Abstract
In the previous two chapters we discussed granulation algorithms that are based on direct manipulation of information granules. Here, we introduce an algorithm for deriving information granules as prototypes in the clustering process. The way of revealing a structure in data is realized by maximizing a certain performance index (objective function) that takes into consideration an overall level of matching (to be maximized) and a similarity level between the prototypes (the component to be minimized). It is shown how the relevance of the prototypes translates into their granularity. The clustering method helps identify and quantify anisotropy of the feature space. We also show how each prototype is equipped with its own weight vector describing the anisotropy property and thus implying some ranking of the features in the data space.
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
Anderberg, M.R. (1973), Cluster Analysis for Applications, Academic Press, N. York.
Bargiela, A. (2001), Interval and ellipsoidal uncertainty models, In: W. Pedrycz (ed.) Granular Computing, Physica Verlag, Heidelberg, 23–57.
Bargiela, A., Pedrycz, W., Hirota, K. (2002), Data granulation through optimization of similarity measure, Archives of Control Sciences, to appear.
Bargiela, A., Pedrycz, W. (2002), A model of granular data: A design problem with the Tschebyshev FCM, International Journal of Soft Computing, to appear.
Bezdek, J.C. (1981), Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, N. York.
Bouchon-Meunier, B., Rifqi, M., Bothorel, S. (1996), Towards general measures of comparison of objects, Fuzzy Sets and Systems, 84, 2, 143–153.
Di Nola, A., Sessa, S., Pedrycz, W., Sanchez, E. (1989), Fuzzy Relational Equations and Their Applications in Knowledge Engineering, Kluwer Academic Press, Dordrecht.
Delgado, M, Gomez-Skarmeta, F., Martin, F. (1997), A fuzzy clustering-based prototyping for fuzzy rule-based modeling, IEEE Transactions on Fuzzy Systems, 5(2), 223–233.
Duda, R.O., Hart, P.E., Stork, D.G. (2001), Pattern Classification, 2nd edition, J. Wiley, NY.
Gabrys, B., Bargiela, A. (2000), General fuzzy Min-Max neural network for clustering and classification, IEEE Trans. on Neural Networks, Vol. 11, No. 3, pp. 769–783.
Hoppner F. et al (1999), Fuzzy Cluster Analysis, J. Wiley, Chichester.
Ishibuchi, H., Nozaki, K., Yamamoto, N., Tanaka, H. (1995), Selecting fuzzy if-then rules for classification problems using genetic algorithms”, IEEE Trans, on Fuzzy Systems, (3)3, 260–270.
Kandel, A. (1986), Fuzzy Mathematical Techniques with Applications, Addison-Wesley, MA.
Pedrycz, W. (1991), Neurocomputations in relational systems, IEEE Trans. on Pattern Analysis and Machine Intelligence, 13, 289–296.
Pedrycz, W., Rocha, A. (1993), Knowledge-based neural networks, IEEE Trans. on Fuzzy Systems, 1, 254–266.
Pedrycz, W. (1997), Computational Intelligence: An Introduction, CRC Press, Boca Raton, Fl.
Pedrycz, W. (1998), Conditional fuzzy clustering in the design of radial basis function neural networks, IEEE Transactions on Neural Networks, 9 no. 4, 601–612.
Pedrycz, W., Vasilakos, A.V. (1999), Linguistic models and linguistic modeling, IEEE Trans. on Systems Man and Cybernetics, vol. 29, no. 6, 745–757.
Pedrycz, W., Bargiela, A. (2001), Information granulation: A search for data structures, Knowledge-based Engineering Systems KES 2001, Osaka, October 2001, 1147–1151.
Pedrycz, W., Bargiela, A. (2002), Granular Clustering: A granular signature of data, IEEE Trans. on Systems Man and Cybernetics, Vol 32, No. 2, 212–224.
Simpson, P.K. (1992), Fuzzy Min-Max neural networks — Part1: Classification, IEEE Trans. on Neural Networks, Vol 3, No. 5, pp. 776–86.
Simpson, P.K. (1993), Fuzzy Min-Max neural networks — Part2: Clustering, IEEE Trans. on Neural Networks, Vol 4, No. 1, pp. 32–45.
Sudkamp, T. (1993), Similarity, interpolation, and fuzzy rule construction, Fuzzy Sets and Systems, vol. 58, no. 1, 73–86.
Zadeh, L.A. (1979), Fuzzy sets and information granularity, In: M.M. Gupta, R.K. Ragade, R.R. Yager, eds., Advances in Fuzzy Set Theory and Applications, North Holland, Amsterdam, 3–18.
Zadeh, L.A. (1996), Fuzzy logic = Computing with words, IEEE Trans. on Fuzzy Systems, vol. 4, 2, 103–111.
Zadeh, L.A. (1997), Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy Sets and Systems, 90, 1997, pp. 111–117.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media New York
About this chapter
Cite this chapter
Bargiela, A., Pedrycz, W. (2003). Granular Prototyping in Fuzzy Clustering. In: Granular Computing. The Springer International Series in Engineering and Computer Science, vol 717. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1033-8_8
Download citation
DOI: https://doi.org/10.1007/978-1-4615-1033-8_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5361-4
Online ISBN: 978-1-4615-1033-8
eBook Packages: Springer Book Archive