基于压缩感知的多尺度最小二乘支持向量机

摘要

A multi-scale least squares support vector machine (LS-SVM) based on compressive sensing (CS) and multi-resolution analysis (MRA) is proposed. First, a multi-scale LS-SVM model is conducted, in which a support vector kernel with the multi-resolution wavelet function is employed; then inspired by CS theory, sparse support vectors of multi-scale LS-SVM are constructed via least squares orthogonal matching pursuit (LS-OMP); finally, sparse support vectors are applied to function approximation. Simulation experiments demonstrate that the proposed method can estimate diverse details of signal by means of wavelet kernel with different scales. What is more, it can achieve good generalization performance with fewer support vectors, reducing the operation cost greatly, performing more superiorly compared to ordinary LS-SVM.%提出一种基于压缩感知(Compressive sensing, CS)和多分辨分析(Multi-resolution analysis, MRA)的多尺度最小二乘支持向量机(Least squares support vector machine, LS-SVM)。首先将多尺度小波函数作为支持向量核,推导出多尺度最小二乘支持向量机模型,然后基于压缩感知理论,利用最小二乘匹配追踪(Least squares orthogonal matching pursuit, LS-OMP)算法对多尺度最小二乘支持向量机的支持向量进行稀疏化,最后用稀疏的支持向量实现函数回归。实验结果表明,本文方法利用不同尺度小波核逼近信号的不同细节,而且以比较少的支持向量能达到很好的泛化性能,大大降低了运算成本,相比普通最小二乘支持向量机,具有更优越的表现力。