2023/03/27 by D'Souza, Niharika S., Venkataraman, Archana
#FOS: Biological sciences #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Neural and Evolutionary Computing (cs.NE) #Neurons and Cognition (q-bio.NC) #Quantitative Methods (q-bio.QM) #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2303.14986
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.