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Superlinear Convergence of a General Algorithm for the Generalized Foley–Sammon Discriminant Analysis

Author

Listed:
  • Lei-Hong Zhang

    (Shanghai University of Finance and Economics)

  • Li-Zhi Liao

    (Hong Kong Baptist University)

  • Michael K. Ng

    (Hong Kong Baptist University)

Abstract

Linear Discriminant Analysis (LDA) is one of the most efficient statistical approaches for feature extraction and dimension reduction. The generalized Foley–Sammon transform and the trace ratio model are very important in LDA and have received increasing interest. An efficient iterative method has been proposed for the resulting trace ratio optimization problem, which, under a mild assumption, is proved to enjoy both the local quadratic convergence and the global convergence to the global optimal solution (Zhang, L.-H., Liao, L.-Z., Ng, M.K.: SIAM J. Matrix Anal. Appl. 31:1584, 2010). The present paper further investigates the convergence behavior of this iterative method under no assumption. In particular, we prove that the iteration converges superlinearly when the mild assumption is removed. All possible limit points are characterized as a special subset of the global optimal solutions. An illustrative numerical example is also presented.

Suggested Citation

  • Lei-Hong Zhang & Li-Zhi Liao & Michael K. Ng, 2013. "Superlinear Convergence of a General Algorithm for the Generalized Foley–Sammon Discriminant Analysis," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 853-865, June.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:3:d:10.1007_s10957-011-9832-4
    DOI: 10.1007/s10957-011-9832-4
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    References listed on IDEAS

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    1. W. J. Krzanowski & P. Jonathan & W. V. McCarthy & M. R. Thomas, 1995. "Discriminant Analysis with Singular Covariance Matrices: Methods and Applications to Spectroscopic Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(1), pages 101-115, March.
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