Attribute reduction in formal decision contexts and its application to finite topological spaces

Abstract

Attribute reduction in formal decision contexts has become one of the key issues in the research and development of formal concept analysis (FCA) and its applications. As far as we know, however, most of the existing reduction methods for formal decision contexts are time-consuming especially for the large-scale data. This paper investigates the attribute reduction method for large-scale formal decision contexts. The computation of a discernibility matrix is an important step in the development of the corresponding reduction method. A simple and powerful method to efficiently calculate the discernibility matrix of formal decision contexts is first presented. In addition, a heuristic algorithm for searching the optimal reduct is then proposed. Thirdly, as an application of the new results, we discuss the problem of finding the minimal subbases of finite topological spaces. It has shown that the method of attribute reduction in formal decision contexts can be used to obtain all the minimal subbases of a finite topological space. Furthermore, we present an algorithm for computing the minimal subbase of a topological space, based on the attribute reduction method proposed in this paper. Finally, two groups of experiments are carried out on some large-scale data sets to verify the effectiveness of the proposed algorithms.

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Acknowledgements

We would like to thank the referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (Nos. 61170107, 61672272 and 11871259), the Natural Science Foundation of Fujian Province (Nos. 2017J01507 and 2018J01548), the Natural Science Foundation of Hebei Province (Nos. A2018205103, F2018205196 and CXZZBS2019076) and the Foundation of Minnan Normal University (No. L11802).

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Correspondence to Jinkun Chen.

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Chen, J., Mi, J., Xie, B. et al. Attribute reduction in formal decision contexts and its application to finite topological spaces. Int. J. Mach. Learn. & Cyber. 12, 39–52 (2021). https://doi.org/10.1007/s13042-020-01147-x

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Keywords

  • Attribute reduction
  • Formal decision contexts
  • Subbases
  • Topological spaces