Feature selection based on robust fuzzy rough sets using kernel-based similarity and relative classification uncertainty measures

The current research on fuzzy rough sets (FRSs) for feature selection has two major problems. On the one hand, most existing methods employ multiple intersection operations of fuzzy relations to define fuzzy dependency functions applied to feature selection. These operations can make the evaluation of the significance of feature subsets less identifiable in high-dimensional data space. On the other hand, the classical FRS implemented for feature selection is highly sensitive to noisy information. Thus, improving the robustness of the FRS model is critical. To address the above issues, first, we propose a radial basis function kernel-based similarity measure for computing fuzzy relations. The value difference metric and Euclidean metric are utilized to measure the distance values of the mixed symbolic and real-valued features. Hereafter, a novel robust FRS model is proposed by introducing the relative classification uncertainty (RCU) measure. k-nearest neighbours and Bayes rules are employed to yield an RCU level. Relative noisy information is detected in this way. Finally, extensive experiments are conducted to illustrate the effectiveness and robustness of the proposed model.