Foundations of Geometric Statistics and Their Application in the Life Sciences

Información del proyecto

G-Statistics

Identificador del acuerdo de subvención: 786854

DOI

10.3030/786854

Proyecto cerrado

Fecha de la firma de la CE 16 Mayo 2018

Fecha de inicio 1 Septiembre 2018

Fecha de finalización 31 Agosto 2024

Financiado con arreglo a

• EXCELLENT SCIENCE - European Research Council (ERC)

Coste total

€ 2 183 583,75

Aportación de la UE

€ 2 183 583,75

Coordinado por

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE
France

CORDIS proporciona enlaces a los documentos públicos y las publicaciones de los proyectos de los programas marco HORIZONTE.

Los enlaces a los documentos y las publicaciones de los proyectos del Séptimo Programa Marco, así como los enlaces a algunos tipos de resultados específicos, como conjuntos de datos y «software», se obtienen dinámicamente de OpenAIRE .

Publicaciones

Book chapters (6)

Advances in Geometric Statistics for Manifold Dimension Reduction

Autores: Xavier Pennec
Publicado en: Handbook of Variational Methods for Nonlinear Geometric Data, 2020, Página(s) 339-359, ISBN 978-3-030-31350-0
Editor: Springer International Publishing
DOI: 10.1007/978-3-030-31351-7_11

Beyond Riemannian geometry: The affine connection setting for transformation groups

Autores: Pennec, Xavier; Lorenzi, Marco
Publicado en: Riemannian Geometric Statistics in Medical Image Analysis, 2021, Página(s) pp.169-229, ISBN 978-0-12-814725-2
Editor: Academic Press
DOI: 10.1016/b978-0-12-814725-2.00012-1

Manifold-valued image processing with SPD matrices

Autores: Xavier Pennec
Publicado en: Riemannian Geometric Statistics in Medical Image Analysis, 2020, Página(s) 75-134, ISBN 9780-128147252
Editor: 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

Autores: Nicolas Guigui; Xavier Pennec
Publicado en: Handbook of Statistics, volume 46: Geometry and Statistics; Editors: Frank Nielsen; Arni S.R. Srinivasa Rao; C.R. Rao., Edición 46, 2022, Página(s) 285-326, ISBN 978-0-323-91345-4
Editor: 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

Autores: Xavier Pennec
Publicado en: Digital Anatomy - Applications of Virtual, Mixed and Augmented Reality, 2021, Página(s) 159-183, ISBN 978-3-030-61904-6
Editor: Springer International Publishing
DOI: 10.1007/978-3-030-61905-3_9

Bias on estimation in quotient space and correction methods

Autores: Nina Miolane, Loic Devilliers, Xavier Pennec
Publicado en: Riemannian Geometric Statistics in Medical Image Analysis, 2024, Página(s) 343-376, ISBN 978-0-12-814725-2
Editor: Academic Press
DOI: 10.1016/b978-0-12-814725-2.00017-0

Thesis and dissertations (4)

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

Autores: Elodie Maignant
Publicado en: Edición 06-12-2023, 2023
Editor: Université Côte d’Azur

Riemannian and stratified geometries on covariance and correlation matrices

Autores: Thanwerdas, Yann
Publicado en: Edición 2022-05-22, 2022
Editor: Universite Côte d'Azur

Riemannian and sub-riemannian methods for dimension reduction

Autores: Morten Akhøj Pedersen
Publicado en: Edición 23-11-2023, 2023
Editor: 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

Autores: Guigui, Nicolas
Publicado en: Edición 2023-11-18, 2021
Editor: Univresité Côte d'Azur

Peer reviewed articles (14)

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

Autores: Emmanuel Chevallier, Nicolas Guigui
Publicado en: Entropy, Edición 22/4, 2020, Página(s) 432, ISSN 1099-4300
Editor: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/e22040432

O(n)-invariant Riemannian metrics on SPD matrices

Autores: Yann Thanwerdas; Xavier Pennec
Publicado en: Linear Algebra and its Applications, Edición Vol. 661, 2023, Página(s) 163-201, ISSN 0024-3795
Editor: Elsevier BV
DOI: 10.1016/j.laa.2022.12.009

Theoretically and computationally convenient geometries on full-rank correlation matrices

Autores: Yann Thanwerdas; Xavier Pennec
Publicado en: SIAM Journal on Matrix Analysis and Applications, Edición Vol. 43, no 4, 2022, Página(s) 1851 - 1872, ISSN 1095-7162
Editor: SIAM
DOI: 10.48550/arxiv.2201.06282

The Measurement and Analysis of Shapes

Autores: Benn, James; Marsland, Stephen
Publicado en: Annals of Global Analysis and Geometry, inPress, 62, pp.47-70., Edición 62, 2022, Página(s) 47–70, ISSN 0232-704X
Editor: Kluwer Academic Publishers
DOI: 10.1007/s10455-022-09839-z

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

Autores: Yann Thanwerdas
Publicado en: SIAM Journal on Matrix Analysis and Applications, Edición 45, 2024, Página(s) 930-953, ISSN 0895-4798
Editor: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m1538144

