Clustering by Fuzzy Neural Gas and Evaluation of Fuzzy Clusters

We consider some modifications of the neural gas algorithm. First, fuzzy assignments as known from fuzzy c-means and neighborhood cooperativeness as known from self-organizing maps and neural gas are combined to obtain a basic Fuzzy Neural Gas. Further, a kernel variant and a simulated annealing approach are derived. Finally, we introduce a fuzzy extension of the ConnIndex to obtain an evaluation measure for clusterings based on fuzzy vector quantization.

[1]  G H Ball,et al.  A clustering technique for summarizing multivariate data. , 1967, Behavioral science.

[2]  Thomas Villmann,et al.  Fuzzy Neural Gas for Unsupervised Vector Quantization , 2012, ICAISC.

[3]  Thomas Villmann,et al.  Divergence-Based Vector Quantization , 2011, Neural Computation.

[4]  James C. Bezdek,et al.  An integrated approach to fuzzy learning vector quantization and fuzzy c-means clustering , 1997, IEEE Trans. Fuzzy Syst..

[5]  Marie Cottrell,et al.  SOM-based algorithms for qualitative variables , 2004, Neural Networks.

[6]  Jean-Marc Constans,et al.  Fuzzy kappa for the agreement measure of fuzzy classifications , 2007, Neurocomputing.

[7]  Delbert Dueck,et al.  Clustering by Passing Messages Between Data Points , 2007, Science.

[8]  Christopher K. I. Williams.  Computing with Infinite Networks , 1996, NIPS.

[9]  Thomas Villmann,et al.  Modified Conn-Index for the evaluation of fuzzy clusterings , 2012, ESANN.

[10]  Teuvo Kohonen,et al.  Self-Organizing Maps , 2010 .

[11]  J. C. Dunn,et al.  A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters , 1973 .

[12]  Thomas Villmann,et al.  Gradient Based Learning in Vector Quantization Using Differentiable Kernels , 2012, WSOM.

[13]  N. Aronszajn.  Theory of Reproducing Kernels. , 1950 .

[14]  James C. Bezdek,et al.  A Convergence Theorem for the Fuzzy ISODATA Clustering Algorithms , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  David A. Landgrebe,et al.  Signal Theory Methods in Multispectral Remote Sensing , 2003 .

[16]  Alexander J. Smola,et al.  Learning with kernels , 1998 .

[17]  Lorenzo Bruzzone,et al.  Kernel-based methods for hyperspectral image classification , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[18]  Erzsébet Merényi,et al.  A Validity Index for Prototype-Based Clustering of Data Sets With Complex Cluster Structures , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[19]  Benoît Frénay,et al.  Parameter-insensitive kernel in extreme learning for non-linear support vector regression , 2011, Neurocomputing.

[20]  Teuvo Kohonen,et al.  The self-organizing map , 1990, Neurocomputing.

[21]  Thomas Martinetz,et al.  'Neural-gas' network for vector quantization and its application to time-series prediction , 1993, IEEE Trans. Neural Networks.

[22]  Kelly A. Shaw,et al.  A Study of Neural Network Input Data for Ground Cover Identification in Satellite Images , 1993 .