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By N. V. Boulgouris, Konstantinos N. Plataniotis, Evangelia Micheli-Tzanakou

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Additional resources for Biometrics: Theory, Methods, and Applications (IEEE Press Series on Computational Intelligence)

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Following the work in reference 50, Baudat and Anouar [51] proposed the generalized discriminant analysis (GDA) algorithm for multiclass problems. The equivalence relationship between kernel discriminant analysis (KDA) and kernel regression has been studied in reference 35 for binary-class problems. The analysis presented in this chapter can be applied to extend this equivalence result to multiclass problems. A symmetric function κ : X × X → R, where X denotes the input space, is called a kernel function if it satisfies the finitely positive semidefinite property [46].

Soc. Ser. B 67:427–444, 2005. 35. S. D. thesis, University of Technology, Berlin, 2002. 36. Y. Lee, Y. Lin, and G. Wahba, Multicategory support vector machines, theory, and application to the classification of microarray data and satellite radiance data, J. Am. Stat. Assoc. 99:67–81, 2004. 18 Chapter 1 Discriminant Analysis for Dimensionality Reduction 37. Y. Guermeur, A. Lifchitz, and R. Vert, A kernel for protein secondary structure prediction, in Kernel Methods in Computational Biology, The MIT Press, Cambridge, MA, 2004, pp.

27(2):230–244, 2005. 58. G. R. G. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui, and M. I. Jordan, Learning the kernel matrix with semidefinite programming, J. Mach. Learning Res. 5:27–72, 2004. 59. G. Fung, M. Dundar, J. Bi, and B. Rao, A fast iterative algorithm for Fisher discriminant using heterogeneous kernels, in Proceedings of the Twenty-First International Conference on Machine Learning, 2004. 60. L. Vandenberghe and S. Boyd, Semidefinite programming, SIAM Rev. 38(1):49–95, 1996. References 19 61.

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