Granular matrix method of attribute reduction in formal contexts
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METHODOLOGIES AND APPLICATION
Granular matrix method of attribute reduction in formal contexts Yidong Lin1,2 · Jinjin Li2
· Hongkun Wang3
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Granular reduction has been of great interests for formal context analysis. From the perspective of granular computing, granular matrices are proposed to represent the extensions and intensions of formal concepts. Within this framework, irreducible elements are studied. Furthermore, similarity degree, information granular and information entropy are developed to specify the significance of attribute. In this case, heuristic approaches for granular reduct are proposed. Finally, several data sets are experimented to demonstrate the feasibility and efficiency of our method. Our methods present a new framework for granular reduction in formal concept analysis. Keywords Formal contexts · Granular reduction · Irreducible elements · Matrix method
1 Introduction Formal concept analysis (FCA) is a theoretical framework for data analysis and knowledge processing put forward by Wille (Ganter and Wille 1999; Will 2005). It has turn into an meaningful mathematical model in knowledge discovery in recent years. Formal context as well as formal concept lattice are two main notions of FCA. The latter is the set of all concepts derived from the former. Up to present, this theory has been successfully applied to many scientific issues (Carpineto and Romano 1996; Deng et al. 2017, 2019; Ganter and Wille 1999; Fenza and Senatore 2010; Huang et al. 2017; Hao et al. 2018; Lang et al. 2017; Ma et al. 2014, 2017; Rajapakse and Denham 2006; Valtchev et al. 2004; Wille 2002; Yang and Hu 2018; Zhao et al. 2019). It is known that knowledge reduction in FCA has attracted much interests, and many approaches have been formulated to it (Ch et al. 2015; Dias and Vieira 2015, 2017; Huang et al. 2016; Kardo˘s et al. 2016; Kumar and Srinivas 2010; Li et al. 2011a, b, 2012a, b, 2016, 2017b; Martin et al. 2013; Communicated by V. Loia.
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Jinjin Li [email protected]
1
School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
2
School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China
3
Georgetown University, Washington, DC 20057, USA
Ma et al. 2014; Qi 2009; Shao et al. 2014; Shao and Leung 2014; Wei et al. 2008; Zhang et al. 2005a). Generally speaking, knowledge reduction for concept lattice mainly focuses on concept reduction and attribute reduction. The former is to find the minimal contextual structure to maintain the structure consistency and avoid redundancy. For instance, Ch et al. (2015) addressed this issue in terms of non-negative matrix factorization. Dias and Vieira (2015) divided concept lattice reduction into three groups. Attribute reduction is another pertinent issue in FCA. In this case, the kernel is to search a minimal attribute subset by which some predefined properties are preserved, and remove non-essential attributes from the formal contexts. Ganter and Wille (1999)
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