Granular-conditional-entropy-based attribute reduction for partially labeled data with proxy labels

Attribute reduction is attracting considerable attention in the theory of rough sets, and thus many rough-set-based attribute reduction methods have been presented. However, most of them are specifically designed for either labeled or unlabeled data, whereas many real-world applications involve partial supervision. In this paper, we propose a rough-set based semi-supervised attribute reduction method for partially labeled data. Specifically, using prior class-distribution information, we first develop a simple yet effective strategy to produce proxy labels for unlabeled data. Then, the concept of information granularity is integrated into an information-theoretic measure, based on which, a novel granular conditional entropy measure is proposed, and its monotonicity is theoretically proved. Furthermore, a fast heuristic algorithm is provided to generate the optimal reduct of partially labeled data, which could accelerate the process of attribute reduction by removing irrelevant examples and simultaneously excluding redundant attributes. Extensive experiments conducted on UCI data sets demonstrate that the proposed semi-supervised attribute reduction method is promising and, in terms of classification performance, it even compares favorably with supervised methods on labeled and unlabeled data with true labels (Our code and experimental data are released at Mendeley Data https://doi.org/10. 17632/v3byhx2v8s.1). (c) 2021 Elsevier Inc. All rights reserved.