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Connectomics has emerged as a powerful tool in neuroimaging and has spurredrecent advancements in statistical and machine learning methods forconnectivity data. Despite connectomes inhabiting a matrix manifold, mostanalytical frameworks ignore the underlying data geometry. This is largelybecause simple operations, such as mean estimation, do not have easilycomputable closed-form solutions. We propose a geometrically aware neuralframework for connectomes, i.e., the mSPD-NN, designed to estimate the geodesicmean of a collections of symmetric positive definite (SPD) matrices. ThemSPD-NN is comprised of bilinear fully connected layers with tied weights andutilizes a novel loss function to optimize the matrix-normal equation arisingfrom Fr\'echet mean estimation. Via experiments on synthetic data, wedemonstrate the efficacy of our mSPD-NN against common alternatives for SPDmean estimation, providing competitive performance in terms of scalability androbustness to noise. We illustrate the real-world flexibility of the mSPD-NN inmultiple experiments on rs-fMRI data and demonstrate that it uncovers stablebiomarkers associated with subtle network differences among patients withADHD-ASD comorbidities and healthy controls.

mSPD-NN: A Geometrically Aware Neural Framework for Biomarker Discovery from Functional Connectomics Manifolds