Riemannian Trust-Region Method for the Maximal Correlation Problem

The maximal correlation problem (MCP) arising in the canonical correlation analysis is very important to assess the relationship between sets of random variables. Efficient and fast methods for solving MCP are desired in broad statistical and nonstatistical applications. Some early proposed algorithms are based on the first-order information of MCP, and fast convergence could not be expected. In this article, we turn the generic Riemannian trust-region method of Absil et al. 2 P.-A. Absil , C. G. Baker , and K. A. Gallivan ( 2007 ). Trust-region methods on Riemannian manifolds . Found. Comput. Math. 7 : 303 – 330 . Google Scholar]] into a practical algorithm for MCP, which enjoys the global convergence and local superlinear convergence rate. The structure-exploiting preconditioning technique is also discussed in solving the trust-region subproblem. Numerical empirical evaluation and a comparison against other methods are reported, which shows that the method is efficient in solving MCPs.