An Alternating Manifold Proximal Gradient Method for Sparse PCA and Sparse CCA
This addresses optimization challenges in high-dimensional statistics for data analysts, but it is incremental as it builds on existing methods with improved guarantees.
The paper tackles the numerical difficulties in sparse PCA and sparse CCA by proposing a new alternating manifold proximal gradient method, providing a unified convergence analysis and demonstrating advantages in numerical experiments.
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.