Biometrics: Theory, Methods, and Applications (IEEE Press by N. V. Boulgouris, Konstantinos N. Plataniotis, Evangelia

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

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F. Frangi, J. Yang, D. Zhang, and Z. Jin, KPCA plus LDA: A complete kernel fisher discriminant framework for feature extraction and recognition. IEEE Trans. Pattern Anal. Mach. Intell. 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.

20. L. F. Chen, H. Y. M. Liao, M. T. Ko, J. C. Lin, and G. J. Yu, A new lda-based face recognition system which can solve the small sample size problem, Pattern Recognit 33:1713–1726, 2000. 21. Y. Guo, T. Hastie, and R. Tibshirani, Regularized linear discriminant analysis and its application in microarrays, Biostatistics 8(1):86–100, 2007. 22. A. M. Martinez and A. C. Kak, PCA versus LDA, IEEE Trans. Pattern Anal. Mach. Intell. 23(2):228– 233, 2001. 23. X. Wang and X. Tang, A unified framework for subspace face recognition.

XM } is available. Each tensor object Xm ∈ RI1 ×I2 ×···×IN assumes values in the tensor space RI1 ⊗ RI2 · · · ⊗ RIN , where In is the n-mode dimension of the tensor. The objective of MLDA-TPP is to find a multilinear mapping {U(n) ∈ RIn ×Pn , n = 1, . . , N} from the original tensor space RI1 ⊗ RI2 · · · ⊗ RIN into a tensor subspace RP1 ⊗ RP2 . . ⊗ RPN (with Pn < In , for n = 1, . . , N): T T T Ym = Xm ×1 U(1) ×2 U(2) · · · ×N U(N) , m = 1, . . 15) based on the optimization of a certain separation criterion, such that an enhanced separability between different classes is achieved.

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