An alternating variable method for the maximal correlation problem

Lei Hong Zhang, Lizhi LIAO*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

The maximal correlation problem (MCP) aiming at optimizing correlations between sets of variables plays an important role in many areas of statistical applications. Up to date, algorithms for the general MCP stop at solutions of the multivariate eigenvalue problem (MEP), which serves only as a necessary condition for the global maxima of the MCP. For statistical applications, the global maximizer is quite desirable. In searching the global solution of the MCP, in this paper, we propose an alternating variable method (AVM), which contains a core engine in seeking a global maximizer. We prove that (i) the algorithm converges globally and monotonically to a solution of the MEP, (ii) any convergent point satisfies a global optimal condition of the MCP, and (iii) whenever the involved matrix A is nonnegative irreducible, it converges globally to the global maximizer. These properties imply that the AVM is an effective approach to obtain a global maximizer of the MCP. Numerical testings are carried out and suggest a superior performance to the others, especially in finding a global solution of the MCP.

Original languageEnglish
Pages (from-to)199-218
Number of pages20
JournalJournal of Global Optimization
Volume54
Issue number1
DOIs
Publication statusPublished - Sep 2012

Scopus Subject Areas

  • Computer Science Applications
  • Management Science and Operations Research
  • Control and Optimization
  • Applied Mathematics

User-Defined Keywords

  • Canonical correlation
  • Gauss-Seidal method
  • Global maximizer
  • Maximal correlation problem
  • Multivariate eigenvalue problem
  • Multivariate statistics
  • Power method

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