Abstract: 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.

Key words: linear equation, least square approximation, classification, regression analysis, proximal support vector machine