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Constructing lattice based on irreducible concepts

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Abstract

The construction of concept lattices is one of the key issues of formal concept analysis. Many methods and algorithms are proposed to build a lattice, among which, incremental algorithms are more appropriate in real-life applications that work with dynamic datasets. But they cost much time to locate generators before generating a real concept. The batch algorithms generate concepts quickly. However, they ignore the procedure of building lattice relationship. In this paper, we build the lattice from meet-irreducible attribute concepts by using generators directly, and make optimizations in key steps. We yield the relationship among concepts during the generating process that saves much time in contrast to other batch algorithms. In addition to proving the correctness of our algorithm, we evaluate its performance on some real datasets and compare it with an incremental algorithm called FastAddIntent. The results show that our algorithm mainly depends on the numbers of concepts and the numbers of attributes, which achieves good performance, especially to large formal contexts.

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Acknowledgments

This work was supported by Grants from the National Natural Science Foundation of China (Nos. 61173181, 61272021, 61363056, 61573321, 61673396), National Social Science Foundation of China (No. 14XXW004), Shandong Provincial Natural Science Foundation (No. 2015ZRE28145), the Fundamental Research Funds for the Central Universities (Nos. 15CX02049A, 15CX02119A).

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Authors and Affiliations

  1. College of Computer and Communication Engineering, China University of Petroleum (East China), Qingdao, 266580, China

    Xin Li & Ming-Wen Shao

  2. College of Computer Science and Software, Shenzhen University, Shenzhen, 518060, China

    Xing-Min Zhao

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  1. Xin Li
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Correspondence to Ming-Wen Shao.

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Li, X., Shao, MW. & Zhao, XM. Constructing lattice based on irreducible concepts. Int. J. Mach. Learn. & Cyber. 8, 109–122 (2017). https://doi.org/10.1007/s13042-016-0587-y

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