Abstract:

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).