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arXiv · 1903.11576

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

Shixiang Chen·Shiqian Ma·Lingzhou Xue·Hui Zou
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Abstract

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.

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Shixiang Chen, Shiqian Ma, Lingzhou Xue, Hui Zou. 2019-03-27. An Alternating Manifold Proximal Gradient Method for Sparse PCA and Sparse CCA. https://arxiv.org/abs/1903.11576

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