Scalable NMF via linearly optimized data compression.

Orthonormal projective non-negative matrix factorization (opNMF) has been widely used in neuroimaging and clinical neuroscience applications to derive representations of the brain in health and disease. The non-negativity and orthonormality constraints of opNMF result in intuitive and well-localized factors. However, the advantages of opNMF come at a steep computational cost that prohibits its use in large-scale data. In this work, we propose novel and scalable optimization schemes for orthonormal projective non-negative matrix factorization that enable the use of the method in large-scale neuroimaging settings. We replace the high-dimensional data matrix with its corresponding singular value decomposition (SVD) and QR decompositions and combine the decompositions with opNMF multiplicative update algorithm. Empirical validation of the proposed methods demonstrated significant speed-up in computation time while keeping memory consumption low without compromising the accuracy of the solution.