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

Lei-Hong Zhang (), Li-Zhi Liao () and Michael K. Ng ()
Additional contact information
Lei-Hong Zhang: Shanghai University of Finance and Economics
Li-Zhi Liao: Hong Kong Baptist University
Michael K. Ng: Hong Kong Baptist University

Journal of Optimization Theory and Applications, 2013, vol. 157, issue 3, No 15, 853-865

Abstract: 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.

Keywords: Dimensionality reduction; Linear discriminant analysis; Generalized Foley–Sammon transform; The trace ratio optimization problem; Superlinear convergence (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-011-9832-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:157:y:2013:i:3:d:10.1007_s10957-011-9832-4

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-011-9832-4

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().