Abstract
Retrieval of structured cases using similarity has been studied in CBR but there has been less activity on defining similarity on description logics (DL). In this paper we present an approach that allows us to present two similarity measures for feature logics, a subfamily of DLs, based on the concept of refinement lattice. The first one is based on computing the anti-unification (AU) of two cases to assess the amount of shared information. The second measure decomposes the cases into a set of independent properties, and then assesses how many of these properties are shared between the two cases. Moreover, we show that the defined measures are applicable to any representation language for which a refinement lattice can be defined. We empirically evaluate our measures comparing them to other measures in the literature in a variety of relational data sets showing very good results.
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
Aït-Kaci, H., Podelski, A.: Towards a meaning of life. Technical Report 11, Digital Research Laboratory (1992)
Arcos, J.L.: The Noos representation language. PhD thesis, Universitat Politècnica de Catalunya (1997)
Armengol, E., Plaza, E.: Relational case-based reasoning for carcinogenic activity prediction. Artif. Intell. Rev. 20(1-2), 121–141 (2003)
Bergmann, R., Stahl, A.: Similarity measures for object-oriented case representations. In: Smyth, B., Cunningham, P. (eds.) EWCBR 1998. LNCS (LNAI), vol. 1488, pp. 8–13. Springer, Heidelberg (1998)
Bisson, G.: Learing in fol with a similarity measure. In: Proceedings of AAAI 1992, pp. 82–87 (1992)
Borgida, A., Walsh, T., Hirsh, H.: Towards measuring similarity in description logics. In: Horrocks, I., Sattler, U., Wolter, F. (eds.) Proceedings of the 2005 International Workshop on Description Logics (DL 2005), Edinburgh, Scotland, UK, July 26-28. CEUR Workshop Proceedings, vol. 147, CEUR-WS.org (2005)
Börner, K.: Structural similarity as a guidance in case-based design. In: Haton, J.-P., Manago, M., Keane, M.A. (eds.) EWCBR 1994. LNCS, vol. 984, pp. 197–208. Springer, Heidelberg (1994)
Carpenter, B.: Typed feature structures: an extension of first-order terms. In: Saraswat, V., Ueda, K. (eds.) Proceedings of the International Symposium on Logic Programming, San Diego, pp. 187–201 (1991)
López De Mántaras, R.: A distance-based attribute selection measure for decision tree induction. Mach. Learn. 6(1), 81–92 (1991)
Emde, W., Wettschereck, D.: Relational instance based learning. In: Saitta, L. (ed.) Proceedings of 13th International Conference on Machine Learning, pp. 122–130. Morgan Kaufmann Publishers, San Francisco (1996)
Hinton, G.E.: Learning distributed representations of concepts. In: Proceedings of CogSci. (1986)
Hutchinson, A.: Metrics on terms and clauses. In: van Someren, M., Widmer, G. (eds.) ECML 1997, vol. 1224, pp. 138–145. Springer, Heidelberg (1997)
Kramer, S., Lavrač, N., Flach, P.: Propositionalization approaches to relational data mining, pp. 262–286 (2000)
van der Laag, P.R.J., Nienhuys-Cheng, S.-H.: Subsumption and refinement in model inference. Technical report (1992)
Larson, J., Michalski, R.S.: Inductive inference of vl decision rules. SIGART Bull. (63), 38–44 (1977)
Lavrač, N., Džeroski, S.: Inductive Logic Programming. Techniques and Applications. Ellis Horwood (1994)
Mitchell, T.: Generalization as search. Artificial Intelligence 18(2), 203–226 (1982)
Plaza, E., Armengol, E., Ontañón, S.: The explanatory power of symbolic similarity in case-based reasoning. Artif. Intell. Rev. 24(2), 145–161 (2005)
Plotkin, G.D.: A note on inductive generalization. Machine Intelligence 5 (1970)
Quinlan, J.R.: Induction of decision trees. Machine Learning 1(1), 81–106 (1986)
Shapiro, E.Y.: Inductive inference of theories from facts. Technical Report 624, Department of Computer Science, Yale University (1981)
Horváth, T., Wrobel, S., Bohnebeck, U.: Relational instance-based learning with lists and terms. Machine Learning 43(1-2), 53–80 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ontañón, S., Plaza, E. (2009). On Similarity Measures Based on a Refinement Lattice. In: McGinty, L., Wilson, D.C. (eds) Case-Based Reasoning Research and Development. ICCBR 2009. Lecture Notes in Computer Science(), vol 5650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02998-1_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-02998-1_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02997-4
Online ISBN: 978-3-642-02998-1
eBook Packages: Computer ScienceComputer Science (R0)