In fields such as pattern recognition and computational intelligence, attribute subset selection has gradually attracted the attention of researchers as a challenging issue, particularly in big data. In rough sets community, many of the selection methods until now have been proposed based on one-directional and non-adaptive rough approximation sets, which increase the uncertainty of granular computing. Based on a series of bi-directional adaptive neighborhood rough sets models, a novel attribute subset selection method is proposed in this paper. In contrast to classical one-directional k-nearest neighborhood relations, the proposed model not only allocates different numbers of neighbors to each sample, but also takes the support information of the neighbors into account in the construction of information granularity. On the basis of set operators, two specific bi-directional neighborhood relations as well as optimistic and pessimistic rough set models are discussed in detail. Several propositions and uncertainty measures not only show the relationship between the traditional and the proposed models, but also present the intrinsic connection of three discussed models. In addition, we propose an optimal neighbor selection scheme, in which justifiable granularity is fused with evidence theory to obtain an optimal k value for each sample. Finally, in the attribute selection process, we prove non-monotonic property of the neighborhood entropy and describe an upgraded forward greedy algorithm. The proposed algorithm is compared with existing algorithms using a ten-fold cross-validation method on several UCI datasets. The experimental results show the advantages of our models in terms of computational performance and classification accuracy, respectively.
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