Abstract
The formal modeling of analogical proportions (i.e., statements of the form “a is to b as c is to d”) has led in the last past years to different proposals for classification algorithms, which have been quite successful on benchmarks where data are described by binary or nominal features. As far as we know and up to one exception, numerical data have never been considered. We propose here a new algorithm for handling numerical data. Starting from multiple-valued logical modelings of analogical proportions, more or less strongly encoding the idea that the change from a to b is the same as the change from c to d, we investigate different implementations leading to very good results on classical benchmarks.
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.
Similar content being viewed by others
References
Bayoudh, S., Miclet, L., Delhay, A.: Learning by analogy: A classification rule for binary and nominal data. In: Proc. Inter. Join. Conf. on Artificial Intelligence, IJCAI 2007, pp. 678–683 (2007)
Boughanem, M., Loiseau, Y., Prade, H.: Refining aggregation functions for improving document ranking in information retrieval. In: Prade, H., Subrahmanian, V.S. (eds.) SUM 2007. LNCS (LNAI), vol. 4772, pp. 255–267. Springer, Heidelberg (2007)
Bounhas, M., Prade, H., Richard, G.: Analogical classification: A new way to deal with examples. Tech. Rep. RR–2014-03–FR, Institut de Recherche en Informatique de Toulouse (IRIT), March, to appear in Proc. 21st Europ. Conf. on Artificial Intelligence, Prague, August 18-22 (2014)
Bounhas, M., Prade, H., Richard, G.: Analogical classification: A rule-based view. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 2014, Part II. CCIS, vol. 443, pp. 485–495. Springer, Heidelberg (2014)
Demsar, J.: Statistical comparisons of classifiers over multiple data sets. Journal of Machine Learning Research 7, 1–30 (2006)
Dubois, D., Prade, H., Richard, G.: Multiple-valued extensions of analogical proportions - A discussion (submitted)
Gentner, D., Holyoak, K.J., Kokinov, B.N.: The Analogical Mind: Perspectives from Cognitive Science. Cognitive Science, and Philosophy. MIT Press, Cambridge (2001)
Helman, D.H. (ed.): Analogical Reasoning: Perspectives of Artificial Intelligence. Cognitive Science, and Philosophy. Kluwer, Dordrecht (1988)
Lepage, Y.: Analogy and formal languages. Electr. Notes Theor. Comput. Sci. 53 (2001)
Mertz, J., Murphy, P.: UCI repository of machine learning databases (2000), ftp://ftp.ics.uci.edu/pub/machine-learning-databases
Miclet, L., Bayoudh, S., Delhay, A.: Analogical dissimilarity: definition, algorithms and two experiments in machine learning. JAIR 32, 793–824 (2008)
Miclet, L., Prade, H.: Handling analogical proportions in classical logic and fuzzy logics settings. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS, vol. 5590, pp. 638–650. Springer, Heidelberg (2009)
Moraes, R.M., Machado, L.S., Prade, H., Richard, G.: Classification based on homogeneous logical proportions. In: Bramer, M., Petridis, M. (eds.) Proc. of AI-2013, The Thirty-third SGAI International Conference on Innovative Techniques and Applications of Artificial Intelligence, Cambridge, England, UK, pp. 53–60. Springer, Heidelberg (2013)
Prade, H., Richard, G.: Reasoning with logical proportions. In: Lin, F.Z., Sattler, U., Truszczynski, M. (eds.) Proc. 12th Int. Conf. on Principles of Knowledge Representation and Reasoning, KR 2010, Toronto, May 9-13, pp. 545–555. AAAI Press (2010)
Prade, H., Richard, G.: Analogical proportions and multiple-valued logics. In: van der Gaag, L.C. (ed.) ECSQARU 2013. LNCS, vol. 7958, pp. 497–509. Springer, Heidelberg (2013)
Prade, H., Richard, G.: Homogeneous logical proportions: Their uniqueness and their role in similarity-based prediction. In: Brewka, G., Eiter, T., McIlraith, S.A. (eds.) Proc. 13th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR 2012), Roma, June 10-14, pp. 402–412. AAAI Press (2012)
Prade, H., Richard, G.: From analogical proportion to logical proportions. Logica Universalis 7(4), 441–505 (2013)
Prade, H., Richard, G. (eds.): Computational Approaches to Analogical Reasoning: Current Trends. SCI, vol. 548. Springer, Heidelberg (2014)
Prade, H., Richard, G.: Multiple-valued logic interpretations of analogical, reverse analogical, and paralogical proportions. In: Proc. 40th IEEE Int. Symp. on Multiple-Valued Logic (ISMVL 2010), Barcelona, pp. 258–263 (2010)
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.: An analogical learner for morphological analysis. In: Online Proc. 9th Conf. Comput. Natural Language Learning (CoNLL 2005), pp. 120–127 (2005)
Stroppa, N., Yvon, F.: Analogical learning and formal proportions: Definitions and methodological issues. Tech. rep. (June 2005)
Yvon, F., Stroppa, N., Delhay, A., Miclet, L.: Solving analogical equations on words. Tech. rep., Ecole Nationale Supérieure des Télécommunications (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Bounhas, M., Prade, H., Richard, G. (2014). Analogical Classification: Handling Numerical Data. In: Straccia, U., Calì, A. (eds) Scalable Uncertainty Management. SUM 2014. Lecture Notes in Computer Science(), vol 8720. Springer, Cham. https://doi.org/10.1007/978-3-319-11508-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-11508-5_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11507-8
Online ISBN: 978-3-319-11508-5
eBook Packages: Computer ScienceComputer Science (R0)