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tSSNALM: A fast two-stage semi-smooth Newton augmented Lagrangian method for sparse CCA

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  • Xiu, Xianchao
  • Yang, Ying
  • Kong, Lingchen
  • Liu, Wanquan

Abstract

Canonical correlation analysis (CCA) is a very useful tool for measuring the linear relationship between two multidimensional variables. However, it often fails to extract meaningful features in high-dimensional settings. This motivates the sparse CCA problem, in which ℓ1 constraints are applied to the canonical vectors. Although some sparse CCA solvers exist in the literature, we found that none of them is efficient. We propose a fast two-stage semi-smooth Newton augmented Lagrangian method (tSSNALM) to solve sparse CCA problems, and we provide convergence analysis. Numerical comparisons between our approach and a number of state-of-the-art solvers, on simulated data sets, are presented to demonstrate its efficiency. To the best of our knowledge, this is the first time that duality has been integrated with a semi-smooth Newton method for solving sparse CCA.

Suggested Citation

  • Xiu, Xianchao & Yang, Ying & Kong, Lingchen & Liu, Wanquan, 2020. "tSSNALM: A fast two-stage semi-smooth Newton augmented Lagrangian method for sparse CCA," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    • Handle: RePEc:eee:apmaco:v:383:y:2020:i:c:s0096300320302411
    DOI: 10.1016/j.amc.2020.125272
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    References listed on IDEAS

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    1. Adrian S. Lewis & Jérôme Malick, 2008. "Alternating Projections on Manifolds," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 216-234, February.
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