Introduction to riemannian geometry and geometric statistics: from basic theory to implementation with geomstats
As data is a predominant resource in applications, Riemannian geometry is a natural
framework to model and unify complex nonlinear sources of data. However, the …
framework to model and unify complex nonlinear sources of data. However, the …
Riemannian and stratified geometries on covariance and correlation matrices
Y Thanwerdas - 2022 - hal.science
In many applications, the data can be represented by covariance matrices or correlation
matrices between several signals (EEG, MEG, fMRI), physical quantities (cells, genes), or …
matrices between several signals (EEG, MEG, fMRI), physical quantities (cells, genes), or …
A survey of manifold learning and its applications for multimedia
H Fassold - arXiv preprint arXiv:2310.12986, 2023 - arxiv.org
arXiv:2310.12986v1 [cs.MM] 8 Sep 2023 Page 1 A survey of manifold learning and its
applications for multimedia Hannes Fassold JOANNEUM RESEARCH - DIGITAL hannes.fassold@joanneum.at …
applications for multimedia Hannes Fassold JOANNEUM RESEARCH - DIGITAL hannes.fassold@joanneum.at …
Riemannian data-dependent randomized smoothing for neural networks certification
P Labarbarie, H Hajri, M Arnaudon - arXiv preprint arXiv:2206.10235, 2022 - arxiv.org
Certification of neural networks is an important and challenging problem that has been
attracting the attention of the machine learning community since few years. In this paper, we …
attracting the attention of the machine learning community since few years. In this paper, we …
A Metric-based Principal Curve Approach for Learning One-dimensional Manifold
EH Cui, S Shao - arXiv preprint arXiv:2405.12390, 2024 - arxiv.org
Principal curve is a well-known statistical method oriented in manifold learning using
concepts from differential geometry. In this paper, we propose a novel metric-based principal …
concepts from differential geometry. In this paper, we propose a novel metric-based principal …
Unveiling cellular morphology: statistical analysis using a Riemannian elastic metric in cancer cell image datasets
Elastic metrics can provide a powerful tool to study the heterogeneity arising from cellular
morphology. To assess their potential application (eg classifying cancer treated cells), we …
morphology. To assess their potential application (eg classifying cancer treated cells), we …
Adaptive filter with Riemannian manifold constraint
The adaptive filtering theory has been extensively developed, and most of the proposed
algorithms work under the assumption of Euclidean space. However, in many applications …
algorithms work under the assumption of Euclidean space. However, in many applications …
Kinematics Estimation and Evaluation of Carpus From 4D MRI Sequences
N Dang - 2023 - search.proquest.com
This thesis aims to develop a pipeline for studying motion patterns of wrist and identifying
carpal instability. Early detection of carpal instability is important as it can lead to wearing of …
carpal instability. Early detection of carpal instability is important as it can lead to wearing of …
Estimation statistique dans les variétés Riemanniennes: implémentation et application à l'étude des déformations cardiaques
N Guigui - 2021 - theses.fr
Résumé L'étude des formes anatomiques et de leur mouvement est au cœur des
préoccupations dans de nombreuses spécialités de la médecine. En cardiologie, des …
préoccupations dans de nombreuses spécialités de la médecine. En cardiologie, des …
Using a Riemannian elastic metric for statistical analysis of tumor cell shape heterogeneity
We examine how a specific instance of the elastic metric, the Square Root Velocity (SRV)
metric, can be used to study and compare cellular morphologies from the contours they form …
metric, can be used to study and compare cellular morphologies from the contours they form …