Abstract
The Rand index is a measure commonly used to compare crisp partitions. Campello (2007) and Hüllermeier and Rifqi (2009) respectively, proposed two extensions of this index capable to compare fuzzy partitions. These approaches are useful when continuous values of attributes are discretized using fuzzy sets. In previous works we experimented with these extensions and compared their accuracy with the one of the crisp Rand index. In this paper we propose the ε-procedure, an alternative way to deal with attributes taking continuous values. Accuracy results on some known datasets of the Machine Learning repository using the ε-procedure as crisp discretization method jointly with the crisp Rand index are comparable to the ones given using the crisp Rand index and its fuzzifications with standard crisp and fuzzy discretization methods respectively.
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
Yang, Y., Webb, G.I., Wu, X.: Discretization Methods. In: The Data Mining and Knowledge Discovery Handbook, ch. 6, pp. 113–130. Springer (2005)
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)
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)
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 the 2009 IFSA/EUSFLAT Conference, pp. 1294–1298 (2009)
Rand, W.M.: Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association 66(336), 846–850 (1971)
Ruspini, E.H.: A new approach to clustering. Information and Control 15(1), 22–32 (1969)
Frigui, H., Hwang, C., Rhee, F.C.H.: Clustering and aggregation of relational data with applications to image database categorization. Pattern Recognition 40, 3053–3068 (2007)
Brower, R.: Extending the Rand, adjusted Rand and Jaccard indices to fuzzy partitions. Journal of Intelligent Informtion Systems 32, 213–235 (2009)
Anderson, D.T., Bezdek, J.C., Popescu, M., Keller, J.M.: Comparing fuzzy, probabilistic, and possibilistic partitions. IEEE Transactions on Fuzzy Systems 18(5), 906–918 (2010)
Hüllermeier, E., Rifqi, M., Henzgen, S., Senge, R.: Comparing Fuzzy Partitions: A Generalization of the Rand Index and Related Measures. IEEE Transactions on Fuzzy Systems 20(3), 546–556 (2012)
Ishibuchi, H., Yamamoto, T.: Deriving fuzzy discretization from interval discretization. In: Proceedings of FUZZ-IEEE 2003, vol. 1, pp. 749–754 (2003)
Asuncion, A., Newman, D.J.: UCI machine learning repository (2007)
Fayyad, U.M., Irani, K.B.: Multi-interval discretization of continuous-valued attributes for classification learning. In: Proceedings of IJCAI 1993, pp. 1022–1029 (1993)
Witten, I., Frank, E., Trigg, L., Hall, M., Holmes, G., Cunningham, S.: Weka: Practical machine learning tools and techniques with java implementations (1999)
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)
López de Mántaras, R.: A distance-based attribute selection measure for decision tree induction. Machine Learning 6, 81–92 (1991)
Armengol, E., Dellunde, P., García-Cerdaña, À.: 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.) IPMU 2012, Part I. CCIS, vol. 297, pp. 81–90. Springer, Heidelberg (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Armengol, E., García-Cerdaña, À. (2012). Refining Discretizations of Continuous-Valued Attributes. In: Torra, V., Narukawa, Y., López, B., Villaret, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2012. Lecture Notes in Computer Science(), vol 7647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34620-0_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-34620-0_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34619-4
Online ISBN: 978-3-642-34620-0
eBook Packages: Computer ScienceComputer Science (R0)