Bures–Wasserstein Minimizing Geodesics between Covariance Matrices of Different Ranks

Autores: Yann Thanwerdas, Xavier Pennec
Publicado en: SIAM Journal on Matrix Analysis and Applications, Edición 44, 2023, Página(s) 1447-1476, ISSN 0895-4798
Editor: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m149168x

Numerical Accuracy of Ladder Schemes for Parallel Transport on Manifolds

Autores: Nicolas Guigui, Xavier Pennec
Publicado en: Foundations of Computational Mathematics, 2021, ISSN 1615-3375
Editor: Springer Verlag
DOI: 10.1007/s10208-021-09515-x

Geometry of sample spaces

Autores: Philipp Harms, Peter W. Michor, Xavier Pennec, Stefan Sommer
Publicado en: Differential Geometry and its Applications, Edición 90, 2023, Página(s) 102029, ISSN 0926-2245
Editor: Elsevier BV
DOI: 10.1016/j.difgeo.2023.102029

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

Autores: Nicolas Guigui; Nina Miolane; Xavier Pennec
Publicado en: Foundations and Trends® in Machine Learning, Edición Vol 16, Edición 3, 2023, Página(s) 329-493, ISSN 1935-8237
Editor: Now Publishers Inc.
DOI: 10.1561/2200000098

Classifying histograms of medical data using information geometry of beta distributions

Autores: Alice Le Brigant, Nicolas Guigui, Sana Rebbah, Stéphane Puechmorel
Publicado en: IFAC-PapersOnLine, Edición 54, 2021, Página(s) 514-520, ISSN 2405-8963
Editor: 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

Autores: Raphaël Sivera, Nicolas Capet, Valeria Manera, Roxane Fabre, Marco Lorenzi, Hervé Delingette, Xavier Pennec, Nicholas Ayache, Philippe Robert
Publicado en: Neurobiology of Aging, Edición 94, 2020, Página(s) 50-59, ISSN 0197-4580
Editor: Elsevier BV
DOI: 10.1016/j.neurobiolaging.2019.11.020

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

Autores: Yann Thanwerdas; Xavier Pennec
Publicado en: Differential Geometry and its Applications, Edición Vol.81, 2022, Página(s) 101867, ISSN 0926-2245
Editor: Elsevier BV
DOI: 10.1016/j.difgeo.2022.101867

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

Autores: Anna Calissano, Theodore Papadopoulo, Xavier Pennec, Samuel Deslauriers‐Gauthier
Publicado en: Human Brain Mapping, Edición 45, 2024, Página(s) e26554, ISSN 1065-9471
Editor: John Wiley & Sons Inc.
DOI: 10.1002/hbm.26554

Geomstats: A Python Package for Riemannian Geometry in Machine Learning

Autores: 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
Publicado en: JMLR - Journal of Machine Learning Research, Edición 21, 2020, Página(s) 19-027, ISSN 1533-7928
Editor: JMLR

Conference proceedings (15)

Parallel Transport on Kendall Shape Spaces

Autores: Nicolas Guigui, Elodie Maignant, Alain Trouvé, Xavier Pennec
Publicado en: Geometric Science of Information - 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings, Edición 12829, 2021, Página(s) 103-110, ISBN 978-3-030-80208-0
Editor: Springer International Publishing
DOI: 10.1007/978-3-030-80209-7_12

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

Autores: Tom Szwagier, Xavier Pennec
Publicado en: Lecture Notes in Computer Science, Geometric Science of Information, Edición Proc of Geometric Science of Information (GSI 2023) - LNCS 14071, 2023, Página(s) 375-383
Editor: Springer Nature Switzerland
DOI: 10.1007/978-3-031-38271-0_37

Cardiac Motion Modeling With Parallel Transport And Shape Splines

Autores: Nicolas Guigui, Pamela Moceri, Maxime Sermesant, Xavier Pennec
Publicado en: 2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI), 2021, Página(s) 1394-1397, ISBN 978-1-6654-1246-9
Editor: IEEE
DOI: 10.1109/isbi48211.2021.9433887

Towards Quotient Barycentric Subspaces

Autores: Anna Calissano, Elodie Maignant, Xavier Pennec
Publicado en: Lecture Notes in Computer Science, Geometric Science of Information, Edición LNCS 14071, 2023, Página(s) 366-374
Editor: 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

Autores: Yann Thanwerdas, Xavier Pennec
Publicado en: Geometric Science of Information - 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings, Edición 12829, 2021, Página(s) 93-102, ISBN 978-3-030-80208-0
Editor: Springer International Publishing
DOI: 10.1007/978-3-030-80209-7_11

Riemannian Locally Linear Embedding with Application to Kendall Shape Spaces

Autores: Elodie Maignant, Alain Trouvé, Xavier Pennec
Publicado en: Lecture Notes in Computer Science, Geometric Science of Information, Edición LNCS 14071, 2023, Página(s) 12-20
Editor: Springer Nature Switzerland
DOI: 10.1007/978-3-031-38271-0_2

