摘要
基于小波对偶框架和支持向量核函数的条件,提出了一种支持向量小波核函数.该核函数利用小波的多尺度插值特性和稀疏变化特性,不仅提高了模型的精度和迭代的收敛速度,而且还适用于信号的局部分析、信噪分离和突变信号的检测,从而在提高支持向量机(SVM)泛化能力的同时,提高了辨识效果和减少了计算量.基于该核函数和正则化理论提出的最小二乘小波支持向量机用于非线性系统辨识,对SINC函数的逼近,该小波核得到的均方根误差不足高斯径向基核的1/12,对logistic混沌序列预测的均方根误差不超过8×10-6,同时实验表明,预测的长度对预测均方根误差没有显著影响,这表明小波核SVM具有更好的泛化能力.
A wavelet kernel for support vector machine （SVM） based on wavelet dual frame theory and conditions of constructing SVM kernel is presented, where the accuracy and convergent rate of the model are improved, the generalization ability of the SVM and the recognition efficiency are enhanced, and computation burden is weakened. According to the wavelet kernel function and the regularization theory, a least square wavelet support vector machine （LS-WSVM） is proposed to greatly simplify the solving process of SVM. The LS-WSVM is then applied to the nonlinear system identification to test the validity of the wavelet kernel function. In function SINC regression simulation, the mean square error（MSE） is no more than 1/12 of radial base function kernel. In logistic chaos sequence prediction, the MSE is no morethan 8 ×10^-6, meanwhile, the MSE does not increase while increasing the predicting length, which verifies the better generalization ability, especially for local signal analysis, signal-noise separation and detection of jumping signals.
出处
《西安交通大学学报》
EI
CAS
CSCD
北大核心
2005年第8期816-819,共4页
Journal of Xi'an Jiaotong University
基金
国家自然科学基金资助项目(60276037).
关键词
小波核
混沌
支持向量机
泛化能力
wavelet kernel
chaos
support vector machine
predictive ability
