mSPD-NN: A Geometrically Aware Neural Framework for Biomarker Discovery from Functional Connectomics Manifolds
This work addresses a domain-specific problem in neuroimaging for researchers analyzing functional connectomes, offering a novel method for handling geometric constraints in SPD matrix estimation.
The authors tackled the problem of estimating the geodesic mean of symmetric positive definite matrices in connectomics, which lacks closed-form solutions, by proposing mSPD-NN, a geometrically aware neural framework that demonstrated competitive performance in scalability and robustness on synthetic data and uncovered stable biomarkers for ADHD-ASD comorbidities in real-world fMRI data.
Connectomics has emerged as a powerful tool in neuroimaging and has spurred recent advancements in statistical and machine learning methods for connectivity data. Despite connectomes inhabiting a matrix manifold, most analytical frameworks ignore the underlying data geometry. This is largely because simple operations, such as mean estimation, do not have easily computable closed-form solutions. We propose a geometrically aware neural framework for connectomes, i.e., the mSPD-NN, designed to estimate the geodesic mean of a collections of symmetric positive definite (SPD) matrices. The mSPD-NN is comprised of bilinear fully connected layers with tied weights and utilizes a novel loss function to optimize the matrix-normal equation arising from Fréchet mean estimation. Via experiments on synthetic data, we demonstrate the efficacy of our mSPD-NN against common alternatives for SPD mean estimation, providing competitive performance in terms of scalability and robustness to noise. We illustrate the real-world flexibility of the mSPD-NN in multiple experiments on rs-fMRI data and demonstrate that it uncovers stable biomarkers associated with subtle network differences among patients with ADHD-ASD comorbidities and healthy controls.