Abstract
The relations of the logical calculi of association rules and of the measures of the interestingness of association rules are studied. The logical calculi of association rules, 4ft-quantifiers, and known classes of association rules are briefly introduced. New 4ft-quantifiers and association rules are defined by the application of suitable thresholds to known measures of interestingness. It is proved that some of the new 4ft-quantifiers are related to known classes of association rules with important properties. It is shown that new interesting classes of association rules can be defined on the basis of other new 4ft-quantifiers and several results concerning new classes are proved. Open problems are introduced.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hébert, C., Crémilleux, B.: A Unified View of Objective Interestingness Measures. In: Perner, P. (ed.) MLDM 2007. LNCS (LNAI), vol. 4571, pp. 533–547. Springer, Heidelberg (2007)
Hilderman, R., Hamilton, H.: Knowledge Discovery and Measures of Interest, p. 162. Kluwer Academic Publishers, Dordrecht (2001)
Geng, L., Hamilton, H.J.: Interestingness Measures for Data Mining: A survey. ACM Computing Surveys 38(33) (2006)
Pang-Ning, T., Kumar, V., Srivastava, J.: Selecting the Right Objective Measure for Association Analysis. Information Systems 29(4), 293–313 (2004)
Piatetski-Shapiro, G.: Discovery, Analysis, and Presentation of Strong Rules. In: Knowledge Discovery in Databases, pp. 229–248. AAI/MIT Press (1991)
Rauch, J., M. Šimunek, M.: An Alternative Approach to Mining Association Rules. In: Lin, T., et al. (eds.) Data Mining: Foundations, Methods, and Applications, pp. 219–238. Springer, Heidelberg (2005)
Ralbovský, M., Kuchař, T.: Using Disjunctions in Association Mining. In: Perner, P. (ed.) ICDM 2007. LNCS (LNAI), vol. 4597, pp. 339–351. Springer, Heidelberg (2007)
Agraval, R., Imielinski, T., Swami, A.N.: Mining Association Rules between Sets of Items in Large Databases. In: Proc. of the ACM-SIGMOD 1993 Int. Conference on Management of Data, Washington, D.C., pp. 207–216 (1993)
Hájek, P., Havránek, T.: Mechanising Hypothesis Formation - Mathematical Foundations for a General Theory. Springer, Heidelberg (1978)
Rauch, J.: Ein Beitrag zu der GUHA Methode in der dreiwertigen Logik. Kybernetika 11, 101–113 (1975)
Rauch, J.: Logical Foundations of Hypothesis Formation from Databases. Mathematical Institute of the Czechoslovak Academy of Sciences, Prague, Czech Republic, Dissertation (1986) (in Czech)
Rauch, J.: Logical Calculi for Knowledge Discovery in Databases. In: Komorowski, J., Żytkow, J.M. (eds.) PKDD 1997. LNCS, vol. 1263, pp. 47–57. Springer, Heidelberg (1997)
Rauch, J.: Classes of Four-Fold Table Quantifiers. In: Zytkow, J., Quafafou, M. (eds.) PKDD 1998. LNCS, vol. 1510, pp. 203–211. Springer, Heidelberg (1998)
Rauch, J.: Logic of Association Rules. Applied Intelligence 22, 9–28 (2005)
Rauch, J.: Definability of Association Rules in Predicate Calculus. In: Lin, T.Y., Ohsuga, S., Liau, C.J., Hu, X. (eds.) Foundations and Novel Approaches in Data Mining, pp. 23–40. Springer, Heidelberg (2005)
Rauch, J.: Observational Calculi, Classes of Association Rules and F-property. In: Granular Computing 2007, pp. 287–293. IEEE Computer Society Press, Los Alamitos (2007)
Rauch, J.: Classes of Association Rules - an Overview. In: Lin, T., et al. (eds.) Datamining: Foundations and Practice. Studies in Computational Intelligence, vol. 118, pp. 283–297. Springer, Heidelberg (2008)
Rauch, J.: Definability of Association Rules and Tables of Critical Frequencies. In: Lin, T., et al. (eds.) Datamining: Foundations and Practice. Studies in Computational Intelligence, vol. 118, pp. 299–321. Springer, Heidelberg (2008)
Rauch, J.: Measures of Interestingness and Classes of Association Rules. Accepted for Foundations of Data Mining, ICDM 2008 Workshop (2008)
Rauch, J.: Contribution to Logical Foundations of KDD. Faculty of Informatics and Statistics, University of Economics Prague, Czech Republic, Assoc. Prof. Thesis (1998) (in Czech)
Burian, J.: Data Mining and AA (Above Average) Quantifier. In: Svátek, V. (ed.) Proceedings of Znalosti 2003. TU Ostrava, Ostrava (2003) (in Czech)
Chrz, M.: Transparent Deduction Rules for the GUHA Procedures Diploma thesis. Faculty of Mathematics and Physics. Charles University in Prague, p. 63 (2007)
Hájek, P., Havránek, T., Chytil, M.: GUHA Method. Academia, Prague (1983) (in Czech)
Hájek, P., Holeňa, M., Rauch, J.: The GUHA Method and Foundations of (Relational) Data Mining. In: de Swart, H., Orłowska, E., Schmidt, G., Roubens, M., et al. (eds.) Theory and Applications of Relational Structures as Knowledge Instruments. LNCS, vol. 2929, pp. 17–37. Springer, Heidelberg (2003)
Mendelson, E.: Introduction to Mathematical Logic. Princeton, D. Van Nostrand Company, Inc. (1964)
Rauch, J., Šimunek, M.: Semantic Web Presentation of Analytical Reports from Data Mining – Preliminary Considerations. In: Web Intelligence, pp. 3–7. IEEE Computer Society, Los Alamitos (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Rauch, J. (2010). Logical Aspects of the Measures of Interestingness of Association Rules. In: Koronacki, J., Raś, Z.W., Wierzchoń, S.T., Kacprzyk, J. (eds) Advances in Machine Learning II. Studies in Computational Intelligence, vol 263. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05179-1_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-05179-1_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05178-4
Online ISBN: 978-3-642-05179-1
eBook Packages: EngineeringEngineering (R0)