Postsupervised Hard c-Means Classifier

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.

[1]  P. Holland,et al.  Robust regression using iteratively reweighted least-squares , 1977 .

[2]  William H. Press,et al.  Numerical Recipes in FORTRAN - The Art of Scientific Computing, 2nd Edition , 1987 .

[3]  James M. Keller,et al.  A possibilistic approach to clustering , 1993, IEEE Trans. Fuzzy Syst..

[4]  Sadaaki Miyamoto,et al.  Fuzzy clustering by quadratic regularization , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[5]  Hidetomo Ichihashi,et al.  Regularized Discriminant in the Setting of Fuzzy c-Means Classifier , 2006, 2006 IEEE International Conference on Fuzzy Systems.

[6]  Cor J. Veenman,et al.  The nearest subclass classifier: a compromise between the nearest mean and nearest neighbor classifier , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Sadaaki Miyamoto,et al.  A Family of Fuzzy and Defuzzified c-Means Algorithms , 2005, International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06).

[8]  Hidetomo Ichihashi,et al.  Fuzzy c-Means Classifier for Incomplete Data Sets with Outliers and Missing Values , 2005, International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06).

[9]  Sadaaki Miyamoto,et al.  METHODS OF FUZZY C-MEANS AND POSSIBILISTIC CLUSTERING USING A QUADRATIC TERM , 2004 .

[10]  Peter J. Huber,et al.  Robust Statistics , 2005, Wiley Series in Probability and Statistics.

[11]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[12]  Hidetomo Ichihashi,et al.  Fuzzy c-means clustering with regularization by K-L information , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[13]  Christopher M. Bishop,et al.  Mixtures of Probabilistic Principal Component Analyzers , 1999, Neural Computation.

[14]  K. Rose Deterministic annealing for clustering, compression, classification, regression, and related optimization problems , 1998, Proc. IEEE.

[15]  Hidetomo Ichihashi,et al.  ROC Analysis of FCM Classifier With Cauchy Weight , 2006 .

[16]  Donald Gustafson,et al.  Fuzzy clustering with a fuzzy covariance matrix , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[17]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[18]  T. Kunii,et al.  Soft Computing and Human-Centered Machines , 2013, Computer Science Workbench.