Robust classifier learning with fuzzy class labels for large-margin support vector machines

Using class label fuzzification, this study develops the idea of refreshing the attitude of the difficult training examples and gaining a more robust classifier for large-margin support vector machines (SVMs). Fuzzification relaxes the specific hard-limited Lagrangian constraints of the difficult examples, extends the infeasible space of the canonical constraints for optimization, and reconfigures the consequent decision function with a wider margin. With the margin, a classifier capable of achieving a high generalization performance can be more robust. This paper traces the rationale for such a robust performance back to the changes of governing loss function. From the aspect of loss function, the reasons are causally explained. In the study, we also demonstrate a two-stage system for experiments to show the changes corresponding to the label fuzzification. The system first captures the difficult examples in the first-stage preprocessor, and assigns them various fuzzified class labels. Three types of membership functions, including a constant, a linear, and a sigmoidal membership function, are designated in the preprocessor to manipulate the within-class correlations of the difficult examples for reference of the fuzzification. The consequent performance benchmarks confirm the robust and generalized ability due to the label fuzzification. Since the change of y"i^' is fundamental, the idea may be transplanted to different prototypes of SVM.