尺度核函数在最小二乘支持向量机信号逼近中的应用

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%.

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

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 t...