Given the era of big data, sparse principal component analysis is a useful tool for reduction of high-dimensional data in applications of statistics. Many existing methods, however, relax to single-rank PCA or lack convergence guarantees in the optimization problem. In order to guarantee convergence, an alternating manifold proximal gradient (A-ManPG) method was proposed as a general framework for the manifold problem. We propose a formulation of A-ManPG with sparse PCA via penalized matrix approximation and closed-form subproblems to improve performance. Our experimental results on synthetic data proves the efficacy of the formulation.
