Skip to main content

Comparing Partitions by Means of Fuzzy Data Mining Tools

  • Conference paper
Scalable Uncertainty Management (SUM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7520))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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)

    Google Scholar 

  2. 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)

    Article  Google Scholar 

  3. 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)

    Chapter  Google Scholar 

  4. 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)

    Google Scholar 

  5. 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)

    Google Scholar 

  6. Benzécri, J.P.: Cours de Linguistique Mathématique. Université de Rennes, Rennes (1963)

    Google Scholar 

  7. 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)

    Article  MathSciNet  MATH  Google Scholar 

  8. 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)

    MATH  Google Scholar 

  9. 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)

    Article  MathSciNet  Google Scholar 

  10. Bosc, P., Lietard, L., Pivert, O.: Functional Dependencies Revisited Under Graduality and Imprecision. In: Annual Meeting of NAFIPS, pp. 57–62 (1997)

    Google Scholar 

  11. Brouwer, R.K.: Extending the rand, adjusted rand and jaccard indices to fuzzy partitions. Journal of Intelligent Information Systems 32, 213–235 (2009)

    Article  Google Scholar 

  12. 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)

    Google Scholar 

  13. 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)

    Article  Google Scholar 

  14. Campello, R.J.G.B.: Generalized external indexes for comparing data partitions with overlapping categories. Pattern Recognition Letters 31, 966–975 (2010)

    Article  Google Scholar 

  15. Delgado, M., Martín-Bautista, M.J., Sánchez, D., Vila, M.A.: Mining strong approximate dependencies from relational databases. In: Procs. of IPMU 2000 (2000)

    Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. 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)

    Google Scholar 

  18. 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)

    Article  MATH  Google Scholar 

  19. 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)

    Article  MATH  Google Scholar 

  20. Fowlkes, E.B., Mallows, C.L.: A method for comparing two hierarchical clusterings. J. of American Statistical Society 78, 553–569 (1983)

    MATH  Google Scholar 

  21. 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)

    Article  MATH  Google Scholar 

  22. Hubert, L.J., Arabie, P.: Comparing partition. J. Classification 2, 193–218 (1985)

    Article  Google Scholar 

  23. 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)

    Article  Google Scholar 

  24. 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)

    Google Scholar 

  25. Jain, A., Dubes, R.: Algorithms for Clustering Data. Prentice Hall (1988)

    Google Scholar 

  26. Jiang, D., Tang, C., Zhang, A.: Cluster analysis for gene-expression data: A survey. IEEE Trans. Knowledge Data Engineering 16, 1370–1386 (2004)

    Article  Google Scholar 

  27. 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)

    Chapter  Google Scholar 

  28. Pérez-Pujalte, A., Prieto, P.: Mapa de suelos 1:200000 de la provincia de Granada y memoria explicativa. Technical report, CSIC (1980)

    Google Scholar 

  29. Rand, W.M.: Objective criteria for the evaluation of clustering methods. J. of the American Statistical Association 66(336), 846–850 (1971)

    Article  Google Scholar 

  30. 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)

    Chapter  Google Scholar 

  31. 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)

    Chapter  Google Scholar 

  32. 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)

    Article  MathSciNet  MATH  Google Scholar 

  33. Shortliffe, E., Buchanan, B.: A model of inexact reasoning in medicine. Mathematical Biosciences 23, 351–379 (1975)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33362-0_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33361-3

  • Online ISBN: 978-3-642-33362-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics