A dynamic T-S fuzzy systems identification algorithm based on sparsity regularization

Fuzzy systems identification suffers from “rules explosion”, i.e., the number of fuzzy rules grows exponentially with the increase of the dimension of the input variable. In this paper, a dynamic algorithm is exploited to address T-S fuzzy systems identification on the basis of sparsity regularization. With a dynamic increase of fuzzy rules, this method automatically extracts fuzzy rules' antecedent part in a way of iterative vector quantization clustering and estimates the parameters of fuzzy rules' consequent part on the basis of sparsity regularization. In such a way, a minimal number of fuzzy rules and nonzero consequent parameters can be guaranteed in T-S fuzzy systems identification. Finally, some numerical experiments on a well-known benchmark dataset are carried out to verify the effectiveness of the proposed approach.

[1]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[2]  Ron Kohavi,et al.  A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection , 1995, IJCAI.

[3]  Yong-Ming Li,et al.  Approximation theory of fuzzy systems based upon genuine many-valued implications - MIMO cases , 2002, Fuzzy Sets Syst..

[4]  Francisco Herrera,et al.  Ten years of genetic fuzzy systems: current framework and new trends , 2004, Fuzzy Sets Syst..

[5]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  László T. Kóczy,et al.  Separated Antecedent and Consequent Learning for Takagi-Sugeno Fuzzy Systems , 2006, 2006 IEEE International Conference on Fuzzy Systems.

[7]  L X Wang,et al.  Fuzzy basis functions, universal approximation, and orthogonal least-squares learning , 1992, IEEE Trans. Neural Networks.

[8]  Michio Sugeno,et al.  A fuzzy-logic-based approach to qualitative modeling , 1993, IEEE Trans. Fuzzy Syst..

[9]  Michael Elad,et al.  Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing , 2010 .

[10]  O. Nelles.  Nonlinear System Identification , 2001 .

[11]  Robert Babuska,et al.  Fuzzy Modeling for Control , 1998 .

[12]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[13]  O. Nelles.  Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models , 2000 .

[14]  Yong-Ming Li,et al.  Approximation theory of fuzzy systems based upon genuine many-valued implications - MIMO cases , 2002, Fuzzy Sets Syst..

[15]  Edwin Lughofer,et al.  Extensions of vector quantization for incremental clustering , 2008, Pattern Recognit..

[16]  M. MendelJ.,et al.  Fuzzy basis functions , 1995 .

[17]  Junzhou Huang,et al.  Learning with dynamic group sparsity , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[18]  Edwin Lughofer,et al.  SparseFIS: Data-Driven Learning of Fuzzy Systems With Sparsity Constraints , 2010, IEEE Transactions on Fuzzy Systems.

[19]  Jyh-Shing Roger Jang,et al.  ANFIS: adaptive-network-based fuzzy inference system , 1993, IEEE Trans. Syst. Man Cybern..

[20]  Yinghua Lin,et al.  A new approach to fuzzy-neural system modeling , 1995, IEEE Trans. Fuzzy Syst..

[21]  Euntai Kim,et al.  A Simple Identified Sugeno-Type Fuzzy Model via Double Clustering , 1998, Inf. Sci..

[22]  Stephen L. Chiu,et al.  Fuzzy Model Identification Based on Cluster Estimation , 1994, J. Intell. Fuzzy Syst..

[23]  Sung-Kwun Oh,et al.  Identification of Fuzzy Inference Systems Using a Multi-objective Space Search Algorithm and Information Granulation , 2011 .

[24]  Sung-Kwun Oh,et al.  Identification of fuzzy systems by means of an auto-tuning algorithm and its application to nonlinear systems , 2000, Fuzzy Sets Syst..

[25]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986, Encyclopedia of Big Data.

[26]  R. Dennis Cook,et al.  Cross-Validation of Regression Models , 1984 .

[27]  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.

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

[29]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[30]  George E. Tsekouras,et al.  On the use of the weighted fuzzy c-means in fuzzy modeling , 2005, Adv. Eng. Softw..

[31]  Ferenc Szeifert,et al.  Modified Gath-Geva fuzzy clustering for identification of Takagi-Sugeno fuzzy models , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[32]  M. S. Fadali,et al.  Fuzzy TSK positive systems: Stability and control , 2011, Proceedings of the 2011 American Control Conference.

[33]  Sung-Kwun Oh,et al.  Identification of fuzzy models using a successive tuning method with a variant identification ratio , 2008, Fuzzy Sets Syst..

[34]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .