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

Lei Hong Zhang*, Lizhi LIAO, Kwok Po NG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)853-865
Number of pages13
JournalJournal of Optimization Theory and Applications
Volume157
Issue number3
DOIs
Publication statusPublished - Jun 2013

Scopus Subject Areas

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

User-Defined Keywords

  • Dimensionality reduction
  • Generalized Foley-Sammon transform
  • Linear discriminant analysis
  • Superlinear convergence
  • The trace ratio optimization problem

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