Dynamic and low-dimensional modeling of brain functional connectivity on Riemannian manifolds
Modeling brain functional connectivity (FC) is key in investigating brain functions and dysfunctions. FC is typically quantified by symmetric positive definite (SPD) matrices that are located on a Riemannian manifold rather than the regular Euclidean space, whose modeling faces three challenges. Fir...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-07-01
|
| Series: | NeuroImage |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1053811925002460 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849387383059906560 |
|---|---|
| author | Mingyu Wang Yueming Wang Yuxiao Yang |
| author_facet | Mingyu Wang Yueming Wang Yuxiao Yang |
| author_sort | Mingyu Wang |
| collection | DOAJ |
| description | Modeling brain functional connectivity (FC) is key in investigating brain functions and dysfunctions. FC is typically quantified by symmetric positive definite (SPD) matrices that are located on a Riemannian manifold rather than the regular Euclidean space, whose modeling faces three challenges. First, FC can be time-varying and the temporal dynamics of FC matrix time-series need to be modeled within the constraint of the SPD Riemannian manifold geometry, which remains elusive. Second, the FC matrix time-series exhibits considerable stochasticity, whose probability distribution is difficult to model on the Riemannian manifold. Third, FC matrices are high-dimensional and dimensionality reduction methods for SPD matrix time-series are still lacking. Here, we develop a Riemannian state-space modeling framework to simultaneously address the challenges. First, we construct a new Riemannian state-space model (RSSM) to define a hidden SPD matrix state to achieve dynamic, stochastic, and low-dimensional modeling of FC matrix time-series on the SPD Riemannian manifold. Second, we develop a new Riemannian Particle Filter (RPF) algorithm to estimate the hidden low-dimensional SPD matrix state and predict the FC matrix time-series. Third, we develop a new Riemannian Expectation Maximization (REM) algorithm to fit the RSSM parameters. We evaluate the proposed RSSM, RPF, and REM using simulation and real-world EEG datasets, demonstrating that the RSSM enables accurate prediction of the EEG FC time-series and classification of emotional states, outperforming traditional Euclidean methods. Our results have implications for modeling brain FC on the SPD Riemannian manifold to study various brain functions and dysfunctions. |
| format | Article |
| id | doaj-art-85fe99485311414bb5f3adf4b1ffb84f |
| institution | Kabale University |
| issn | 1095-9572 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | NeuroImage |
| spelling | doaj-art-85fe99485311414bb5f3adf4b1ffb84f2025-08-20T03:53:51ZengElsevierNeuroImage1095-95722025-07-0131412124310.1016/j.neuroimage.2025.121243Dynamic and low-dimensional modeling of brain functional connectivity on Riemannian manifoldsMingyu Wang0Yueming Wang1Yuxiao Yang2MOE Frontier Science Center for Brain Science and Brain-machine Integration, Zhejiang University, Hangzhou, China; Nanhu Brain-computer Interface Institute, Hangzhou, China; School of Computer Science and Technology, Zhejiang University, Hangzhou, ChinaNanhu Brain-computer Interface Institute, Hangzhou, China; School of Computer Science and Technology, Zhejiang University, Hangzhou, ChinaMOE Frontier Science Center for Brain Science and Brain-machine Integration, Zhejiang University, Hangzhou, China; Nanhu Brain-computer Interface Institute, Hangzhou, China; School of Computer Science and Technology, Zhejiang University, Hangzhou, China; State Key Laboratory of Brain-machine Intelligence, Zhejiang University, Hangzhou, China; Second Affiliated Hospital, School of Medicine, Zhejiang University, Hangzhou, China; Correspondence to: Zhejiang University, Hangzhou, China.Modeling brain functional connectivity (FC) is key in investigating brain functions and dysfunctions. FC is typically quantified by symmetric positive definite (SPD) matrices that are located on a Riemannian manifold rather than the regular Euclidean space, whose modeling faces three challenges. First, FC can be time-varying and the temporal dynamics of FC matrix time-series need to be modeled within the constraint of the SPD Riemannian manifold geometry, which remains elusive. Second, the FC matrix time-series exhibits considerable stochasticity, whose probability distribution is difficult to model on the Riemannian manifold. Third, FC matrices are high-dimensional and dimensionality reduction methods for SPD matrix time-series are still lacking. Here, we develop a Riemannian state-space modeling framework to simultaneously address the challenges. First, we construct a new Riemannian state-space model (RSSM) to define a hidden SPD matrix state to achieve dynamic, stochastic, and low-dimensional modeling of FC matrix time-series on the SPD Riemannian manifold. Second, we develop a new Riemannian Particle Filter (RPF) algorithm to estimate the hidden low-dimensional SPD matrix state and predict the FC matrix time-series. Third, we develop a new Riemannian Expectation Maximization (REM) algorithm to fit the RSSM parameters. We evaluate the proposed RSSM, RPF, and REM using simulation and real-world EEG datasets, demonstrating that the RSSM enables accurate prediction of the EEG FC time-series and classification of emotional states, outperforming traditional Euclidean methods. Our results have implications for modeling brain FC on the SPD Riemannian manifold to study various brain functions and dysfunctions.http://www.sciencedirect.com/science/article/pii/S1053811925002460Brain functional connectivityRiemannian manifoldStochastic matrix dynamicsDimensionality reductionEEG |
| spellingShingle | Mingyu Wang Yueming Wang Yuxiao Yang Dynamic and low-dimensional modeling of brain functional connectivity on Riemannian manifolds NeuroImage Brain functional connectivity Riemannian manifold Stochastic matrix dynamics Dimensionality reduction EEG |
| title | Dynamic and low-dimensional modeling of brain functional connectivity on Riemannian manifolds |
| title_full | Dynamic and low-dimensional modeling of brain functional connectivity on Riemannian manifolds |
| title_fullStr | Dynamic and low-dimensional modeling of brain functional connectivity on Riemannian manifolds |
| title_full_unstemmed | Dynamic and low-dimensional modeling of brain functional connectivity on Riemannian manifolds |
| title_short | Dynamic and low-dimensional modeling of brain functional connectivity on Riemannian manifolds |
| title_sort | dynamic and low dimensional modeling of brain functional connectivity on riemannian manifolds |
| topic | Brain functional connectivity Riemannian manifold Stochastic matrix dynamics Dimensionality reduction EEG |
| url | http://www.sciencedirect.com/science/article/pii/S1053811925002460 |
| work_keys_str_mv | AT mingyuwang dynamicandlowdimensionalmodelingofbrainfunctionalconnectivityonriemannianmanifolds AT yuemingwang dynamicandlowdimensionalmodelingofbrainfunctionalconnectivityonriemannianmanifolds AT yuxiaoyang dynamicandlowdimensionalmodelingofbrainfunctionalconnectivityonriemannianmanifolds |