Abstract
A novel criterion, namely Maximum Margin Criterion (MMC), is proposed for learning the data-dependent kernel for classification. Different kernels create the different geometrical structures of the data in the feature space, and lead to different class discrimination. Selection of kernel influences greatly the performance of kernel learning. Optimizing kernel is an effective method to improve the classification performance. In this paper, we propose a novel kernel optimization method based on maximum margin criterion, which can solve the problem of Xiong’s work [1] that the optimal solution can be solved by iteration update algorithm owing to the singular problem of matrix. Our method can obtain a unique optimal solution by solving an eigenvalue problem, and the performance is enhanced while time consuming is decreased. Experimental results show that the proposed algorithm gives a better performance and a lower time consuming compared with Xiong’s work.
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References
Yang, J., Frangi, A.F., Yang, J.-y., Zhang, D., Jin, Z.: KPCA Plus LDA: A Complete Kernel Fisher Discriminant Framework for Feature Extraction and Recognition. IEEE Trans. Pattern Analysis and Machine Intelligence 27(2), 230–244 (2005)
Liu, Q., Lu, H., Ma, S.: Improving kernel Fisher discriminant analysis for face recognition. IEEE Trans. Pattern Analysis and Machine Intelligence 14(1), 42–49 (2004)
Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995)
Müller, K.R., Mika, S., Rätsch, G., Tsuda, K., Schölkopf, B.: An introduction to kernel-based learning algorithms. IEEE Trans. Neural Networks 12, 181–201 (2001)
Scholkopf, B., Smola, A., Mu‘ller, K.R.: Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation 10(5), 1299–1319 (1998)
Mika, S., Ratsch, G., Weston, J., Scholkopf, B., Mu‘ller, K.-R.: Fisher Discriminant Analysis with Kernels. In: Proc. IEEE Int’l Workshop Neural Networks for Signal Processing IX, August 1999, pp. 41–48. IEEE Computer Society Press, Los Alamitos (1999)
Lu, J., Plataniotis, K.N., Venetsanopoulos, A.N.: Face recognition using kernel direct discriminant analysis algorithms. IEEE Transactions on Neural Networks 14(1), 117–226 (2003)
Baudat, G., Anouar, F.: Generalized Discriminant Analysis Using a Kernel Approach. Neural Computation 12(10), 2385–2404 (2000)
Liang, Z., Shi, P.: Uncorrelated discriminant vectors using a kernel method. Pattern Recognition 38, 307–310 (2005)
Liang, Z., Shi, P.: Efficient algorithm for kernel discriminant anlaysis. Pattern Recognition 37(2), 381–384 (2004)
Liang, Z., Shi, P.: An efficient and effective method to solve kernel Fisher discriminant analysis. Neurocomputing 61, 485–493 (2004)
Lu, J., Plataniotis, K.N., Venetsanopoulos, A.N.: Face Recognition Using Kernel Direct Discriminant Analysis Algorithms. IEEE Trans. Neural Networks 14(1), 117–126 (2003)
Yang, M.H.: Kernel Eigenfaces vs. Kernel Fisherfaces: Face Recognition Using Kernel Methods. In: Proc. Fifth IEEE Int’l Conf. Automatic Face and Gesture Recognition, May 2002, pp. 215–220 (2002)
Zheng, W., Zou, C., Zhao, L.: Weighted maximum margin discriminant analysis with kernels. Neurocomputing 67, 357–362 (2005)
Huang, J., Yuen, P.C., Chen, W.-S., Lai, J.H.: Kernel Subspace LDA with Optimized Kernel Parameters on Face Recognition. In: Proceedings of the Sixth IEEE International Conference on Automatic Face and Gesture Recognition, IEEE Computer Society Press, Los Alamitos (2004)
Wang, L., Chan, K.L., Xue, P.: A Criterion for Optimizing Kernel Parameters in KBDA for Image Retrieval. IEEE Trans. Systems, Man and Cybernetics-Part B: Cybernetics 35(3), 556–562 (2005)
Chen, W.-S., Yuen, P.C., Huang, J., Dai, D.-Q.: Kernel Machine-Based One-Parameter Regularized Fisher Discriminant Method for Face Recognition. IEEE Trans. Systems, Man and Cybernetics-Part B: Cybernetics 35(4), 658–669 (2005)
Huilin Xiong, Swamy, M.N.S., Omair Ahmad, M.: Optimizing the Kernel in the Empirical Feature Space. IEEE Trans. Neural Networks 16(2), 460–474 (2005)
Samaria, F., Harter, A.: Parameterisation of a Stochastic Model for Human Face Identification. In: Proceedings of 2nd IEEE Workshop on Applications of Computer Vision, Sarasota, FL (December 1994)
Li, H., Jiang, T., Zhang, K.: Efficient and Robust Feature Extraction by Maximum Margin Criterion. IEEE Trans. Neural Networks 17(1), 157–165 (2006)
Amari, S., Wu, S.: Improving support vector machine classifiers by modifying kernel functions. Neural Netw. 12(6), 783–789 (1999)
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Li, JB., Chu, SC., Pan, JS. (2007). A Criterion for Learning the Data-Dependent Kernel for Classification. In: Alhajj, R., Gao, H., Li, J., Li, X., Zaïane, O.R. (eds) Advanced Data Mining and Applications. ADMA 2007. Lecture Notes in Computer Science(), vol 4632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73871-8_34
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DOI: https://doi.org/10.1007/978-3-540-73871-8_34
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