Abstract
Miyamoto et al. derived a hard clustering algorithms by defuzzifying a generalized entropy-based fuzzy c-means in which covariance matrices are introduced as decision variables. We apply the hard c-means (HCM) clustering algorithms to a postsupervised classifier to improve resubstitution error rate by choosing best clustering results from local minima of an objective function. Due to the nature of the prototype based classifier, the error rates can easily be improved by increasing the number of clusters with the cost of computer memory and CPU speed. But, with the HCM classifier, the resubstitution error rate along with the data set compression ratio is improved on several benchmark data sets by using a small number of clusters for each class.
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
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press (1981)
Duda, R.O., Hart, P.E.: Pattern Classification and Scene Analysis. Wiley, New York (1973)
Gustafson, E.E., Kessel, W.C.: Fuzzy clustering with a fuzzy covariance matrix. In: IEEE CDC, San Diego, California, pp. 761–766 (1979)
Holland, P.W., Welsch, R.E.: Robust Regression Using Iteratively Reweighted Least-squares. Communications in Statistics A6(9), 813–827 (1977)
Huber, P.J.: Robust Statistics, 1st edn. Wiley, New York (1981)
Ichihashi, H., Miyagishi, K., Honda, K.: Fuzzy c-Means Clustering with Regularization by K-L Information. In: Proc. of 10th IEEE International Conference on Fuzzy Systems, Melboroune, Australia, vol. 3, pp. 924–927 (2001)
Ichihashi, H., Honda, K.: Fuzzy c-Means Classifier for Incomplete Data Sets with Outliers and Missing Values. In: Proc. of the International Conference on Computational Intelligence for Modelling, Control and Automation, Vienna, Austria, pp. 457–564 (2005)
Ichihashi, H., Honda, K., Hattori, T.: Regularized Discriminant in the Setting of Fuzzy c-Means Classifier. In: Proc. of the IEEE World Congress on Computational Intelligence, Vancouver, Canada (2006)
Ichihashi, H., Honda, K., Matsuura, F.: ROC Analysis of FCM Classifier With Cauchy Weight. In: Proc. of the 3rd International Conference on Soft Computing and Intelligent Systems, Tokyo, Japan (2006)
Krishnapuram, R., Keller, J.: A Possibilistic Approach to Clustering. IEEE Transactions on Fuzzy Systems 1, 98–110 (1993)
Liu, Z.Q., Miyamoto, S. (eds.): Softcomputing and Human-Centered Machines. Springer, Heidelberg (2000)
Miyamoto, S., Yasukochi, T., Inokuchi, R.: A Family of Fuzzy and Defuzzified c-Means Algorithms. In: Proc. of the International Conference on Computational Intelligence for Modelling, Control and Automation, Vienna, Austria, pp. 170–176 (2005)
Miyamoto, S., Umayahara, K.: Fuzzy Clustering by Quadratic Regularization. In: Proc. of FUZZ-IEEE 1998, Anchorage, Alaska, pp. 1394–1399 (1998)
Miyamoto, S., Suizu, D., Takata, O.: Methods of Fuzzy c-Means and Possibilistic Clustering Using a Quadratic Term. Scientiae Mathematicae Japonicae 60(2), 217–233 (2004)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C, The Art of Scientific Computing, 2nd edn. Cambridge University Press, Cambridge (1999)
Rose, K.: Deterministic Annealing for Clustering, Compression, Classification, Regression, and Related Optimization Problems. Proc. of the IEEE 86(11), 2210–2239 (1998)
Tipping, M.E., Bishop, C.M.: Mixtures of Probabilistic Principal Component Analysers. Neural Computation 11, 443–482 (1999)
Veenman, C.J., Reinders, M.J.T.: The Nearest Sub-class Classifier: A Compromise Between the Nearest Mean and Nearest Neighbor Classifier. IEEE Transactions on PAMI 27(9), 1417–1429 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ichihashi, H., Honda, K., Notsu, A. (2006). Postsupervised Hard c-Means Classifier. In: Greco, S., et al. Rough Sets and Current Trends in Computing. RSCTC 2006. Lecture Notes in Computer Science(), vol 4259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11908029_95
Download citation
DOI: https://doi.org/10.1007/11908029_95
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-47693-1
Online ISBN: 978-3-540-49842-1
eBook Packages: Computer ScienceComputer Science (R0)