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An alternating variable method for the maximal correlation problem


  • Lei-Hong Zhang


  • Li-Zhi Liao



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. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Lei-Hong Zhang & Li-Zhi Liao, 2012. "An alternating variable method for the maximal correlation problem," Journal of Global Optimization, Springer, vol. 54(1), pages 199-218, September.
  • Handle: RePEc:spr:jglopt:v:54:y:2012:i:1:p:199-218
    DOI: 10.1007/s10898-011-9758-2

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    References listed on IDEAS

    1. John Geer, 1984. "Linear relations amongk sets of variables," Psychometrika, Springer;The Psychometric Society, vol. 49(1), pages 79-94, March.
    2. Mohamed Hanafi & Jos Berge, 2003. "Global optimality of the successive Maxbet algorithm," Psychometrika, Springer;The Psychometric Society, vol. 68(1), pages 97-103, March.
    3. Paul Horst, 1961. "Relations amongm sets of measures," Psychometrika, Springer;The Psychometric Society, vol. 26(2), pages 129-149, June.
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