  Sparse principal component analysis (PCA) and sparse canonical correlation
analysis (CCA) are two essential techniques from high-dimensional statistics
and machine learning for analyzing large-scale data. Both problems can be
formulated as an optimization problem with nonsmooth objective and nonconvex
constraints. Since non-smoothness and nonconvexity bring numerical
difficulties, most algorithms suggested in the literature either solve some
relaxations or are heuristic and lack convergence guarantees. In this paper, we
propose a new alternating manifold proximal gradient method to solve these two
high-dimensional problems and provide a unified convergence analysis. Numerical
experiment results are reported to demonstrate the advantages of our algorithm.
