Thematic Fuzzy Clusters with an Additive Spectral Approach

  • Susana Nascimento
  • Rui Felizardo
  • Boris Mirkin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7026)

Abstract

This paper introduces an additive fuzzy clustering model for similarity data as oriented towards representation and visualization of activities of research organizations in a hierarchical taxonomy of the field. We propose a one-by-one cluster extracting strategy which leads to a version of spectral clustering approach for similarity data. The derived fuzzy clustering method, FADDIS, is experimentally verified both on the research activity data and in comparison with two state-of-the-art fuzzy clustering methods. Two developed simulated data generators, affinity data of Gaussian clusters and genuine additive similarity data, are described, and comparison of the results over this data are reported.

Keywords

Fuzzy Cluster Spectral Cluster Adjust Rand Index Fuzzy Cluster Algorithm Fuzzy Cluster Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    ACM Computing Classification System (1998), http://www.acm.org/about/class/1998 (Cited September 9, 2008)
  2. 2.
    Bezdek, J., Hathaway, R., Windham, M.: Numerical comparisons of the RFCM and AP algorithms for clustering relational data. Pattern Recognition 24, 783–791 (1991)Google Scholar
  3. 3.
    Bezdek, J., Keller, J., Krishnapuram, R., Pal, T.: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Kluwer Academic Publishers, Dordrecht (1999)CrossRefMATHGoogle Scholar
  4. 4.
    Bezdek, J.C., Hathaway, R.J.: VAT: a tool for visual assessment of (cluster) tendency. In: Procs. of the 2002 International Joint Conference on Neural Networks (IJCNN 2002), pp. 2225–2230 (2002)Google Scholar
  5. 5.
    Brouwer, R.: A method of relational fuzzy clustering based on producing feature vectors using FastMap. Information Sciences 179, 3561–3582 (2009)CrossRefGoogle Scholar
  6. 6.
    Castellano, G., Torsello, M.A.: How to derive fuzzy user categories for web personalization. In: Castellano, G., Jain, L.C., Fanelli, A.M. (eds.) Web Personalization in Intelligent Environments. SCI, vol. 229, pp. 65–79. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Davé, R., Sen, S.: Robust fuzzy clustering of relational data. IEEE Transactions on Fuzzy Systems 10, 713–727 (2002)CrossRefGoogle Scholar
  8. 8.
    Felizardo, R.: A study on parallel versus sequential relational fuzzy clustering methods, Master thesis, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, p. 212 (2011)Google Scholar
  9. 9.
    Hathaway, R., Davenport, J., Bezdek, J.: Relational duals of the c-means algorithms. Pattern Recognition 22, 205–212 (1989)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Hathaway, R.J., Bezdek, J.C.: NERF c-means: Non-Euclidean relational fuzzy clustering. Pattern Recognition 27, 429–437 (1994)CrossRefGoogle Scholar
  11. 11.
    Huang, L., Yan, D., Jordan, M.I., Taft, N.: Spectral clustering with perturbed data. In: Koller, D., Schuurmans, D., Bengio, Y., Bottou, L. (eds.) Proceedings of the Twenty-Second Annual Conference on Neural Information Processing Systems. Advances in Neural Information Processing Systems, vol. 21, pp. 705–712. MIT Press, Vancouver (2009)Google Scholar
  12. 12.
    Hubert, L.J., Arabie, P.: Comparing partitions. Journal of Classification 2, 193–218 (1985)CrossRefMATHGoogle Scholar
  13. 13.
    Inoue, K., Urahama, K.: Sequential fuzzy cluster extraction by a graph spectral method. Pattern Recognition Letters 20, 699–705 (1999)CrossRefGoogle Scholar
  14. 14.
    Krishnapuram, R., Joshi, A., Nasraoui, O., Yi, L.: Low-complexity fuzzy relational clustering algorithms for Web mining. IEEE Transactions on Fuzzy Systems 9(4), 595–607 (2001)CrossRefGoogle Scholar
  15. 15.
    von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17, 395–416 (2007)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Masullia, F., Mitra, S.: Natural computing methods in bioinformatics: A survey. Information Fusion 10(3), 211–216 (2009)CrossRefGoogle Scholar
  17. 17.
    Mirkin, B.: Additive clustering and qualitative factor analysis methods for similarity matrices. Journal of Classification 4(1), 7–31 (1987)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Mirkin, B., Nascimento, S.: Analysis of Community Structure, Affinity Data and Research Activities using Additive Fuzzy Spectral Clustering. Technical Report 6, School of Computer Science, Birkbeck University of London (2009)Google Scholar
