Abstract
Rand index is one of the most popular measures for comparing two partitions over a set of objects. Several approaches have extended this measure for those cases involving fuzzy partitions. In previous works, we developed a methodology for correspondence analysis between partitions in terms of data mining tools. In this paper we discuss how, without any additional cost, it can be applied as an alternate computation of Rand index, allowing us not only to compare both crisp and fuzzy partitions, but also classes inside these partitions.
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References
Agrawal, R., Imielinski, T., Swami, A.: Mining Association Rules between Sets of Items in Large Databases. In: Procs. of ACM SIGMOD Conf., Washington DC, USA, pp. 207–216 (1993)
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)
Anderson, D.T., Bezdek, J.C., Keller, J.M., Popescu, M.: A Comparison of Five Fuzzy Rand Indices. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. CCIS, vol. 80, pp. 446–454. Springer, Heidelberg (2010)
Aranda, V., Calero, J., Delgado, G., Sánchez, D., Serrano, J., Vila, M.A.: Flexible land classification for olive cultivation using user knowledge. In: Proceedings of 1st. Int. ICSC Conf. On Neuro-Fuzzy Technologies (NF 2002), La HaBana, Cuba, Enero 16–19 (2002)
Aranda, V., Calero, J., Delgado, G., Sánchez, D., Serrano, J.M., Vila, M.A.: Using Data Mining Techniques to Analyze Correspondences Between User and Scientific Knowledge in an Agricultural Environment. In: Enterprise Information Systems IV, pp. 75–89. Kluwer Academic Publishers (2003)
Benzécri, J.P.: Cours de Linguistique Mathématique. Université de Rennes, Rennes (1963)
Berzal, F., Blanco, I., Sánchez, D., Serrano, J.M., Vila, M.A.: A definition for fuzzy approximate dependencies. Fuzzy Sets and Systems 149(1), 105–129 (2005)
Berzal, F., Delgado, M., Sánchez, D., Vila, M.A.: Measuring accuracy and interest of association rules: A new framework. Intelligent Data Analysis 6(3), 221–235 (2002)
Blanco, I., Martín-Bautista, M.J., Sánchez, D., Serrano, J.M., Vila, M.A.: Using association rules to mine for strong approximate dependencies. Data Mining and Knowledge Discovery 16(3), 313–348 (2008)
Bosc, P., Lietard, L., Pivert, O.: Functional Dependencies Revisited Under Graduality and Imprecision. In: Annual Meeting of NAFIPS, pp. 57–62 (1997)
Brouwer, R.K.: Extending the rand, adjusted rand and jaccard indices to fuzzy partitions. Journal of Intelligent Information Systems 32, 213–235 (2009)
Calero, J., Delgado, G., Sánchez, D., Serrano, J.M., Vila, M.A.: A Proposal of Fuzzy Correspondence Analysis based on Flexible Data Mining Techniques. In: Soft Methodology and Random Information Systems, pp. 447–454. Springer (2004)
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, 833–841 (2007)
Campello, R.J.G.B.: Generalized external indexes for comparing data partitions with overlapping categories. Pattern Recognition Letters 31, 966–975 (2010)
Delgado, M., Martín-Bautista, M.J., Sánchez, D., Vila, M.A.: Mining strong approximate dependencies from relational databases. In: Procs. of IPMU 2000 (2000)
Delgado, M., Marín, N., Sánchez, D., Vila, M.A.: Fuzzy Association Rules: General Model and Applications. IEEE Transactions on Fuzzy Systems 11(2), 214–225 (2003)
Delgado, M., Ruiz, M.D., Sánchez, D.: A restriction level approach for the representation and evaluation of fuzzy association rules. In: Procs. of the IFSA-EUSFLAT, pp. 1583–1588 (2009)
Delgado, M., Ruiz, M.D., Sánchez, D.: Studying Interest Measures for Association Rules through a Logical Model. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems 18(1), 87–106 (2010)
Delgado, M., Ruiz, M.D., Sánchez, D., Serrano, J.M.: A Formal Model for Mining Fuzzy Rules Using the RL Representation Theory. Information Sciences 181, 5194–5213 (2011)
Fowlkes, E.B., Mallows, C.L.: A method for comparing two hierarchical clusterings. J. of American Statistical Society 78, 553–569 (1983)
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)
Hubert, L.J., Arabie, P.: Comparing partition. J. Classification 2, 193–218 (1985)
Hüllermeier, E., Rifqi, M., Henzgen, S., Senge, R.: Comparing fuzzy partitions: A generalization of the Rand index and related measures. IEEE Transactions of Fuzzy Systems 20(3), 546–556 (2012)
Jaccard, P.: Étude comparative de la distribution florale dans une portion des Alpes et des Jura. Bulletin de la Société Vaudoise des Sciences Naturelles 37, 547–579 (1901)
Jain, A., Dubes, R.: Algorithms for Clustering Data. Prentice Hall (1988)
Jiang, D., Tang, C., Zhang, A.: Cluster analysis for gene-expression data: A survey. IEEE Trans. Knowledge Data Engineering 16, 1370–1386 (2004)
Di Nuovo, A.G., Catania, V.: On External Measures for Validation of Fuzzy Partitions. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds.) IFSA 2007. LNCS (LNAI), vol. 4529, pp. 491–501. Springer, Heidelberg (2007)
Pérez-Pujalte, A., Prieto, P.: Mapa de suelos 1:200000 de la provincia de Granada y memoria explicativa. Technical report, CSIC (1980)
Rand, W.M.: Objective criteria for the evaluation of clustering methods. J. of the American Statistical Association 66(336), 846–850 (1971)
Rauch, J., Simunek, M.: Mining for 4ft Association Rules. In: Morishita, S., Arikawa, S. (eds.) DS 2000. LNCS (LNAI), vol. 1967, pp. 268–272. Springer, Heidelberg (2000)
Runkler, T.A.: Comparing Partitions by Subset Similarities. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS, vol. 6178, pp. 29–38. Springer, Heidelberg (2010)
Sánchez, D., Delgado, M., Vila, M.A., Chamorro-Martínez, J.: On a non-nested level-based representation of fuzziness. Fuzzy Sets and Systems 192, 159–175 (2012)
Shortliffe, E., Buchanan, B.: A model of inexact reasoning in medicine. Mathematical Biosciences 23, 351–379 (1975)
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Molina, C., Prados, B., Ruiz, MD., Sánchez, D., Serrano, JM. (2012). Comparing Partitions by Means of Fuzzy Data Mining Tools. In: Hüllermeier, E., Link, S., Fober, T., Seeger, B. (eds) Scalable Uncertainty Management. SUM 2012. Lecture Notes in Computer Science(), vol 7520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33362-0_26
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DOI: https://doi.org/10.1007/978-3-642-33362-0_26
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