A novel fuzzy c-regression model algorithm using a new error measure and particle swarm optimization

Abstract This paper presents a new algorithm for fuzzy c-regression model clustering. The proposed methodology is based on adding a second regularization term in the objective function of a Fuzzy C-Regression Model (FCRM) clustering algorithm in order to take into account noisy data. In addition, a new error measure is used in the objective function of the FCRM algorithm, replacing the one used in this type of algorithm. Then, particle swarm optimization is employed to finally tune parameters of the obtained fuzzy model. The orthogonal least squares method is used to identify the unknown parameters of the local linear model. Finally, validation results of two examples are given to demonstrate the effectiveness and practicality of the proposed algorithm.

[1]  Xueli An,et al.  T-S fuzzy model identification based on a novel fuzzy c-regression model clustering algorithm , 2009, Eng. Appl. Artif. Intell..

[2]  Yilei Wu,et al.  A robust deterministic annealing algorithm for data clustering , 2007 .

[3]  Hichem Frigui,et al.  A Robust Competitive Clustering Algorithm With Applications in Computer Vision , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Dat Tran,et al.  A robust clustering approach to fuzzy Gaussian mixture models for speaker identification , 1999, 1999 Third International Conference on Knowledge-Based Intelligent Information Engineering Systems. Proceedings (Cat. No.99TH8410).

[5]  Bidyadhar Subudhi,et al.  A differential evolution based neural network approach to nonlinear system identification , 2011, Appl. Soft Comput..

[6]  R.J. Hathaway,et al.  Switching regression models and fuzzy clustering , 1993, IEEE Trans. Fuzzy Syst..

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

[8]  Hidetomo Ichihashi,et al.  On parameter setting in applying Dave's noise fuzzy clustering to Gaussian mixture models , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[9]  M Jacek.  -Insensitive Fuzzy -Regression Models: Introduction to -Insensitive Fuzzy Modeling , 2004 .

[10]  James M. Keller,et al.  Fuzzy Models and Algorithms for Pattern Recognition and Image Processing , 1999 .

[11]  Shih-Wei Lin,et al.  A novel function approximation based on robust fuzzy regression algorithm model and particle swarm optimization , 2011, Appl. Soft Comput..

[12]  Yu-Geng Xi,et al.  A clustering algorithm for fuzzy model identification , 1998, Fuzzy Sets Syst..

[13]  V. J. Rayward-Smith,et al.  Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition , 1999 .

[14]  Zhang Shu-Ling,et al.  Fuzzy Particle Swarm Clustering of Infrared Images , 2009, 2009 Second International Conference on Information and Computing Science.

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

[16]  Euntai Kim,et al.  A transformed input-domain approach to fuzzy modeling , 1998, IEEE Trans. Fuzzy Syst..

[17]  Zi-Qiang Lang,et al.  An Orthogonal Least Squares based approach to FIR designs , 2005, Int. J. Autom. Comput..

[18]  Euntai Kim,et al.  A new TSK fuzzy modeling approach , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[19]  José Ragot,et al.  Non-linear dynamic system identification: A multi-model approach , 1999 .

[20]  Ruiyun Qi,et al.  Indirect adaptive controller based on a self-structuring fuzzy system for nonlinear modeling and control , 2009, Int. J. Appl. Math. Comput. Sci..

[21]  Olfa Nasraoui,et al.  An improved possibilistic C-Means algorithm with finite rejection and robust scale estimation , 1996, Proceedings of North American Fuzzy Information Processing.

[22]  W. Peizhuang.  Pattern Recognition with Fuzzy Objective Function Algorithms (James C. Bezdek) , 1983 .

[23]  Abdelkader Chaari,et al.  Modified fuzzy model identification clustering algorithm for liquid level process , 2010, 18th Mediterranean Conference on Control and Automation, MED'10.

[24]  Rajesh N. Davé,et al.  Characterization and detection of noise in clustering , 1991, Pattern Recognit. Lett..

[25]  Xinzhi Liu,et al.  A Dynamic Clustering Algorithm Based on PSO and Its Application in Fuzzy Identification , 2006, 2006 International Conference on Intelligent Information Hiding and Multimedia.

[26]  Fu-Ding Xie,et al.  Image segmentation using PSO and PCM with Mahalanobis distance , 2011, Expert Syst. Appl..

[27]  Jan Maciej Kościelny,et al.  Fuzzy diagnostic reasoning that takes into account the uncertainty of the relation between faults and symptoms , 2006 .

[28]  H. Kundra.  Comparative Study of Particle Swarm Optimization based Unsupervised Clustering Techniques , 2009 .

