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Imbalanced data learning is one of the most active and important fields in machine learning research. The existing class imbalance learning methods can make Support Vector Machines (SVMs) less sensitive to class imbalance; they still suffer from the disturbance of outliers and noise present in the datasets. A kind of Fuzzy Smooth Support Vector Machines (FSSVMs) are proposed based on the Smooth Support Vector Machine (SSVM) of O. L. Mangasarian. SSVM can be computed by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm or the Newton-Armijo algorithm easily. Two kinds of fuzzy memberships and three smooth functions can be chosen in the algorithms. The fuzzy memberships consider the contribution rate of each sample to the optimal separating hyperplane. The polynomial smooth functions can make the optimization problem more accurate at the inflection point. Those changes play the active effects on trials. The results of the experiments show that the FSSVMs can gain the better accuracy and the shorter time than the SSVMs and some of the other methods

Selecting the Optimal Combination Model of FSSVM for the Imbalance Datasets