Abstract
In this paper we introduce FLM, a divergence measure to compare a fuzzy and a crisp partition. This measure is an extension of LM, the López de Mántaras distance. This extension allows to handle domain objects having attributes with continuous values. This means that for some domains the use of fuzzy sets may report better results than the discretization that is the usual way to deal with continuous values. We experimented with both FLM and LM in the context of the lazy learning method called Lazy Induction of Descriptions useful for classification tasks.
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References
López de Mántaras, R.: A distance-based attribute selection measure for decision tree induction. Machine Learning 6, 81–92 (1991)
Armengol, E., Plaza, E.: Lazy Induction of Descriptions for Relational Case-Based Learning. In: Flach, P.A., De Raedt, L. (eds.) ECML 2001. LNCS (LNAI), vol. 2167, pp. 13–24. Springer, Heidelberg (2001)
Quinlan, J.R.: Induction of decision trees. Machine Learning 1, 81–106 (1986)
Pfitzner, D., Leibbrandt, R., Powers, D.M.W.: Characterization and evaluation of similarity measures for pairs of clusterings. Knowledge Information Systems 19(3), 361–394 (2009)
Armengol, E.: Discovering plausible explanations of carcinogenecity in chemical compounds. In: Perner, P. (ed.) MLDM 2007. LNCS (LNAI), vol. 4571, pp. 756–769. Springer, Heidelberg (2007)
Armengol, E., Puig, S.: Combining two lazy learning methods for classification and knowledge discovery. a case study for malignant melanoma diagnosis. In: Proceedings of the International Conference on Knowledge Discovery and Information Retrieval, pp. 200–207 (2011)
Kuwajima, I., Nojima, Y., Ishibuchi, H.: Effects of constructing fuzzy discretization from crisp discretization for rule-based classifiers. Artificial Life and Robotics 13(1), 294–297 (2008)
Rand, W.M.: Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association 66(336), 846–850 (1971)
Campello, R.J.G.B.: A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment. Pattern Recognition Letters 28(7), 833–841 (2007)
Hüllermeier, E., Rifqi, M.: A fuzzy variant of the Rand index for comparing clustering structures. In: Proceedings of IFSA/EUSFLAT Conference, pp. 1294–1298 (2009)
Armengol, E., García-Cerdaña, À.: Lazy Induction of Descriptions Using Two Fuzzy Versions of the Rand Index. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010, Part I. CCIS, vol. 80, pp. 396–405. Springer, Heidelberg (2010)
Zimmermann, H.: Fuzzy Set Theory and its applications, 2nd edn. Kluver Academic Publishers (1992)
Asuncion, A., Newman, D.J.: UCI machine learning repository (2007)
Witten, I., Frank, E., Trigg, L., Hall, M., Holmes, G., Cunningham, S.: Weka: Practical machine learning tools and techniques with java implementations (1999)
de Luca, A., Termini, S.: A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Information and Control 20(4), 301–312 (1972)
Montes, S., Couso, I., Gil, P., Bertoluzza, C.: Divergence measure between fuzzy sets. International Journal Approximate Reasoning 30(2), 91–105 (2002)
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Armengol, E., Dellunde, P., García-Cerdaña, À. (2012). Towards a Fuzzy Extension of the López de Mántaras Distance. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances on Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 297. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31709-5_9
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DOI: https://doi.org/10.1007/978-3-642-31709-5_9
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