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Title: An Alternating Manifold Proximal Gradient Method for Sparse Principal Component Analysis and Sparse Canonical Correlation Analysis
Sparse principal component analysis and sparse canonical correlation analysis 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. Because nonsmoothness and nonconvexity bring numerical difficulties, most algorithms suggested in the literature either solve some relaxations of them 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 experimental results are reported to demonstrate the advantages of our algorithm.
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Award ID(s):
1915842 1934568 1953189 1953210
Publication Date:
Journal Name:
INFORMS Journal on Optimization
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Sponsoring Org:
National Science Foundation
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