Attribute reduction with fuzzy kernel-induced relations

Fuzzy rough sets have strong ability in dealing with data uncertainty, which have been widely applied in attribute reduction problems. Fuzzy relations are the cornerstones of fuzzy rough sets, and kernel-induced relations can simultaneously reflect the similarities of objects in both original space and high-dimensional Hilbert space. However, existing distance-based fuzzy relations (even kernel-induced) cannot truly reflect the correlations of objects under complex data distributions. To obtain better expressing ability for data, we propose a general optimization framework to get the memberships of objects with respect to categories. Considering various complex data distributions, the concepts of intra-class aggregation degree based on membership and inter-class dispersion degree based on nonmembership are proposed, and a separability measure is constructed to evaluate the importance of attributes to decisions. Correspondingly, a new attribute reduction algorithm is proposed, with a forward evaluation L-step strategy to skip local fluctuations in classification accuracy. Finally, we conduct a series of experiments to verify the effectiveness of the proposed algorithm. From the experiments on UCI, ELVIRA and face recognition datasets, it can be seen that the attribute subset obtained by the proposed algorithm not only has high classification accuracy and computational efficiency, but also has fewer attributes.