Abstract
When compared to crisp clustering, fuzzy clustering provides more flexible and powerful data representation. However, most fuzzy methods require setting some parameters, as is the case for our Graded Possibilistic c-Means clustering method, which has two parameters in addition to number of centroids. However, for this model selection task there is no well established criterion available. Building on our own previous work on fuzzy clustering similarity indexes, we introduce a technique to evaluate the stability of clusterings by using the fuzzy Jaccard index, and use this procedure to select the most suitable values of parameters. The experiments indicate that the procedure is effective.
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
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Kluwer Academic Publishers, Norwell (1981)
Bezdek, J., Hathaway, R., Huband, J.: Visual assessment of clustering tendency for rectangular dissimilarity matrices. IEEE Transactions on Fuzzy Systems 15(5), 890–903 (2007)
Brouwer, R.K.: Extending the Rand, adjusted Rand and Jaccard indices to fuzzy partitions. J. Intell. Inf. Syst. 32(3), 213–235 (2009)
Davé, R.N., Krishnapuram, R.: Robust clustering methods: a unified view. IEEE Transactions on Fuzzy Systems 5(2), 270–293 (1997)
Filippone, M., Masulli, F., Rovetta, S.: Stability and performances in biclustering algorithms. In: Masulli, F., Tagliaferri, R., Verkhivker, G. (eds.) CIBB 2008. LNCS, vol. 5488, pp. 91–101. Springer, Heidelberg (2009)
Fred, A.L.N., Jain, A.K.: Data clustering using evidence accumulation. In: International Conference on Pattern Recognition, 4 (2002), http://dx.doi.org/10.1109/ICPR.2002.1047450
Frigui, H., Krishnapuram, R.: A robust competitive clustering algorithm with applications in computer vision. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(5), 450–465 (1999)
Frigui, H., Krishnapuram, R.: A robust clustering algorithm based on m-estimator. In: Proceedings of the 1st International Conference on Neural, Parallel and Scientific Computations, Atlanta, USA, vol. 1, pp. 163–166 (May 1995)
Hennig, C.: Cluster-wise assessment of cluster stability. Computational Statistics & Data Analysis 52(1), 258–271 (2007)
Huber, P.J.: Robust Statistics. John Wiley and Sons, New York (1981)
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)
Krishnapuram, R., Keller, J.M.: The possibilistic C-Means algorithm: insights and recommendations. IEEE Transactions on Fuzzy Systems 4(3), 385–393 (1996)
Kuncheva, L.I., Vetrov, D.P.: Evaluation of stability of k-means cluster ensembles with respect to random initialization. IEEE Trans. Pattern Anal. Mach. Intell. 28(11), 1798–1808 (2006)
Masulli, F., Rovetta, S.: Soft transition from probabilistic to possibilistic fuzzy clustering. IEEE Transactions on Fuzzy Systems 14(4), 516–527 (2006)
Meilă, M.: Comparing clusterings–an information based distance. Journal of Multivariate Analysis 98(5), 873–895 (2007)
Menger, K.: Statistical metrics. Proceedings of the National Academy of Sciences of the United States of America 28(12), 535–537 (1942)
Nasraoui, O., Krishnapuram, R.: A robust estimator based on density and scale optimizations and its application to clustering. In: FUZZ-IEEE 1996: Proceedings of the International Conference on Fuzzy Systems, pp. 1031–1035. IEEE, New Orleans (1996)
Rand, W.: Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association 66, 846–850 (1971)
Rose, K., Gurewitz, E., Fox, G.: A deterministic annealing approach to clustering. Pattern Recognition Letters 11, 589–594 (1990)
Rovetta, S., Masulli, F.: An experimental validation of some indexes of fuzzy clustering similarity. In: Gesù, V.D., Pal, S.K., Petrosino, A. (eds.) WILF 2009. LNCS, vol. 5571, pp. 132–139. Springer, Heidelberg (2009)
Shi, G.: Multivariate data analysis in palaeoecology and palaeobiogeographya review. Palaeogeography, Palaeoclimatology, Palaeoecology 105(3-4), 199–234 (1993)
Strehl, A., Ghosh, J.: Cluster ensembles — a knowledge reuse framework for combining multiple partitions. J. Mach. Learn. Res. 3, 583–617 (2003)
Zadeh, L.A.: Fuzzy sets. Information and Control 8(3), 338–353 (1965)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rovetta, S., Masulli, F., Adel, T. (2011). Tuning Graded Possibilistic Clustering by Visual Stability Analysis. In: Fanelli, A.M., Pedrycz, W., Petrosino, A. (eds) Fuzzy Logic and Applications. WILF 2011. Lecture Notes in Computer Science(), vol 6857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23713-3_21
Download citation
DOI: https://doi.org/10.1007/978-3-642-23713-3_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23712-6
Online ISBN: 978-3-642-23713-3
eBook Packages: Computer ScienceComputer Science (R0)