Abstract
The Least Squares Support Vector Machines (LS-SVM) is an improvement to the SVM. Combined the LS-SVM with the Multi-Resolution Analysis (MRA), this letter proposes the Multi-resolution LS-SVM (MLS-SVM). The proposed algorithm has the same theoretical framework as MRA but with better approximation ability. At a fixed scale MLS-SVM is a classical LS-SVM, but MLS-SVM can gradually approximate the target function at different scales. In experiments, the MLS-SVM is used for nonlinear system identification, and achieves better identification accuracy.
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References
V. Vapnik. The Nature of Statistical Learning Theory. New York, Springer Verlag, 1995, 168–209.
V. Vapnik. An overview of statistical learning theory. IEEE Trans. on Neural Networks, 10(1999)5, 988–999.
C. J. C. Burges. A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 2(1998)2, 56–89.
A. J. Smola, B. Scholkopf. A tutorial on support vector regression. NeuroCOLT, rep.19, 1998, Available at http://svm.first.gmd.de.
J. A. K. Suykens, J. Vandewalle. Least squares support vector machine classifiers. Neural Processing Lett., 9(1999)7, 293–300.
J. A. K. Suykens, J. Vandewalle. Recurrent least squares support vector machines. IEEE Trans. on Circuits and Systems I, 47(2000)2, 1109–1114.
J. A. K. Suykens, L. Lukas, J. Vandewalle. Sparse approximation using least squares support vector machines. IEEE Int. Symposium on Circuits and Systems (ISCAS’00), Geneva, Switzerland, 26–27 May 2000, 757–759.
Xuhui Shao. Model selection using statistical learning theory. [Ph.D. dissertation], The University of Minnesota, March 1999.
Xuhui Shao, Vladimir Cherkassky. Multi-resolution support vector machine. International Joint Conference on Neural Networks (IJCNN’99), Washington DC, July 1999, 1065–1070.
S. Mallat. A theory of multiresolution signal decomposition: The wavelet transform. IEEE Trans. on Circuits and Systems I, 11(1989)7, 674–693.
S. Mallat. Multiresolution approximation and wavelet orthonormal bases of L2. Trans. Amer. Math. Soc., 315(1989)11. 69–87.
Zhang Zongping, Liu Guizhong, Dong Enqing. De-noising via dyadic wavelet transform. Journal of Electronics & Information Technology, 23(2001)11, 1083–1090 (in Chinese). 张宗, 贵, 恩, 于进波换信去, 子信学, 23(2001)11, 1083–1090.
S. Saitoh. Theory of Reproducing Kernels and Its Applications. Harlow, U.K., Longman, 1988, 356–412.
N. Aronszajn. Theory of reproducing kernels. Trans. Amer. Math. Soc., 68(1950)2, 337–404.
B. Scholkopf, S. Mika, C. J. C. Burges, et al. Input space versus feature space in kernel-based methods. IEEE Trans. on Neural Networks, 10(1999)9, 1000–1017.
K. Narendra, K. Parthasarathy. Identification and control of dynamical systems using neural networks. IEEE Trans. on Neural Networks. 1(1990)1, 4–27.
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Communication author: Wang Liejun, born in 1976, male, doctor candidate. Dept of Information and Communication Engineering, Xi’an Jiaotong University, Xi’an 710049, China.
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Wang, L., Zhang, T. & Zhou, Y. Multi-Resolution Least Squares Support Vector Machines. J. of Electron.(China) 24, 701–704 (2007). https://doi.org/10.1007/s11767-006-0270-7
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DOI: https://doi.org/10.1007/s11767-006-0270-7
Key words
- Support Vector Machines (SVM)
- Least square method
- Multi-Resolution Analysis (MRA)
- Nonlinear system identification