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

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

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Article ID: iaor20132829
Volume: 157
Issue: 3
Start Page Number: 853
End Page Number: 865
Publication Date: Jun 2013
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: programming: linear
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.

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