Abstract
A classification method based on a measure of analogical dissimilarity has been proposed some years ago by Laurent Miclet and his colleagues, which was giving very good results. We restart this study on a slightly different basis. Instead of estimating analogical dissimilarity, we use the logical definition of an analogical proportion. We also consider other related logical proportions and their link with analogical proportion. The paper reports on an ongoing work and contributes to a comparative study of the logical proportions predictive accuracy on a set of standard benchmarks coming from UCI repository. Logical proportions constitute an interesting framework to deal with binary and/or nominal classification tasks without introducing any metrics or numerical weights.
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
Notes
- 1.
\(\overline{a}\) is a compact notation for the negation of \(a\) and \(a\overline{b}\) is short for \(a\wedge \overline{b}\), and so on.
References
Bache, K., Lichman, M.: UCI machine learning repository (2013). http://archive.ics.uci.edu/ml
Bayoudh, S., Miclet, L., Delhay, A.: Learning by analogy: A classification rule for binary and nominal data. Proc. Inter. Conf. on, Artificial Intelligence IJCAI07 pp. 678–683 (2007).
Gentner, D., Holyoak, K.J., Kokinov, B.N.: The Analogical Mind: Perspectives from Cognitive Science. Cognitive Science, and Philosophy. MIT Press, Cambridge, MA (2001).
Hall, M., Frank, E., Holmes, G., Pfahringer, B., Reutemann, P., Witten, I.H.: The weka data mining software: An update. SIGKDD Explorations 11(1), 10–18 (2009).
Melis, E., Veloso, M.: Analogy in problem solving. In: Handbook of Practical Reasoning: Computational and Theoretical Aspects. Oxford Univ. Press (1998).
Miclet, L., Bayoudh, S., Delhay, A.: Analogical dissimilarity: definition, algorithms and two experiments in machine learning. JAIR, 32 pp. 793–824 (2008).
Miclet, L., Prade, H.: Handling analogical proportions in classical logic and fuzzy logics settings. In: Proc. 10th Eur. Conf. on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU’09), Verona, pp. 638–650. Springer, LNCS 5590 (2009).
Prade, H., Richard, G.: Logical proportions—typology and roadmap. In: E. Hüllermeier, R. Kruse, F. Hoffmann (eds.) Computational Intelligence for Knowledge-Based Systems Design: Proc. 13th Inter. Conf. on Information Processing and Management of Uncertainty (IPMU’10), Dortmund, June 28 – July 2, LNCS, vol. 6178, pp. 757–767. Springer (2010).
Prade, H., Richard, G.: Reasoning with logical proportions. In: Proc. 12th Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR’10), Toronto, Ontario, Canada, May 9–13, (F. Z. Lin, U. Sattler, M. Truszczynski, eds.), pp. 545–555. AAAI Press (2010).
Prade, H., Richard, G.: Homogeneous logical proportions: Their uniqueness and their role in similarity-based prediction. In: G. Brewka, T. Eiter, S.A. McIlraith (eds.) Proc. 13th Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR’12), Roma, June 10–14, pp. 402–412. AAAI Press (2012).
Prade, H., Richard, G.: Analogical proportions and multiple-valued logics. In: L.C. van der Gaag (ed.) Proc. 12th Europ. Conf. on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU’13), Utrecht, July 8–10, LNCS, vol. 7958, pp. 497–509. Springer (2013).
Prade, H., Richard, G., Yao, B.: Enforcing regularity by means of analogy-related proportions-a new approach to classification. International Journal of Computer Information Systems and Industrial Management Applications 4, 648–658 (2012).
Stroppa, N., Yvon, F.: Analogical learning and formal proportions: Definitions and methodological issues. ENST Paris report (2005).
Acknowledgments
This work is supported by CNPq, processes 246939/2012-5, 246938/2012-9, 310561/2012-4, 310470/2012-9 and INCT-MACC (process 181813/2010-6).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Moraes , R.M., Machado, L.S., Prade, H., Richard, G. (2013). Classification Based on Homogeneous Logical Proportions. In: Bramer, M., Petridis, M. (eds) Research and Development in Intelligent Systems XXX. SGAI 2013. Springer, Cham. https://doi.org/10.1007/978-3-319-02621-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-02621-3_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02620-6
Online ISBN: 978-3-319-02621-3
eBook Packages: Computer ScienceComputer Science (R0)