A Kernel PBM Index for Fuzzy Clustering of Numeric Data

Clustering is a fundamental technique for pattern recognition and machine learning. This paper proposes an improvement in the estimation of the well known PBM index which has been widely used for validating the results obtained from data clustering. Experimental results supporting the improvement are presented to show that despite the change the newer version performs the same as the original version of the index.

[1]  Frank Klawonn,et al.  Visual Inspection of Fuzzy Clustering Results , 2003 .

[2]  Sanghamitra Bandyopadhyay,et al.  Classification and learning using genetic algorithms - applications in bioinformatics and web intelligence , 2007, Natural computing series.

[3]  S. Bandyopadhyay,et al.  Nonparametric genetic clustering: comparison of validity indices , 2001, IEEE Trans. Syst. Man Cybern. Syst..

[4]  Ujjwal Maulik,et al.  Genetic algorithm-based clustering technique , 2000, Pattern Recognit..

[5]  Donald W. Bouldin,et al.  A Cluster Separation Measure , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Enrique H. Ruspini,et al.  Numerical methods for fuzzy clustering , 1970, Inf. Sci..

[7]  Kuo-Sheng Cheng,et al.  A New Clustering Method for the Distribution Analysis of Hearing Neurons , 2007 .

[8]  J. Dunn Well-Separated Clusters and Optimal Fuzzy Partitions , 1974 .

[9]  Gerardo Beni,et al.  A Validity Measure for Fuzzy Clustering , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Paul S. Bradley,et al.  Refining Initial Points for K-Means Clustering , 1998, ICML.

[11]  Ujjwal Maulik,et al.  Validity index for crisp and fuzzy clusters , 2004, Pattern Recognit..

[12]  Ujjwal Maulik,et al.  Performance Evaluation of Some Clustering Algorithms and Validity Indices , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Anil K. Jain,et al.  Data clustering: a review , 1999, CSUR.

[14]  Ujjwal Maulik,et al.  Genetic clustering for automatic evolution of clusters and application to image classification , 2002, Pattern Recognit..