A Hierarchical Manifold Learning Framework for High-Dimensional Neuroimaging Data

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Better understanding of large-scale brain dynamics with functional magnetic resonance imaging (fMRI) data is a major goal of modern neuroscience. In this work, we propose a novel hierarchical manifold learning framework for time-synchronized fMRI data for elucidating brain dynamics. Our framework—labelled 2-step diffusion maps (2sDM)—is based on diffusion maps, a nonlinear dimensionality reduction method. First, 2sDM learns the manifold of fMRI data for each individual separately and then learns a low-dimensional group-level embedding by integrating individual information. We also propose a method for out-of-sample extension within our hierarchical framework. Using 2sDM, we constructed a single manifold structure based on 6 different task-based fMRI (tfMRI) runs. Results on the tfMRI data show a clear manifold structure with four distinct clusters, or brain states. We extended this to embedding resting-state fMRI (rsfMRI) data by first synchronizing across individuals using an optimal orthogonal transformation. The rsfMRI data from the same individuals cleanly embedded onto the four clusters, suggesting that rsfMRI is a collection of different brains states. Overall, our results highlight 2sDM as a powerful method to understand brain dynamics and show that tfMRI and rsfMRI data share representative brain states.