime Sermesant, Xavier Pennec
Pubblicato in: Geometric Science of Information - 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings, Numero 11712, 2019, Pagina/e 759-768, ISBN 978-3-030-26979-1
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-26980-7_79

Is Affine-Invariance Well Defined on SPD Matrices? A Principled Continuum of Metrics

Autori: Yann Thanwerdas, Xavier Pennec
Pubblicato in: Geometric Science of Information - 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings, Numero 11712, 2019, Pagina/e 502-510, ISBN 978-3-030-26979-1
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-26980-7_52

Wrapped statistical models on manifolds: motivations, the case SE(n), and generalization to symmetric spaces

Autori: Emmanuel Chevallier; Nicolas Guigui
Pubblicato in: Proc. of SPIGL 2020: Geometric Structures of Statistical Physics, Information Geometry, and Learning, 2021, Pagina/e 96–106
Editore: Springer
DOI: 10.1007/978-3-030-77957-3_5

Introduction to Geometric Learning in Python with Geomstats

Autori: 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, Xavier Pennec
Pubblicato in: Proceedings of the 19th Python in Science Conference, 2020, Pagina/e 48-57
Editore: SciPy
DOI: 10.25080/majora-342d178e-007

A Reduced Parallel Transport Equation on Lie Groups with a Left-Invariant Metric

Autori: Nicolas Guigui, Xavier Pennec
Pubblicato in: Geometric Science of Information - 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings, Numero 12829, 2021, Pagina/e 119-126, ISBN 978-3-030-80208-0
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-80209-7_14

Characterization of Invariant Inner Products

Autori: Yann Thanwerdas, Xavier Pennec
Pubblicato in: Lecture Notes in Computer Science, Geometric Science of Information, Numero Proc of Geometric Science of Information (GSI 2023) - LNCS 14071, 2023, Pagina/e 384-391
Editore: Springer Nature Switzerland
DOI: 10.1007/978-3-031-38271-0_38

Tangent Phylogenetic PCA

Autori: Morten Akhøj, Xavier Pennec, Stefan Sommer
Pubblicato in: Lecture Notes in Computer Science, Image Analysis, Numero Proc of Scandinavian Conference on Image Analysis 2023, LNCS13886, 2023, Pagina/e 77-90
Editore: Springer Nature Switzerland
DOI: 10.1007/978-3-031-31438-4_6

Investigation of the Impact of Normalization on the Study of Interactions Between Myocardial Shape and Deformation

Autori: Maxime Di Folco, Nicolas Guigui, Patrick Clarysse, Pamela Moceri, Nicolas Duchateau
Pubblicato in: Lecture Notes in Computer Science, Functional Imaging and Modeling of the Heart, Numero LNCS 12738, 2024, Pagina/e 223-231
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-78710-3_22

The curse of isotropy: from principal components to principal subspaces

Autori: Tom Szwagier, Xavier Pennec
Pubblicato in: 2024
Editore: arxiv preprint
DOI: 10.48550/arxiv.2307.15348

The Geometry of Right-Invariant Metrics

Autori: James Benn, Stephen Marsland
Pubblicato in: https://hal.science/hal-04360903, 2024
Editore: hal preprint

Flagfolds

Autori: Buet, Blanche; Pennec, Xavier
Pubblicato in: https://inria.hal.science/hal-04112465, 2023
Editore: arxiv preprint
DOI: 10.48550/arxiv.2305.10583

Principal subbundles for dimension reduction

Autori: Akhøj, Morten; Benn, James; Grong, Erlend; Sommer, Stefan; Pennec, Xavier
Pubblicato in: https://inria.hal.science/hal-04156036, 2023
Editore: arxiv preprint
DOI: 10.48550/arxiv.2307.03128

Effective formulas for the geometry of normal homogeneous spaces. Application to flag manifolds

Autori: Rabenoro, Dimbihery; Pennec, Xavier
Pubblicato in: https://doi.org/10.48550/arxiv.2302.14810, 2024
Editore: arxiv preprint
DOI: 10.48550/arxiv.2302.14810

The Currents Space of Graphs

Autori: Benn, James; Calissano, Anna; Marsland, Stephen; Pennec, Xavier
Pubblicato in: https://hal.inria.fr/hal-03910825, 2022
Editore: arxiv preprint

Curvature effects on the empirical mean in Riemannian and affine Manifolds: a non-asymptotic high concentration expansion in the small-sample regime

Autori: Pennec, Xavier
Pubblicato in: https://inria.hal.science/hal-02157952, 2019
Editore: arxiv preprint
DOI: 10.48550/arxiv.1906.07418

A geometric framework for asymptotic inference of principal subspaces in PCA

Autori: Rabenoro, Dimbihery; Pennec, Xavier
Pubblicato in: https://inria.hal.science/hal-03842125, 2024
Editore: arxiv preprint
DOI: 10.48550/arxiv.2209.02025

Riemannian Geometric Statistics in Medical Image Analysis

Autori: Xavier Pennec, Stefan Sommer, Tom Fletcher
Pubblicato in: 2020, ISBN 9780-128147252
Editore: Academic Press
DOI: 10.1016/C2017-0-01561-6

Multimodal Brain Image Analysis and Mathematical Foundations of Computational Anatomy - 4th International Workshop, MBIA 2019, and 7th International Workshop, MFCA 2019, Held in Conjunction with MICCAI 2019, Shenzhen, China, October 17, 2019, Proceedings

Autori: Dajiang Zhu, Jingwen Yan, Heng Huang, Li Shen, Paul M. Thompson, Carl-Fredrik Westin, Xavier Pennec, Sarang Joshi, Mads Nielsen, Tom Fletcher, Stanley Durrleman, Stefan Sommer
Pubblicato in: Lecture Notes in Computer Science (LNCS), Numero 11846, 2019, ISBN 978-3-030-33226-6
Editore: Springer
DOI: 10.1007/978-3-030-33226-6

Pubblicazioni

Condividi questa pagina Condividi questa pagina sui social network

Scarica Scarica il contenuto della pagina