Smooth SVM research: A polynomial-based approach

Classification can be promoted by using SVM to acquire hypersurface due to the direct induction of the support vectors. In traditional SVM solution algorithms, objective function is a strictly convex unconstrained optimization problem and it is not differentiable, so it can not use the most used optimization method to solve the problem. The undifferential model could be converted into a differential one by using polynomial to approximate the plus function x₊. This paper gives the procedure of using cubic spline interpolation and Hermite interpolation method to deduce the quadratic polynomial smoothing the plus function x₊, it also presents a new smooth technology using circular arc polynomial. The proposed approach is experimentally evaluated in three datasets that are benchmarks for data mining applications, leading to interesting results.