Ha Sung Min, Bani Abdalla, Sotiras Aristeidis
Department of Radiology, Washington University in St. Louis, USA.
Institute for Informatics, Washington University in St. Louis, St. Louis, USA.
Proc SPIE Int Soc Opt Eng. 2023 Feb;12464. doi: 10.1117/12.2654282. Epub 2023 Apr 3.
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.
正交投影非负矩阵分解（opNMF）已广泛应用于神经影像学和临床神经科学应用中，以推导健康和疾病状态下大脑的表征。opNMF的非负性和正交性约束产生了直观且定位良好的因子。然而，opNMF的优势是以高昂的计算成本为代价的，这限制了其在大规模数据中的应用。在这项工作中，我们提出了用于正交投影非负矩阵分解的新颖且可扩展的优化方案，使该方法能够在大规模神经影像学设置中使用。我们用其相应的奇异值分解（SVD）和QR分解替换高维数据矩阵，并将这些分解与opNMF乘法更新算法相结合。对所提方法的实证验证表明，在不影响解的准确性的情况下，计算时间显著加快，同时内存消耗较低。
