最小二乘支持向量机变型算法研究

推导出最小二乘支持向量机(LSSVM)的分类几何意义,再将近似支持向量机(PSVM)等价推广至回归问题,最后提出PSVM的另一种非线性模型--直接支持向量机(DSVM).与LSSVM相比,PSVM和DSVM增强了问题的凸性,计算复杂度低.且对非线性时,DSVM比PSVM更简单,替换核函数就可实现线性与非线性的统一.数值实验表明,线形情况下PSVM比LSSVM的训练速度至少快一倍,非线性时,DSVM比PSVM速度要快一倍左右;在泛化能力方面线性PSVM不低于LSSVM,非线性时DSVM最高.

Research on variations of least square support vector machine

The geometric meaning of the Least Square Support Vector Machine(LSSVM) for classification is presented. Then the Proximal Support Vector Machine(PSVM) is extended equivalently to the regression problem, and a new nonlinear model of PSVM, the so-called Direct Support Vector Machine(DSVM), is proposed. Compared with LSSVM, both PSVM and DSVM enforce the convexity of the problem and the computing complexity is small. But in the nonlinear case, DSVM is simpler than PSVM and the nonlinear model coincides with the linear, by substituting the kernel function. Numerical experiments show that, the linear PSVM is at least twice faster than the LSSVM, and that the nonlinear DSVM is about twice faster than the PSVM in terms of the training speed. The linear LSSVM and PSVM almost have the equal generalized abilities, but the DSVM has a higher one than the nonlinear PSVM.