Abstract
Taking the spirit of descriptive statistic methods data mining is viewed as a deductive science, no inductive generalizations or predicative assertions. We call this approach descriptive/deductive data mining (DDM) to stress spirit of descriptive statistic methods and the role of mathematical deductions.
Such a seemingly restrictive methodology, somewhat surprisingly, turns out to be quite far reaching. Previously, we have observed in ICDM02 that (1) Isomorphic relations have isomorphic patterns (classical association rules). This observation implies, from data mining prospect, that relations and patterns are syntactic in nature. We also have reported that (2) attributes or features (including un-interpreted ones) of a given relation can be enumerated mathematically, though, in intractable time. In this paper, we proved (3) generalized association rules (including un-interpreted rules) can be discovered by solving a finite set of integral linear inequalities within polynomial time.
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References
Agrawal, R., Imielinski, T., Swami, A.: Mining Association Rules Between Sets of Items in Large Databases. In: Proceeding of ACM-SIGMOD international Conference on Management of Data, Washington, DC, June 1993, pp. 207–216 (1993)
Birkhoff, G., MacLane, S.: A Survey of Modern Algebra. Macmillan, Basingstoke (1977)
Brualdi, R.A.: Introductory Combinatorics. Prentice-Hall, Englewood Cliffs (1992)
Cai, Y.D., Cercone, N., Han, J.: Attribute-oriented induction in relational databases. In: Knowledge Discovery in Databases, pp. 213–228. AAAI/MIT Press, Cambridge (1991)
Freund, J.E.: Modern Elementary Statistics. Prentice-Hall, Englewood Cliffs (1952)
Barr, A., Feigenbaum, E.A.: The handbook of Artificial Intelligence. William Kaufmann (1981)
Lee, T.T.: Algebraic Theory of Relational Databases. The Bell System Technical Journal 62(10), 3159–3204 (1983)
Lin, T.Y.: Database Mining on Derived Attributes. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 14–32. Springer, Heidelberg (2002)
Lin, T.Y.: Mathematical Foundation of Association Rules - Mining Generalized Associations by Integral Linear Inequalities. In: The Proceedings of Foundation of Data Mining and Discovery Workshop (which is part of IEEE international Conference on Data Mining), Maebashi, Japan, December 9-12, pp. 81–88 (2002)
Lin, T.Y.: Attribute (Feature) Completion – The Theory of Attributes from Data Mining Prospect. In: Proceeding of IEEE international Conference on Data Mining, Maebashi, Japan, December 9-12, pp. 282–289 (2002)
Lin, T.Y.: Data Mining and Machine Oriented Modeling: A Granular Computing Approach. Journal of Applied Intelligence 13(2), 113–124 (2000)
Lin, T.Y.: Attribute Transformations on Numerical Databases. In: Terano, T., Chen, A.L.P. (eds.) PAKDD 2000. LNCS, vol. 1805, pp. 181–192. Springer, Heidelberg (2000)
Lin, T.Y.: Data Mining: Granular Computing Approach. In: Zhong, N., Zhou, L. (eds.) PAKDD 1999. LNCS (LNAI), vol. 1574, pp. 24–33. Springer, Heidelberg (1999)
Lin, T.Y.: Granular Computing on Binary Relations I: Data Mining and Neighborhood Systems. In: Skoworn, A., Polkowski, L. (eds.) Rough Sets In Knowledge Discovery, pp. 107–121. Springer, Heidelberg (1998)
Liu, H., Motoda, H.: Feature Transformaion and Subset Selection. IEEE Intelligent Systems 13(2), 26–28 (1998)
Liu, H., Motoda, H. (eds.): Feature Extraction, Construction and Selection – A Data Mining Perspective. Kluwer Academic Pubihsers, Dordrecht (1998)
Motoda, H., Liu, H.: Feature Selection, Extraction and Construction. Communication of IICM (Institute of Information and Computing Machinery, Taiwan) 5(2), 67–72 (2002); Proceeding for the workshop “Toward the Foundation on Data Mining” in PAKDD 2002, May 6 (2002)
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Lin, T.Y. (2004). Mining Un-interpreted Generalized Association Rules by Linear Inequalities. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds) Rough Sets and Current Trends in Computing. RSCTC 2004. Lecture Notes in Computer Science(), vol 3066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25929-9_24
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DOI: https://doi.org/10.1007/978-3-540-25929-9_24
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