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Sparse principal component analysis (PCA) and sparse canonical correlationanalysis (CCA) are two essential techniques from high-dimensional statisticsand machine learning for analyzing large-scale data. Both problems can beformulated as an optimization problem with nonsmooth objective and nonconvexconstraints. Since non-smoothness and nonconvexity bring numericaldifficulties, most algorithms suggested in the literature either solve somerelaxations or are heuristic and lack convergence guarantees. In this paper, wepropose a new alternating manifold proximal gradient method to solve these twohigh-dimensional problems and provide a unified convergence analysis. Numericalexperiment results are reported to demonstrate the advantages of our algorithm.

An Alternating Manifold Proximal Gradient Method for Sparse PCA and Sparse CCA