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

Abstract

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.