Comparing Partitions by Means of Fuzzy Data Mining Tools

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.

[1]  Daniel Sánchez,et al.  Measuring the accuracy and interest of association rules: A new framework , 2002, Intell. Data Anal..

[2]  Daniel Sánchez,et al.  Using association rules to mine for strong approximate dependencies , 2008, Data Mining and Knowledge Discovery.

[3]  Ricardo J. G. B. Campello,et al.  Generalized external indexes for comparing data partitions with overlapping categories , 2010, Pattern Recognit. Lett..

[4]  Ricardo J. G. B. Campello,et al.  A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment , 2007, Pattern Recognit. Lett..

[5]  James M. Keller,et al.  A Comparison of Five Fuzzy Rand Indices , 2010, IPMU.

[6]  J. Alexander,et al.  Theory and Methods: Critical Essays in Human Geography , 2008 .

[7]  L. Hubert,et al.  Comparing partitions , 1985 .

[8]  P. Jaccard,et al.  Etude comparative de la distribution florale dans une portion des Alpes et des Jura , 1901 .

[9]  James M. Keller,et al.  Comparing Fuzzy, Probabilistic, and Possibilistic Partitions , 2010, IEEE Transactions on Fuzzy Systems.

[10]  Anil K. Jain,et al.  Algorithms for Clustering Data , 1988 .

[11]  Patrick Bosc,et al.  Functional dependencies revisited under graduality and imprecision , 1997, 1997 Annual Meeting of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.97TH8297).

[12]  Thomas A. Runkler.  Comparing Partitions by Subset Similarities , 2010, IPMU.

[13]  William M. Rand,et al.  Objective Criteria for the Evaluation of Clustering Methods , 1971 .

[14]  Eyke Hüllermeier,et al.  Computational Intelligence for Knowledge-Based Systems Design, 13th International Conference on Information Processing and Management of Uncertainty, IPMU 2010, Dortmund, Germany, June 28 - July 2, 2010. Proceedings , 2010, IPMU.

[15]  Hichem Frigui,et al.  Clustering and aggregation of relational data with applications to image database categorization , 2007, Pattern Recognit..

[16]  Das Amrita,et al.  Mining Association Rules between Sets of Items in Large Databases , 2013 .

[17]  Witold Pedrycz,et al.  Foundations of Fuzzy Logic and Soft Computing, 12th International Fuzzy Systems Association World Congress, IFSA 2007, Cancun, Mexico, June 18-21, 2007, Proceedings , 2007, IFSA.

[18]  Daniel Sánchez,et al.  Fuzzy association rules: general model and applications , 2003, IEEE Trans. Fuzzy Syst..

[19]  Daniel Sánchez,et al.  A Proposal of Fuzzy Correspondence Analysis Based on Flexible Data Mining Techniques , 2004 .

[20]  Edward H. Shortliffe,et al.  A model of inexact reasoning in medicine , 1990 .

[21]  Jan Rauch,et al.  Mining for 4ft Association Rules , 2000, Discovery Science.

[22]  Roelof K. Brouwer.  Extending the rand, adjusted rand and jaccard indices to fuzzy partitions , 2008, Journal of Intelligent Information Systems.

[23]  Vincenzo Catania,et al.  On External Measures for Validation of Fuzzy Partitions , 2007, IFSA.

[24]  Daniel Sánchez,et al.  A formal model for mining fuzzy rules using the RL representation theory , 2011, Inf. Sci..

[25]  C. Mallows,et al.  A Method for Comparing Two Hierarchical Clusterings , 1983 .

[26]  Aidong Zhang,et al.  Cluster analysis for gene expression data: a survey , 2004, IEEE Transactions on Knowledge and Data Engineering.

[27]  Daniel Sánchez,et al.  Using data mining techniques to analyze correspondences between user and scientific knowledge in an agricultural environment , 2003 .

[28]  Daniel Sánchez,et al.  On a non-nested level-based representation of fuzziness , 2012, Fuzzy Sets Syst..

[29]  Daniel Sánchez,et al.  Studying Interest Measures for Association Rules through a Logical Model , 2010, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[30]  Eyke Hüllermeier,et al.  Comparing Fuzzy Partitions: A Generalization of the Rand Index and Related Measures , 2012, IEEE Transactions on Fuzzy Systems.

[31]  Daniel Sánchez,et al.  A definition for fuzzy approximate dependencies , 2005, Fuzzy Sets Syst..

[32]  Daniel Sánchez,et al.  A Restriction Level Approach for the Representation and Evaluation of Fuzzy Association Rules , 2009, IFSA/EUSFLAT Conf..