USING FRINGES FOR MINIMAL CONCEPTUAL DECOMPOSITION OF BINARY CONTEXTS

Ali Jaoua (), Mohamed Salah, Sadok Ben Yahia and Jihad M. Al-Ja'am
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Ali Jaoua: Computer Science and Engineering Department, College of Engineering, Qatar University, P.O. Box 2713, Doha, Qatar
Mohamed Salah: Computer Science and Engineering Department, College of Engineering, Qatar University, P.O. Box 2713, Doha, Qatar
Sadok Ben Yahia: University of Al-Manar, Faculty of Sciences of Tunis, Department of Computer Science, Le belvedere, 2092, Tunis, Tunisia
Jihad M. Al-Ja'am: Computer Science and Engineering Department, College of Engineering, Qatar University, P.O. Box 2713, Doha, Qatar

New Mathematics and Natural Computation (NMNC), 2012, vol. 08, issue 03, 385-394

Abstract: Extracting knowledge from huge data in a reasonable time is still a challenging problem. Most real data (structured or not) can be mapped to an equivalent binary context, with or without using a scaling method, as for extracting associations between words in a text, or in machine learning systems. In this paper, our objective is to find a minimal coverage of a relation${\mathcal R}$with formal concepts. The problem is known to be NP-complete.1In this paper, we exploit a particular difunctional relation embedded in any binary relation${\mathcal R}$, the fringe of${\mathcal R}$, to find an approximate conceptual coverage of${\mathcal R}$. We use formal properties of fringes to find better algorithms calculating the minimal rectangular coverage of binary relation. Here, a formal context is considered as a binary relation. By exploiting some background on relational algebra in the present work, we merge some results of Belohlavek and Vichodyl,2using formal concept analysis with previous results obtained by Kcherifet al.3using relational algebra. We finally propose decomposition algorithms based on the relational formalization and fringe relations.

Keywords: Fringe relations; non enlargeable rectangles; minimal coverage; knowledge extraction (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1142/S1793005712500093

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