Grey self-organizing feature maps

In each training iteration of the self-organizing feature maps (SOFM), the adjustable output nodes can be determined by the neighborhood size ofthe winning node. However, it seems that the SOFM ignores some important information, which is the relationships that actually exist between the input training data and each adjustable output node, in the learning rule. By viewing input data and each adjustable node as a reference sequence and a comparative sequence, respectively, the grey relations between these sequences can be seen. This paper thus incorporates the grey relational coe8cient into the learning rule ofthe SOFM, and a grey clustering method, namely the GSOFM, is proposed. From the simulation results, we can see that the best result ofthe proposed method applied f or analysis ofthe iris data outperf orms those ofother known unsupervised neural network models. Furthermore, the proposed method can e:ectively solve the traveling salesman problem. c 2002 Elsevier Science B.V. All rights reserved.

[1]  Laura I. Burke,et al.  The guilty net for the traveling salesman problem , 1992, Comput. Oper. Res..

[2]  Deng Ju-Long,et al.  Control problems of grey systems , 1982 .

[3]  Chien-Ming Chen,et al.  A novel fuzzy logic system based on N-version programming , 2000, IEEE Trans. Fuzzy Syst..

[4]  Michael J. A. Berry,et al.  Data mining techniques - for marketing, sales, and customer support , 1997, Wiley computer publishing.

[5]  Casimir A. Kulikowski,et al.  Computer Systems That Learn: Classification and Prediction Methods from Statistics, Neural Nets, Machine Learning and Expert Systems , 1990 .

[6]  James C. Bezdek,et al.  Two soft relatives of learning vector quantization , 1995, Neural Networks.

[7]  Bernard Angéniol,et al.  Self-organizing feature maps and the travelling salesman problem , 1988, Neural Networks.

[8]  E. Mizutani,et al.  Neuro-Fuzzy and Soft Computing-A Computational Approach to Learning and Machine Intelligence [Book Review] , 1997, IEEE Transactions on Automatic Control.

[9]  A. K. Pujari,et al.  Data Mining Techniques , 2006 .

[10]  Yo-Ping Huang,et al.  Real-valued genetic algorithms for fuzzy grey prediction system , 1997, Fuzzy Sets Syst..

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

[12]  Chyun-Shin Cheng,et al.  Grey Neural Network , 1998 .

[13]  J. J. Hopfield,et al.  “Neural” computation of decisions in optimization problems , 1985, Biological Cybernetics.

[14]  Mohamed A. Ismail,et al.  Fuzzy query processing using clustering techniques , 1990, Inf. Process. Manag..

[15]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[16]  Wan-Chi Siu,et al.  New approach for solving the travelling salesman problem using self-organizing learning , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[17]  Takao Enkawa,et al.  A self‐organizing neural network approach for multiple traveling salesman and vehicle routing problems , 1999 .

[18]  B. John Oommen,et al.  The Kohonen network incorporating explicit statistics and its application to the travelling salesman problem , 1999, Neural Networks.

[19]  James C. Bezdek,et al.  Generalized clustering networks and Kohonen's self-organizing scheme , 1993, IEEE Trans. Neural Networks.

[20]  Abhijit S. Pandya,et al.  Pattern Recognition with Neural Networks in C++ , 1995 .

[21]  Terrance L. Huntsberger,et al.  PARALLEL SELF-ORGANIZING FEATURE MAPS FOR UNSUPERVISED PATTERN RECOGNITION , 1990 .

[22]  James C. Bezdek,et al.  Sequential Competitive Learning and the Fuzzy c-Means Clustering Algorithms , 1996, Neural Networks.

[23]  R. Fisher.  THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

[24]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..