Fuzzy smooth support vector machine with different smooth functions

Smooth support vector machine (SSVM) changs the normal support vector machine (SVM) into the unconstrained optimization by using the smooth sigmoid function. The method can be solved under the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm and the Newdon-Armijio (NA) algorithm easily, however the accuracy of sigmoid function is not as good as that of polynomial smooth function. Furthermore, the method cannot reduce the influence of outliers or noise in dataset. A fuzzy smooth support vector machine (FSSVM) with fuzzy membership and polynomial smooth functions is introduced into the SVM. The fuzzy membership considers the contribution rate of each sample to the optimal separating hyperplane and makes the optimization problem more accurate at the inflection point. Those changes play a positive role on trials. The results of the experiments show that those FSSVMs can obtain a better accuracy and consume the shorter time than SSVM and lagrange support vector machine (LSVM).