Concept lattice compression in incomplete contexts based on K -medoids clustering
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ORIGINAL ARTICLE
Concept lattice compression in incomplete contexts based on K-medoids clustering Caiping Li • Jinhai Li • Miao He
Received: 26 November 2013 / Accepted: 11 July 2014 Ó Springer-Verlag Berlin Heidelberg 2014
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
C. Li M. He Department of Mathematics, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, People’s Republic of China e-mail: [email protected] M. He e-mail: [email protected] J. Li (&) Faculty of Science, Kunming University of Science and Technology, Kunming 650500, Yunnan, People’s Republic of China e-mail: [email protected]
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 e and K, and show the average rate of compression of approximate concept lattice. Keywords Incomplete context Approximate concept lattice Similarity measure K-medoids clustering Concept lattice compression
1 Introduction Formal concept analysis (FCA), proposed by Wille in 1982 [1], has been extended and developed by Wille and Ganter [2] and other scholars [3–5]. FCA is an efficient tool for data analysis and knowledge discovery. In this theory, the basic dataset is represented by a formal context which is defined as a binary relation between objects and attributes, and the basic output is generally described by a concept lattice which is a hierarchy of formal concepts. In fact, the concept lattice of a formal context reflects the relationship of specialization and generalization among formal concepts. Up to now, FCA has been applied to various fields such as data mining [6–8], knowledge discovery [9–13], information retrieval [14], and software engineering [15]. Since in general the number of nodes in the concept lattice of a formal context increases exponentially, a complicated concept lattice will be
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