  19. 19.
    Mirkin, B., Nascimento, S., Pereira, L.M.: Cluster-lift method for mapping research activities over a concept tree. In: Koronacki, J., Raś, Z.W., Wierzchoń, S.T., Kacprzyk, J. (eds.) Advances in Machine Learning II. SCI, vol. 263, pp. 245–257. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  20. 20.
    Mirkin, B., Nascimento, S., Fenner, T., Pereira, L.M.: Constructing and Mapping Fuzzy Thematic Clusters to Higher Ranks in a Taxonomy. In: Bi, Y., Williams, M.-A. (eds.) KSEM 2010. LNCS (LNAI), vol. 6291, pp. 329–340. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  21. 21.
    Nadler, B., Lafon, S., Coifman, R.R., Kevrekidis, I.G.: Diffusion Maps, Spectral Clustering and Reaction Coordinates of Dynamical Systems. Applied and Computational Harmonic Analysis (21), 113–127 (2006)Google Scholar
  22. 22.
    Nasraoui, O., Frigui, H.: Extracting Web User Profiles Using Relational Competitive Fuzzy Clustering. International Journal on Artificial Intelligence Tools (IJAIT) 9(4), 509–526 (2000)CrossRefGoogle Scholar
  23. 23.
    Ng, A., Jordan, M., Weiss, Y.: On spectral clustering: analysis and an algorithm. In: Ditterich, T.G., Becker, S., Ghahramani, Z. (eds.) Advances in Neural Information Processing Systems, vol. 14, pp. 849–856. MIT Press, Cambridge (2002)Google Scholar
  24. 24.
    Pal, N.R., Aguan, K., Sharma, A., Amari, S.: Discovering biomarkers from gene expression data for predicting cancer subgroups using neural networks and relational fuzzy clustering. BMC Bioinformatics, 8(1)(5) (2007)Google Scholar
  25. 25.
    Popescu, M., Keller, J.M., Mitchell, J.A.: Fuzzy Measures on the Gene Ontology for Gene Product Similarity. Journal IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB) 3(3), 263–274 (2006)CrossRefGoogle Scholar
  26. 26.
    Roubens, M.: Pattern classification problems and fuzzy sets. Fuzzy Sets and Systems 1, 239–253 (1978)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Runkler, T.A., Bezdek, J.C.: Web mining with relational clustering. International Journal of Approximate Reasoning, Elsevier Science 32(2-3), 217–236 (2003)CrossRefMATHGoogle Scholar
  28. 28.
    Sato, M., Sato, Y., Jain, L.C.: Fuzzy Clustering Models and Applications. Physica, Heidelberg (1997)MATHGoogle Scholar
  29. 29.
    Shepard, R.N., Arabie, P.: Additive clustering: representation of similarities as combinations of overlapping properties. Psychological Review 86, 87–123 (1979)CrossRefGoogle Scholar
  30. 30.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(8), 888–905 (2000)CrossRefGoogle Scholar
  31. 31.
    Sledge, I.J., Bezdek, J.C., Havens, T.C., Keller, J.M.: Relational Generalizations of Cluster Validity Indices. IEEE Transactions on Fuzzy Systems 18(4), 771–786 (2010)CrossRefGoogle Scholar
  32. 32.
    Suryavanshi, B.S., Shiri, N., Mudur, S.P.: An Efficient Technique for Mining Usage Profiles Using Relational Fuzzy Subtractive Clustering. In: Procs. of the International Workshop on Challenges in Web Information Retrieval and Integration (WIRI 2005), pp. 23–29 (2005)Google Scholar
  33. 33.
    Windham, M.P.: Numerical classification of proximity data with assignment measures. Journal of Classification 2, 157–172 (1985)CrossRefGoogle Scholar
  34. 34.
    Xu, D., Keller, J.M., Popescu, M., Bondugula, R.: Applications of Fuzzy Logic in Bioinformatics. Imperial College Press, London (2008)CrossRefMATHGoogle Scholar
  35. 35.
    Yang, M., Shih, H.: Cluster analysis based on fuzzy relations. Fuzzy Sets and Systems 120, 197–212 (2001)MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    Zhang, S., Wang, R.-S., Zhang, X.-S.: Identification of overlapping community structure in complex networks using fuzzy c-means clustering. Physica A 374, 483–490 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Susana Nascimento
    • 1
  • Rui Felizardo
    • 1
  • Boris Mirkin
    • 2
    • 3
  1. 1.Department of Computer Science and Centre for Artificial Intelligence (CENTRIA), Faculdade de Ciências e TecnologiaUniversidade Nova de LisboaCaparicaPortugal
  2. 2.Department of Computer ScienceBirkbeck University of LondonLondonUK
  3. 3.School of Applied Mathematics and InformaticsHigher School of EconomicsMoscowRussia

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