Abstract: Yuan et al use a 2nd-order polynomial as a smoothing function, and propose a smooth support vector machine based on 2nd-order polynomial. As a new smooth model, there are four problems: Can other 2nd-order polynomials be used as smoothing functions to obtain other smooth support vector machines? How many are there in this class of smooth model? Do these smooth models converge? Is the performance of classification improved? This paper addresses these problems by studying 2nd-order polynomials as smoothing functions and the resultant 2nd-order polynomial smooth support vector machines. Finally, it solves the above four problems.

Key words: classification, support vector machine, polynomial, smooth