Abstract
In clustering we often face the situation that only a subset of the available attributes is relevant for forming clusters, even though this may not be known beforehand. In such cases it is desirable to have a clustering algorithm that automatically weights attributes or even selects a proper subset. In this paper I study such an approach for fuzzy clustering, which is based on the idea to transfer an alternative to the fuzzifier (Klawonn and Höppner, What is fuzzy about fuzzy clustering? Understanding and improving the concept of the fuzzifier, In: Proc. 5th Int. Symp. on Intelligent Data Analysis, 254–264, Springer, Berlin, 2003) to attribute weighting fuzzy clustering (Keller and Klawonn, Int J Uncertain Fuzziness Knowl Based Syst 8:735–746, 2000). In addition, by reformulating Gustafson–Kessel fuzzy clustering, a scheme for weighting and selecting principal axes can be obtained. While in Borgelt (Feature weighting and feature selection in fuzzy clustering, In: Proc. 17th IEEE Int. Conf. on Fuzzy Systems, IEEE Press, Piscataway, NJ, 2008) I already presented such an approach for a global selection of attributes and principal axes, this paper extends it to a cluster-specific selection, thus arriving at a fuzzy subspace clustering algorithm (Parsons, Haque, and Liu, 2004).
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References
Bezdek, J. C., Keller, J., Krishnapuram, R., & Pal, N. (1999). Fuzzy models and algorithms for pattern recognition and image processing. Dordrecht: Kluwer.
Bezdek, J. C., & Pal, N. (1992). Fuzzy models for pattern recognition. New York: IEEE Press.
Blake, C. L., & Merz, C. J. (1998). UCI repository of machine learning databases. Irvine, CA: University of California.
Borgelt, C. (2005). Prototype-based classification and clustering. Habilitation thesis, University of Magdeburg, Germany.
Borgelt, C. (2008). Feature weighting and feature selection in fuzzy clustering. In Proceedings of 17th IEEE International Confonfrence on Fuzzy Systems (FUZZ-IEEE 2008, Hongkong, China). Piscataway, NJ: IEEE Press.
Butterworth, R., Piatetsky-Shapiro, G., & Simovici, D. A. (2005). On feature selection through clustering. In Proceedings of 5th IEEE International Confonfrence on Data Mining (ICDM 2005, Houston, TX) (pp. 581–584). Piscataway, NJ: IEEE Press.
Dash, M., Choi, K., Scheuermann, P., & Liu, H. (2002). Feature selection for clustering: A filter solution. In Proceedings of 2nd IEEE International Confonfrence on Data Mining (ICDM 2002, Maebashi, Japan) (pp. 51–58). Piscataway: IEEE Press.
Dash, M., & Liu, H. (2000). Feature selection for clustering. In Proceedings of 4th Pacific-Asia Confonfrence on Knowledge Discovery and Data Mining (PAKDD 2000, Kyoto, Japan) (pp. 110–121). London: Springer.
Dy, J. G., & Brodley, C. E. (2000). Visualization and interactive feature selection for unsupervised data. In Proceedings of 6th ACM International Confonfrence on Knowledge Discovery and Data Mining (KDD 2000, Boston, MA) (pp. 360–364). New York: ACM Press.
Golub, G. H., & Van Loan, C. F. (1996). Matrix computations (3rd ed.). Baltimore, MD: The Johns Hopkins University Press.
Gustafson, E. E., & Kessel, W. C. (1979). Fuzzy clustering with a fuzzy covariance matrix. In Proceedings of the IEEE Confonfrence on Decision and Control (CDC 1979, San Diego, CA) (pp. 761–766). Piscataway, NJ: IEEE Press. Reprinted in Bezdek and Pal (1992) (pp. 117–122).
Höppner, F., Klawonn, F., Kruse, R., & Runkler, T. (1999). Fuzzy cluster analysis. Chichester, UK: Wiley.
Jouve, P.-E., & Nicoloyannis, N. (2005). A filter feature selection method for clustering. In Proceedings of 15th International Symposium on Foundations of Intelligent Systems (ISMIS 2005, Saratoga Springs, NY) (pp. 583–593). Heidelberg: Springer.
Keller, A., & Klawonn, F. (2000). Fuzzy clustering with weighting of data variables. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, 8, 735–746. Hackensack, NJ: World Scientific.
Klawonn, F., & Höppner, F. (2003). What is fuzzy about fuzzy clustering? Understanding and improving the concept of the fuzzifier. In Proceedings of 5th International Symposium on Intelligent Data Analysis (IDA 2003, Berlin, Germany) (pp. 254–264). Berlin: Springer.
Klawonn, F., & Kruse, R. (1997). Constructing a fuzzy controller from data. Fuzzy Sets and Systems, 85, 177–193. Amsterdam: North-Holland.
Law, M. H. C., Figueiredo, M. A. T., & Jain, A. K. (2004). Simultaneous feature selection and clustering using mixture models. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 26(9), 1154–1166. Piscataway, NJ: IEEE Press.
Parsons, L., Haque, E., & Liu, H. (2004). Subspace clustering for high-dimensional data: A review. ACM SIGKDD Explorations Newsletter, 6(1), 90–105. New York: ACM Press.
Roth, V., & Lange, T. (2004). Feature selection in clustering problems. Advances in Neural Information Processing 16: Proceedings of 17th Annual Conference (NIPS 2003, Vancouver, Canada). Cambridge, MA: MIT Press.
Wang, X., Wang, Y., & Wang, L. (2004). Improving fuzzy c-means clustering based on feature-weight learning. Pattern Recognition Letters, 25(10), 1123–1132. New York: Elsevier.
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Borgelt, C. (2009). Fuzzy Subspace Clustering. In: Fink, A., Lausen, B., Seidel, W., Ultsch, A. (eds) Advances in Data Analysis, Data Handling and Business Intelligence. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01044-6_8
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