Large‐scale brain dynamics are believed to lie in a latent, low‐dimensional space. Typically, the embeddings of brain scans are derived independently from different cognitive tasks or resting‐state data, ignoring a potentially large—and shared—portion of this space. Here, we establish that a shared, robust, and interpretable low‐dimensional space of brain dynamics can be recovered from a rich repertoire of task‐based functional magnetic resonance imaging (fMRI) data. This occurs when relying on nonlinear approaches as opposed to traditional linear methods. The embedding maintains proper temporal progression of the tasks, revealing brain states and the dynamics of network integration. We demonstrate that resting‐state data embeds fully onto the same task embedding, indicating similar brain states are present in both task and resting‐state data. Our findings suggest analysis of fMRI data from multiple cognitive tasks in a low‐dimensional space is possible and desirable.

Abstract-In the wake of recent advances in experimental methods in neuroscience, the ability to record in-vivo neuronal activity from awake animals has become feasible. The availability of such rich and detailed physiological measurements calls for the development of advanced data analysis tools, as commonly used techniques do not suffice to capture the spatio-temporal network complexity. In this paper, we propose a new hierarchical coupled geometry analysis, which exploits the hidden connectivity structures between neurons and the dynamic patterns at multiple time-scales. Our approach gives rise to the joint organization of neurons and dynamic patterns in data-driven hierarchical data structures. These structures provide local to global data representations, from local partitioning of the data in flexible trees through a new multiscale metric to a global manifold embedding. The application of our techniques to in-vivo neuronal recordings demonstrate the capability of extracting neuronal activity patterns and identifying temporal trends, associated with particular behavioral events and manipulations introduced in the experiments.

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UMAP provides an additional method to visualize microbiome data. The method is extensible to any beta diversity metric used with PCoA, and our results demonstrate that UMAP can indeed improve visualization quality and correspondence with biological and technical variables of interest.