GeoMind: A Geometric Neural Network of State Space Model for Understanding Brain Dynamics on Riemannian Manifold
Keywords: Geometric deep learning, state space model, brain dynamics, Riemannian Manifold
Abstract: State space model (SSM) is a powerful tool in neuroscience field to characterize the dynamic nature of brain functions by elucidating the mechanism of how brain system transits between brain states and how underlying states give rise to the observed neural activities. Although tremendous efforts have been made to lend the power of deep learning and mathematical insight of SSM in various functional neuroimaging studies, current state-of-the-art methods lack a holistic view of brain state evolution as a self-organized dynamical system where each part of the brain is functionally inter-connected. Since the topological co-activation of functional fluctuations exhibits an intrinsic geometric pattern (symmetric and positive definite, or SPD) on the Riemannian manifold, the call for understanding how a selective set of functional connectivities in the brain supports diverse behavior and cognition emerges a new machine learning scenario of manifold-based SSM for large-scale functional neuroimages. To that end, we propose a geometric neural networks, coined *GeoMind*, designed to uncover evolving brain states by tracking the trajectory of functional dynamics on a high-dimensional Riemannian manifold of SPD matrices. Our *GeoMind* demonstrates promising results in identifying specific brain states based on task-based functional Magnetic Resonance Imaging (fMRI) data, as well as in diseases early diagnosis for Alzheimer's disease, Parkinson's disease and Autism. These results highlight the applicability of the proposed *GeoMind* in neuroscience research. Furthermore, to assess the generalization capabilities of our model, we applied it to the domain of human action recognition (HAR), achieving promising performance on three benchmark datasets (UTKinect, Florence and HDM05). This demonstrates the scalability and robustness of the proposed geometry deep model of SSM in capturing complex spatio-temporal dynamics across diverse fields.
Primary Area: applications to neuroscience & cognitive science
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Submission Number: 3107
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