Abstract
Formal concept analysis has become an active field of study for data analysis and knowledge discovery. A formal concept C is determined by its extent (the set of objects that fall under C) and its intent (the set of properties or attributes covered by C). The intent for C, also called a closed itemset, is the maximum set of attributes that characterize C. The minimal generators for C are the minimal subsets of C’s intent which can similarly characterize C. This paper introduces the s uccinct s ystem of m inimal g enerators (SSMG) as a minimal representation of the minimal generators of all concepts, and gives an efficient algorithm for mining SSMGs. The SSMGs are useful for revealing the equivalence relationship among the minimal generators, which may be important for medical and other scientific discovery; and for revealing the extent-based semantic equivalence among associations. The SSMGs are also useful for losslessly reducing the size of the representation of all minimal generators, similar to the way that closed itemsets are useful for losslessly reducing the size of the representation of all frequent itemsets. The removal of redudancies will help human users to grasp the structure and information in the concepts.
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References
Agrawal, R., et al.: Mining association rules between sets of items in large databases. In: SIGMOD 1993 (1993)
Alon, U., et al.: Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc. Nat. Academy of Sciences of the United States of American 96, 6745–675 (1999)
Boulicaut, J.-F., et al.: Free-sets: A condensed representation of boolean data for the approximation of frequency queries. Data Mininig and Knowledge Discovery 7(1), 5–22 (2003)
Burdick, D., et al.: MAFIA: A maximal frequent itemset algorithm for transactional databases. In: ICDE 2001 (2001)
Calders, T., Goethals, B.: Mining all non-derivable frequent itemsets. In: PKDD 2002 (2002)
Dong, G., Li, J.: Efficient mining of emerging patterns: Discovering trends and differences. In: KDD 1999 (1999)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)
Hereth, J., et al.: Conceptual knowledge discovery and data analysis. In: Int. Conf. on Conceptual Structures, pp. 421–437 (2000)
Mineau, G., Ganter, B. (eds.): Proc. Int. Conf. on Conceptual Structures. LNCS, vol. 1867. Springer, Heidelberg (2000)
Pasquier, N., et al.: Discovering frequent closed itemsets for association rules. In: ICDT 1999 (1999)
Pei, J., et al.: CLOSET: An efficient algorithm for mining frequent closed itemsets. In: ACM SIGMOD DMKD 2000 (2000)
Pfaltz, J.L., Taylor, C.M.: Closed set mining of biological data. In: BIOKDD 2002 (2002)
Rymon, R.: Search through systematic set enumeration. In: Proc. of Int’l Conf. on Principles of Knowledge Representation and Reasoning, Cambridge MA, pp. 539–550 (1992)
Wang, J., et al.: Closet+: Searching for the best strategies for mining frequent closed itemsets. In: KDD 2003 (2003)
Zaki, M., Hsiao, C.: CHARM: An efficient algorithm for closed itemset mining. In: SDM 2002 (2002)
Zaki, M.J.: Generating non-redundant association rules. In: KDD 2000 (2000)
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© 2005 Springer-Verlag Berlin Heidelberg
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Dong, G., Jiang, C., Pei, J., Li, J., Wong, L. (2005). Mining Succinct Systems of Minimal Generators of Formal Concepts. In: Zhou, L., Ooi, B.C., Meng, X. (eds) Database Systems for Advanced Applications. DASFAA 2005. Lecture Notes in Computer Science, vol 3453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11408079_17
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DOI: https://doi.org/10.1007/11408079_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25334-1
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