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71 jmlr-2008-On the Equivalence of Linear Dimensionality-Reducing Transformations


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Author: Marco Loog

Abstract: In this JMLR volume, Ye (2008) demonstrates the essential equivalence of two sets of solutions to a generalized Fisher criterion used for linear dimensionality reduction (see Ye, 2005; Loog, 2007). Here, I point out the basic flaw in this new contribution. Keywords: linear discriminant analysis, equivalence relation, linear subspaces, Bayes error


reference text

K. Fukunaga. Introduction to Statistical Pattern Recognition. Academic Press, New York, 1990. M. Loog. A complete characterization of a family of solutions to a generalized fisher criterion. Journal of Machine Learning Research, 8:2121–2123, 2007. J. Ye. Characterization of a family of algorithms for generalized discriminant analysis on undersampled problems. Journal of Machine Learning Research, 6:483–502, 2005. J. Ye. Comments on the complete characterization of a family of solutions to a generalized fisher criterion. Journal of Machine Learning Research, 9:517–519, 2008. 2490