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Research on Two Main Construction Methods of Concept Lattices

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Abstract

Because of the completeness of concept lattices, the time complexity of constructing concept lattices has become the main factor affecting the application of formal concept analysis (FCA). The key problems in the research of concept lattices are how to improve the generation efficiency and how to reduce the space and time complexity of constructing concept lattices. So far, reviews on lattice construction algorithms have not been comprehensive. In view of this situation, we give a detailed review on two categories of construction algorithms: batch methods and incremental methods. The first category is a formal context that cannot be updated once the concept lattice has been constructed; the second category is a formal context that can be updated after a new object being added to the formal context. We briefly introduce classical and improved construction methods, illustrate the deficiencies of some algorithms and point out the improvements of the follow-up algorithms. Furthermore, we compare and discuss several key algorithms, and also pay attention to the application of concept lattices. Finally, two further research directions of concept lattices are proposed, including parallel construction methods of concept lattices and research of heterogeneous data concept lattices.

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Authors and Affiliations

  1. School of Computer Engineering and Science, Shanghai University, Shanghai, 200444, China

    Ying Dong  (董颖), Yue Wu  (吴悦) & Zongtian Liu  (刘宗田)

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  1. Ying Dong  (董颖)
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  2. Yue Wu  (吴悦)
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  3. Zongtian Liu  (刘宗田)
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Correspondence to Ying Dong  (董颖).

Additional information

Foundation item: the National Natural Science Foundation of China (No. 61273328), and the National Key Foundation for Exploring Scientific Instrument of China (No. 51227803)

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Dong, Y., Wu, Y. & Liu, Z. Research on Two Main Construction Methods of Concept Lattices. J. Shanghai Jiaotong Univ. (Sci.) 24, 243–253 (2019). https://doi.org/10.1007/s12204-019-2058-6

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  • DOI: https://doi.org/10.1007/s12204-019-2058-6

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