[29]  B. Marx,et al.  Design of observers for TakagiߝSugeno descriptor systems with unknown inputs and application to fault diagnosis , 2007 .

[30]  Rajesh N. Davé,et al.  Robust clustering methods: a unified view , 1997, IEEE Trans. Fuzzy Syst..

[31]  Taher Niknam,et al.  An efficient hybrid approach based on PSO, ACO and k-means for cluster analysis , 2010, Appl. Soft Comput..

[32]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[33]  Hidetomo Ichihashi,et al.  Fuzzy PCA-Guided Robust $k$-Means Clustering , 2010, IEEE Transactions on Fuzzy Systems.

[35]  S. Sen,et al.  Clustering of relational data containing noise and outliers , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[36]  Didier Maquin,et al.  Observer based actuator fault tolerant control for nonlinear Takagi-Sugeno systems : an LMI approach , 2010, 18th Mediterranean Conference on Control and Automation, MED'10.

[37]  Qiang Niu,et al.  An improved fuzzy C-means clustering algorithm based on PSO , 2011, J. Softw..

[38]  Mieczysław A. Brdyś,et al.  FUZZY LOGIC GAIN SCHEDULING FOR NON-LINEAR SERVO TRACKING , 2002 .

[39]  Moez. Soltani,et al.  A modified fuzzy c-regression model clustering algorithm for T-S fuzzy model identification , 2011, Eighth International Multi-Conference on Systems, Signals & Devices.

[40]  Musa Alci,et al.  Fuzzy rule-base driven orthogonal approximation , 2008, Neural Computing and Applications.

[41]  Ben Niu,et al.  A multi-swarm optimizer based fuzzy modeling approach for dynamic systems processing , 2008, Neurocomputing.

[42]  Jacek M. Leski.  Epsiv-insensitive Fuzzy C-regression Models: Introduction to Epsiv-insensitive Fuzzy Modeling , 2004, IEEE Trans. Syst. Man Cybern. Part B.

[43]  Leon G. Higley,et al.  Forensic Entomology: An Introduction , 2009 .

[44]  Jacek Kluska.  Analytical Methods in Fuzzy Modeling and Control , 2009, Studies in Fuzziness and Soft Computing.

[45]  Miin-Shen Yang,et al.  Alternative c-means clustering algorithms , 2002, Pattern Recognit..

[46]  Kacprzyk. Janusz.  Analytical Methods in Fuzzy Modeling and Control , 2009 .

[47]  Mohammad Hossein Fazel Zarandi,et al.  Data-driven fuzzy modeling for Takagi-Sugeno-Kang fuzzy system , 2010, Inf. Sci..

[48]  Andri Riid,et al.  Identification of transparent, compact, accurate and reliable linguistic fuzzy models , 2011, Inf. Sci..

[49]  Jung-Hua Wang,et al.  A new robust clustering algorithm-density-weighted fuzzy c-means , 1999, IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028).

[50]  Sheng Chen,et al.  Orthogonal least squares methods and their application to non-linear system identification , 1989 .

[51]  I. Burhan Türksen,et al.  Enhanced Fuzzy System Models With Improved Fuzzy Clustering Algorithm , 2008, IEEE Transactions on Fuzzy Systems.

[52]  Hao Ying,et al.  Fuzzy Control and Modeling: Analytical Foundations and Applications , 2000 .

[53]  J. C. Peters,et al.  Fuzzy Cluster Analysis : A New Method to Predict Future Cardiac Events in Patients With Positive Stress Tests , 1998 .

[54]  XuLei Yang,et al.  A robust deterministic annealing algorithm for data clustering , 2005, Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005..

[55]  Dimiter Driankov,et al.  Fuzzy model identification - selected approaches , 1997 .

[56]  Isak Gath,et al.  Unsupervised Optimal Fuzzy Clustering , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[57]  Xueli An,et al.  A new T-S fuzzy-modeling approach to identify a boiler-turbine system , 2010, Expert Syst. Appl..

[58]  Hidetomo Ichihashi,et al.  Robust PCA with Intra-Sample Outlier Process Based on Fuzzy Mahalanobis Distances and Noise Clustering , 2005, The 14th IEEE International Conference on Fuzzy Systems, 2005. FUZZ '05..

[59]  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.

[60]  B. M. Arx.  Design of observers for Takagi-Sugeno descriptor systems with unknown inputs and application to fault diagnosis , 2008 .

[61]  Yong Zeng,et al.  Eliciting compact T-S fuzzy models using subtractive clustering and coevolutionary particle swarm optimization , 2009, Neurocomputing.

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