Adaptive resolution min-max classifiers

A high automation degree is one of the most important features of data driven modeling tools and it should be taken into consideration in classification systems design. In this regard, constructive training algorithms are essential to improve the automation degree of a modeling system. Among neuro-fuzzy classifiers, Simpson's (1992) min-max networks have the advantage of being trained in a constructive way. The use of the hyperbox, as a frame on which different membership functions can be tailored, makes the min-max model a flexible tool. However, the original training algorithm evidences some serious drawbacks, together with a low automation degree. In order to overcome these inconveniences, in this paper two new learning algorithms for fuzzy min-max neural classifiers are proposed: the adaptive resolution classifier (ARC) and its pruning version (PARC). ARC/PARC generates a regularized min-max network by a succession of hyperbox cuts. The generalization capability of ARC/PARC technique mostly depends on the adopted cutting strategy. By using a recursive cutting procedure (R-ARC and R-PARC) it is possible to obtain better results. ARC, PARC, R-ARC, and R-PARC are characterized by a high automation degree and allow to achieve networks with a remarkable generalization capability. Their performances are evaluated through a set of toy problems and real data benchmarks. The paper also proposes a suitable index that can be used for the sensitivity analysis of the classification systems under consideration.

[1]  Antonello Rizzi,et al.  A constructive algorithm for fuzzy neural networks , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[2]  Patrick K. Simpson,et al.  Fuzzy min-max neural networks. I. Classification , 1992, IEEE Trans. Neural Networks.

[3]  Andrzej Bargiela,et al.  General fuzzy min-max neural network for clustering and classification , 2000, IEEE Trans. Neural Networks Learn. Syst..

[4]  James C. Bezdek,et al.  Fuzzy models—What are they, and why? [Editorial] , 1993, IEEE Transactions on Fuzzy Systems.

[5]  Antonello Rizzi,et al.  A recursive algorithm for fuzzy min-max networks , 2000, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium.

[6]  J. Rissanen.  Stochastic Complexity and Modeling , 1986 .

[7]  P. K. Simpson.  Fuzzy Min-Max Neural Networks-Part 1 : Classification , 1992 .

[8]  Vladimir Vapnik,et al.  Chervonenkis: On the uniform convergence of relative frequencies of events to their probabilities , 1971 .

[9]  S. Hyakin,et al.  Neural Networks: A Comprehensive Foundation , 1994 .

[10]  Mahesan Niranjan,et al.  On the Practical Applicability of VC Dimension Bounds , 1995, Neural Computation.

[11]  James C. Bezdek,et al.  A geometric approach to cluster validity for normal mixtures , 1997, Soft Comput..

[12]  Elias N. Houstis,et al.  On neurobiological, neuro-fuzzy, machine learning, and statistical pattern recognition techniques , 1997, IEEE Trans. Neural Networks.

[13]  Vassilios Petridis,et al.  Fuzzy lattice neural network (FLNN): a hybrid model for learning , 1998, IEEE Trans. Neural Networks.

[14]  James C. Bezdek,et al.  A Review of Probabilistic, Fuzzy, and Neural Models for Pattern Recognition , 1996, J. Intell. Fuzzy Syst..

[15]  Antonello Rizzi,et al.  Generalized min-max classifier , 2000, Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063).

[16]  Antonello Rizzi,et al.  Adaptive resolution min-max classifier , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[17]  Bagrat R. Amirikian,et al.  What size network is good for generalization of a specific task of interest? , 1994, Neural Networks.

[18]  Antonello Rizzi,et al.  A nonexclusive classification system based on co-operative fuzzy clustering , 1998, 9th European Signal Processing Conference (EUSIPCO 1998).

[19]  David Haussler,et al.  What Size Net Gives Valid Generalization? , 1989, Neural Computation.

[20]  G. Costantini,et al.  TWO NONEXCLUSIVE NEURO-FUZZY CLASSIFIERS FOR RECOGNITION OF MUSICAL INSTRUMENTS , 2000 .

[21]  Antonello Rizzi.  Automatic Training of Min-Max Classifiers , 2000 .

[22]  Roberto Tagliaferri,et al.  Fuzzy neural networks for classification and detection of anomalies , 1998, IEEE Trans. Neural Networks.

[23]  B. Ripley,et al.  Pattern Recognition , 1968, Nature.