Taming dimensionality in big neuroimaging data: Efficient orthonormal projective NMF via stochastic learning and data compression.

Large-scale neuroimaging datasets present remarkable opportunities for advancing our understanding of human brain structure and function. Data-driven pattern analysis methods such as Orthonormal Projective Non-negative Matrix Factorization (opNMF) are particularly well suited to uncover multivariate relationships within these data, offering greater interpretability and reproducibility than more conventional approaches such as principal component analysis (PCA) and independent component analysis (ICA). Despite its utility in clinical computational neuroscience, the application of opNMF in large cohort studies has been impeded by computational challenges and scalability limitations. In this work, we address these issues by introducing a stochastic optimization strategy that processes mini-batches of the data, substantially improving scalability. We further accelerate computation through random data compression and leverage repulsive point processes to diversify mini-batches, reducing redundancy and the variance of updates. We first evaluated our method on gray matter tissue density maps from 1,000 participants in the Open Access Series of Imaging Studies (OASIS). Compared with the original approach, it achieved similar approximation accuracy and factor interpretability while greatly reducing computational cost. To demonstrate practical utility, we then applied the framework to 10,000 participants from the UK Biobank, identifying 20 patterns of structural covariance (PSCs) and examined associations between visceral adipose tissue (VAT) and PSC loadings, finding significant relationships for 13 PSCs in females and 11 PSCs in males, most of which were negative. We further show how these patterns refine in higher-rank decompositions with 40 and 60 components. This enhanced opNMF framework opens new possibilities for large-scale neuroimaging analyses, facilitating deeper insights into brain structure in both health and disease.