Exploration of Balanced Metrics on Symmetric Positive Definite Matrices

Autores: Yann Thanwerdas, Xavier Pennec
Publicado en: Geometric Science of Information - 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings, Edición 11712, 2019, Página(s) 484-493, ISBN 978-3-030-26979-1
Editor: Springer International Publishing
DOI: 10.1007/978-3-030-26980-7_50

Symmetric Algorithmic Components for Shape Analysis with Diffeomorphisms

Autores: Nicolas Guigui, Shuman Jia, Maxime Sermesant, Xavier Pennec
Publicado en: Geometric Science of Information - 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings, Edición 11712, 2019, Página(s) 759-768, ISBN 978-3-030-26979-1
Editor: 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

Autores: Yann Thanwerdas, Xavier Pennec
Publicado en: Geometric Science of Information - 4th International Conference, GSI 2019, Toulouse, France, August 27–29, 2019, Proceedings, Edición 11712, 2019, Página(s) 502-510, ISBN 978-3-030-26979-1
Editor: 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

Autores: Emmanuel Chevallier; Nicolas Guigui
Publicado en: Proc. of SPIGL 2020: Geometric Structures of Statistical Physics, Information Geometry, and Learning, 2021, Página(s) 96–106
Editor: Springer
DOI: 10.1007/978-3-030-77957-3_5

Introduction to Geometric Learning in Python with Geomstats

Autores: 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
Publicado en: Proceedings of the 19th Python in Science Conference, 2020, Página(s) 48-57
Editor: SciPy
DOI: 10.25080/majora-342d178e-007

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

Autores: Nicolas Guigui, Xavier Pennec
Publicado en: Geometric Science of Information - 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings, Edición 12829, 2021, Página(s) 119-126, ISBN 978-3-030-80208-0
Editor: Springer International Publishing
DOI: 10.1007/978-3-030-80209-7_14

Characterization of Invariant Inner Products

Autores: Yann Thanwerdas, Xavier Pennec
Publicado en: Lecture Notes in Computer Science, Geometric Science of Information, Edición Proc of Geometric Science of Information (GSI 2023) - LNCS 14071, 2023, Página(s) 384-391
Editor: Springer Nature Switzerland
DOI: 10.1007/978-3-031-38271-0_38

Tangent Phylogenetic PCA

Autores: Morten Akhøj, Xavier Pennec, Stefan Sommer
Publicado en: Lecture Notes in Computer Science, Image Analysis, Edición Proc of Scandinavian Conference on Image Analysis 2023, LNCS13886, 2023, Página(s) 77-90
Editor: 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

Autores: Maxime Di Folco, Nicolas Guigui, Patrick Clarysse, Pamela Moceri, Nicolas Duchateau
Publicado en: Lecture Notes in Computer Science, Functional Imaging and Modeling of the Heart, Edición LNCS 12738, 2024, Página(s) 223-231
Editor: Springer International Publishing
DOI: 10.1007/978-3-030-78710-3_22

Other (8)

The curse of isotropy: from principal components to principal subspaces

Autores: Tom Szwagier, Xavier Pennec
Publicado en: 2024
Editor: arxiv preprint
DOI: 10.48550/arxiv.2307.15348

The Geometry of Right-Invariant Metrics

Autores: James Benn, Stephen Marsland
Publicado en: https://hal.science/hal-04360903, 2024
Editor: hal preprint

Flagfolds

Autores: Buet, Blanche; Pennec, Xavier
Publicado en: https://inria.hal.science/hal-04112465, 2023
Editor: arxiv preprint
DOI: 10.48550/arxiv.2305.10583

Principal subbundles for dimension reduction

Autores: Akhøj, Morten; Benn, James; Grong, Erlend; Sommer, Stefan; Pennec, Xavier
Publicado en: https://inria.hal.science/hal-04156036, 2023
Editor: arxiv preprint
DOI: 10.48550/arxiv.2307.03128

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

Autores: Rabenoro, Dimbihery; Pennec, Xavier
Publicado en: https://doi.org/10.48550/arxiv.2302.14810, 2024
Editor: arxiv preprint
DOI: 10.48550/arxiv.2302.14810

The Currents Space of Graphs

Autores: Benn, James; Calissano, Anna; Marsland, Stephen; Pennec, Xavier
Publicado en: https://hal.inria.fr/hal-03910825, 2022
Editor: arxiv preprint

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

Autores: Pennec, Xavier
Publicado en: https://inria.hal.science/hal-02157952, 2019
Editor: arxiv preprint
DOI: 10.48550/arxiv.1906.07418

A geometric framework for asymptotic inference of principal subspaces in PCA

Autores: Rabenoro, Dimbihery; Pennec, Xavier
Publicado en: https://inria.hal.science/hal-03842125, 2024
Editor: arxiv preprint
DOI: 10.48550/arxiv.2209.02025

Monographic books (2)

Riemannian Geometric Statistics in Medical Image Analysis

Autores: Xavier Pennec, Stefan Sommer, Tom Fletcher
Publicado en: 2020, ISBN 9780-128147252
Editor: 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

Autores: 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
Publicado en: Lecture Notes in Computer Science (LNCS), Edición 11846, 2019, ISBN 978-3-030-33226-6
Editor: Springer
DOI: 10.1007/978-3-030-33226-6