一种基于支持向量机的多分辨率信号逼近算法  

A Multiresolution Signal Approximation Algorithm Based on Support Vector Machine

作　　者：周亚同[1] 张太镒[1] 陈志刚[1] 

机构地区：[1]西安交通大学电子与信息工程学院,西安710049

出　　处：《西安交通大学学报》2006年第10期1083-1086,共4页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(90207012)

摘　　要：为了进一步提升多分辨率信号逼近算法(MSA)的逼近性能,提出了一种基于支持向量机(SVM)的信号多分辨率逼近算法(SVM-MSA).SVM-MSA以尺度子空间是再生核希尔伯特空间为前提,先在MSA中集成SVM的逼近准则并得到一个无约束规划,再引入松弛变量将无约束规划转化为约束规划,最后借助拉格朗日乘子法求解约束规划,获得逼近系数与逼近表达式.SVM-MSA不仅保留了MSA的多分辨率逐级逼近特点,而且兼具SVM良好的逼近准确度与平滑度.实验结果表明:在逼近sinc信号时,SVM-MSA具有比MSA更好的逼近准确度与平滑度;在噪声环境下,当输入信噪比大于约2 dB时,具有更强的稳健性.To further improve the approximation performance of multiresolution signal approximation （MSA） algorithm, a new MSA algorithm based on support vector machine （SVM）, named SVM-MSA is proposed. Under the premise that the scale subspaces are reproducing kernel Hilbert spaces, the proposed algorithm firstly integrates the approximation criterion of SVM into MSA, and then an unconstrained programming is derived. Following that, the unconstrained programming is reformulated as a constrained programming by introducing some slack variables. Finally, for solving the constrained programming the Lagrangian multiplier method is utilized to obtain the approximation coefficients and expressions. Theoretical analysis illustrates that SVMMSA not only preserves the MSA＇s characteristics of hierarchical approximation, but also has good approximation accuracy and smoothness that SVM holds. Experiments show that in approximating sinc signal the SVM-MSA has better approximation accuracy and smoothness than MSA. Furthermore, in the noise environment SVM-MSA has stronger robustness than MSA if input signal-noise-ratio is larger than about 2 dB.

关 键 词：多分辨率 支持向量机 逼近 再生核希尔伯特空间 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]