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Concept lattice compression in incomplete contexts based on K-medoids clustering

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Abstract

Incomplete contexts are a kind of formal contexts in which information about the relationship between some objects and attributes is not available or is lost. Knowledge discovery in incomplete contexts is of interest because such databases are frequently encountered in the real world. The existing work has proposed an approach to construct the approximate concept lattice of an incomplete context. Generally speaking, however, the huge nodes in the approximate concept lattice make the obtained conceptual knowledge difficult to be understood and weaken the efficiency of the related decision-making analysis as well. Motivated by this problem, this paper puts forward a method to compress the approximate concept lattice using K-medoids clustering. To be more concrete, firstly we discuss the accuracy measure of approximate concepts in incomplete contexts. Secondly, the similarity measure between approximate concepts is presented via the importance degrees of an object and an attribute. And then the approximate concepts of an incomplete context are clustered by means of K-medoids clustering. Moreover, we define the so-called K-deletion transformation to achieve the task of compressing the approximate concept lattice. Finally, we conduct some experiments to perform a robustness analysis of the proposed clustering method with respect to the parameters \(\varepsilon\) and K, and show the average rate of compression of approximate concept lattice.

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Acknowledgments

The authors would like to thank Editor-in-Chief and three anonymous reviewers for their valuable comments and helpful suggestions which lead to a significant improvement on the manuscript. This work was supported by the National Natural Science Foundation of China (Nos. 61305057 and 11371014) and the Natural Science Research Foundation of Kunming University of Science and Technology (No. 14118760).

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Authors and Affiliations

  1. Department of Mathematics, Baoji University of Arts and Sciences, Baoji, 721013, Shaanxi, People’s Republic of China

    Caiping Li & Miao He

  2. Faculty of Science, Kunming University of Science and Technology, Kunming, 650500, Yunnan, People’s Republic of China

    Jinhai Li

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  1. Caiping Li
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  2. Jinhai Li
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  3. Miao He
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Correspondence to Jinhai Li.

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Li, C., Li, J. & He, M. Concept lattice compression in incomplete contexts based on K-medoids clustering. Int. J. Mach. Learn. & Cyber. 7, 539–552 (2016). https://doi.org/10.1007/s13042-014-0288-3

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  • DOI: https://doi.org/10.1007/s13042-014-0288-3

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