Nonconvex alternating direction method of multipliers for distributed sparse principal component analysis

In this paper, we propose distributed algorithms to perform sparse principal component analysis (SPCA). The key benefit of the proposed algorithms is their ability to handle distributed data sets. Our algorithms are able to handle a few sparse-promoting regularizers (i.e., the convex norm and the nonconvex log-sum penalty) as well as different forms of data partition (i.e., partition across rows or columns of the data matrix). Our methods are based on a nonconvex ADMM framework, and they are shown to converge to stationary solutions of various nonconvex SPCA formulations. Numerical experiments based on both real and synthetic data sets, conducted on high performance computing (HPC) clusters, demonstrate the effectiveness of our approaches.