Application of a Scaling Kernel in Signal Approximation of Least Squares Support Vector Machines

穆向阳 1; 2; 张太镒 1; 周亚同 3

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Application of a Scaling Kernel in Signal Approximation of Least Squares Support Vector Machines

更新时间：2025-12-08

- Application of a Scaling Kernel in Signal Approximation of Least Squares Support Vector Machines
- Vol. 42, Issue 12, Pages: 1464-1467+1480(2008)
- 作者机构：
  
  1. 西安交通大学电子与信息工程学院,西安,710049
  2. 西安石油大学电子工程学院,西安,710065
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP18
- Online First：10 December 2008，
  
  Published：2008
- 稿件说明：
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穆向阳 1, 2, 张太镒 1, et al. Application of a Scaling Kernel in Signal Approximation of Least Squares Support Vector Machines[J]. 2008, 42(12): 1464-1467+1480.
DOI：

穆向阳 1, 2, 张太镒 1, et al. Application of a Scaling Kernel in Signal Approximation of Least Squares Support Vector Machines[J]. 2008, 42(12): 1464-1467+1480. DOI：

摘要

针对目前常采用高斯核的最小二乘支持向量机(LS-SVM)不能对信号多尺度逼近的问题

提出一种采用尺度核的LS-SVM.首先

在再生核希尔伯特空间的框架下构建了一种点积型的尺度核函数

它满足Mercer条件

并具备平移和扩张的特性

是尺度子空间的一组完备的基.然后

利用拉格朗日乘子法求解LS-SVM逼近的约束规划问题

在结构风险最小化逼近准则下获得了逼近系数.与传统核函数相比

采用尺度核的LS-SVM可以实现多尺度逼近任意信号

且应用时仅需对尺度参数调节选优

简便、实用.实验结果表明:所提算法的逼近性能与小波核性能相当; 与传统的高斯核函数相比

其均方根误差提高8.4%.

Abstract

In order to overcome the problem that the least square support vector machines(LS-SVM)using Gaussian kernel cannot approximate arbitrary signal with multi-scale

a scaling kernel for LS-SVM is proposed. The scaling kernel in dot-product type is constructed under the framework of reproducing kernel Hilbert spaces. The kernel satisfies the Mercer condition

has the characteristic of dilation and translation

and forms a set of complete bases in the scale subspace. Then the Lagrangian multiplier is used to obtain the approximation coefficients under the criterion of structure risk minimization by solving the constrained programming of LS-SVM in signal approximation. The LS-SVM with scaling kernel can approximate arbitrary signal with multi-scale

and the proposed algorithm is promising in application since only one free parameter is adjusted for optimization. Simulation results show that the approximation performance of the scaling kernel is similar to the wavelet kernel; and compared with the traditional Gaussian kernel

the normalized root mean squared error increases about 8.4%.

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references

MULLER K R, MIKA S, RATSCH G, et al. An introduction to kernel-based learning algorithms [J]. IEEE Trans Neural Networks, 2001, 12(2): 181-201.

CRISTIANINI N, TAYLOR J S. An introduction to support vector machines and other kernel-based learning methods[M]. Cambridge, UK: Cambridge University Press, 2000.

SUYKENS J A K, GESTEL T V,BRABANTER J D, et al. Least squares support vector machines [M]. Singapore: World Scientific Pub Co., 2002.

ZHANG Li, ZHOU Weida,JIAO Licheng. Wavelet support vector machine[J]. IEEE Trans System, Man, Cybernetics, 2003, 34(1): 34-39

周伟达. 核机器学习方法研究[D]. 西安: 西安电子科技大学电子工程学院, 2003.

OPFER R. Tight frame expansions of multiscale reproducing kernels in Sobolev spaces[J]. Applied and Computational Harmonic Analysis, 2006, 20(1):357-374.

AMATO U, ANTONIADIS A,PENSKY M. Wavelet kernel penalized estimation for non-equispaced design regression [J]. Statistics and Computing, 2006, 16(1): 37-55.

RAKOTOMAMONJY A,CANU S. Frame, reproducing kernel, regularization and learning [J]. Journal of Machine Learning Research, 2005, 6(12): 1485-1515.

WALTER G G. A sample theorem for wavelet subspaces [J]. IEEE Trans Information Theory, 1992, 38(2):881-884.

MALLAT S. A theory for multiresolution signal decomposition: the wavelet representation [J]. IEEE Trans Pattern Anal Mach Intell, 1989, 11(7): 674-693.

GIROSI F. An equivalence between sparse approximation and support vector machines [J]. Neural Computation, 1998, 10(6):1455-1480.

CHAPELLE O,VAPNIK V. Model selection for support vector machines [M]∥Advances in Neural Information Processing Systems. Cambridge, MA, USA: MIT Press, 2000: 349-355.

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