On Horn Axiomatizations for Sequential Data
We propose a notion of deterministic association rules for ordered data. We prove that our proposed rules can be formally justified by a purely logical characterization, namely, a natural notion of empirical Horn approximation for ordered data which involves background Horn conditions; these ensure the consistency of the propositional theory obtained with the ordered context. The main proof resorts to a concept lattice model in the framework of Formal Concept Analysis, but adapted to ordered contexts. We also discuss a general method to mine these rules that can be easily incorporated into any algorithm for mining closed sequences, of which there are already some in the literature.
KeywordsAssociation Rule Input Sequence Closure Operator Minimal Generator Concept Lattice
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- 2.Balcázar, J.L., Baixeries, J.: Discrete deterministic datamining as knowledge compilation. In: Workshop on Discrete Mathematics and Data Mining, in SIAM Int. Conf. (2003)Google Scholar
- 3.Cadoli, M.: Knowledge compilation and approximation: Terminology, questions, references. In: AI/MATH 1996, 4th. Int. Symposium on Artificial Intelligence and Mathematics (1996)Google Scholar
- 4.Casas-Garriga, G.: Towards a formal framework for mining general patterns from structured data. In: Workshop Multi-relational Datamining in KDD Int. Conf. (2003)Google Scholar
- 5.Casas-Garriga, G.: Statistical strategies to remove all the uniteresting association rules. In: Proceedings of 16th European Conference on Artificial Intelligence, pp. 430–435 (2004)Google Scholar
- 7.Ganter, B., Wille, R.: Formal Concept Analysis. Mathematical Foundations. Springer, Heidelberg (1998)Google Scholar
- 9.Pasquier, N., Bastide, Y., Taouil, R., Lakhal, L.: Closed set based discovery of small covers for association rules. In: Proceedings of the 15th Int. Conference on Advanced Databases, pp. 361–381 (1999)Google Scholar
- 10.Pfaltz, J.L., Taylor, C.M.: Scientific knowledge discovery through iterative transformations of concept lattices. In: Workshop on Discrete Mathematics and Data Mining in SIAM Int. Conf., pp. 65–74 (2002)Google Scholar
- 12.Wang, J., Han, J.: BIDE: Efficient mining of frequent closed sequences. In: Proceedings of the 19th Int. Conference on Data Engineering, pp. 79–90 (2003)Google Scholar
- 13.Yan, X., Han, J., Afshar, R.: Clospan: Mining closed sequential patterns in large datasets. In: Proceedings of the Int. Conference SIAM Data Mining (2003)Google Scholar
- 14.Zaki, M.: Generating non-redundant association rules. In: Proceedings of the 6th Int. Conference on Knowledge Discovery and Data Mining, pp. 34–43 (2000)Google Scholar
- 15.Zaki, M., Ogihara, M.: Theoretical foundations of association rules. In: Workshop on Research Issues in Data Mining and Knowledge Discovery in SIGMOD-DMKD Int. Conf. (1998)Google Scholar