Function Approximation with ARTMAP Architectures
Keywords:
fuzzy ARTMAP, universal approximation, regressionAbstract
We analyze function approximation (regression) capability of Fuzzy ARTMAP (FAM) architectures - well-known incremental learning neural networks. We focus especially on the universal approximation property. In our experiments, we compare the regression performance of FAM networks with other standard neural models. It is the first time that ARTMAP regression is overviewed, both from theoretical and practical points of view.
References
Girosi, F.; Poggio, T. (1989); Networks and the Best Approximation Property, Biological Cybernetics, 63: 169-176. http://dx.doi.org/10.1007/BF00195855
Hecht-Nielsen, R. (1987); Kolmogorov's mapping neural network existence theorem, Proceedings of IEEE First Annual International Conference on Neural Networks, 3: III-11-III-14.
Cybenko, G. (1992); Approximation by superpositions of a sigmoidal function, Mathematics of Control, Signals, and Systems, 5(4): 455-455. http://dx.doi.org/10.1007/BF02134016
Chen, T.; Chen, H. (1995); Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems, IEEE Transactions on Neural Networks, 6(4): 911-917. http://dx.doi.org/10.1109/72.392253
Hartman, E; Keeler, J.D.; Kowalski, J.M. (1990); Layered neural networks with Gaussian hidden units as universal approximations, Neural Computations, 2(2): 210-215.
Park, J.; Sandberg, I.W. (1991); Neural Computations, 3(2): 246-257.
Park, J.; Sandberg, I.W. (1993); Neural Computations, Approximation and radial-basisfunction networks, 5(2): 305-316.
Carpenter, G.A.; Grossberg, S.; Markuzon, N.; Reynolds, J.H.; Rosen, D.B. (1992); IEEE Transactions on Neural Networks, Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps, 3(5): 698-713.
Williamson, J. (1996); Neural Networks, Gaussian ARTMAP: A neural network for fast incremental learning of noisy multidimensional maps, 9:881-897.
Marriott, S.; Harrison, R.F. (1995); Neural Networks, A modified fuzzy ARTMAP architecture for the approximation of noisy mappings, 8(4): 619-641.
Andonie, R.; Sasu, L. (2006); IEEE Transactions on Neural Networks, Fuzzy ARTMAP with Input Relevances, 17: 929-941.
Yap, K.S.; Lim, C.P. Abidi, I.Z. (2008); IEEE Transactions on Neural Networks, A Hybrid ART-GRNN Online Learning Neural Network With a ε-Insensitive Loss Function, 19: 1641- 1646.
Yap, K.S.; Lim, C.P. Junita, M.S. (2010);
Yap, K.S.; Lim, C.P. Junita, M.S. (2010); Journal of Intelligen & Fuzzy Systems, An enhanced generalized adaptive resonance theory neural network and its application to medical pattern classification, 21: 65-78.
Marti, L.; Policriti, A.; Garcia, L. (2002); Hybrid Information Systems, First International Workshop on Hybrid Intelligent Systems, Adelaide, Australia, December 11-12, 2001, Proceedings, AppART: An ART Hybrid Stable Learning Neural Network for Universal Function Approximation, 93-119.
Verzi, S.J.; Heileman, G.L.; Georgiopoulos, M.; Anagnostopoulos, G.C. (2003); Proceedings of the IEEE International Joint Conference on Neural Networks (IJCNN 2003), Universal Approximation with Fuzzy ART and Fuzzy ARTMAP, (3): 1987-1992.
MacKay, D.J.C. (1996); Computation in Neural Systems, Probable networks and plausible predictions - a review of practical Bayesian methods for supervised neural networks, 6: 469-505.
Vigdor, B.; Lerner, B. (2007); IEEE Transactions on Neural Networks, The Bayesian ARTMAP, 18: 1628-1644.
Moore, B. (1988); Proceedings of the 1988 Connectionist Model Summer School, ART1 and Pattern Clustering, 174-185.
Carpenter, G.A.; Grossberg, S.; Reynolds, J.H. (1991); Neural Networks, Fuzzy ART: fast stable learning and categorization of analog patterns by an adaptive resonance system, (4): 759-771.
Lim, C.P.; Harrison, R.F. (1997); Neural Networks, 10(5), An Incremental Adaptive Network for On-line Supervised Learning and Probability Estimation, 925-939.
Lerner, B.; Guterman, H. (2008); Computational Intelligence Paradigms - Studies in Computational Intelligence, Springer, Advanced Developments and Applications of the Fuzzy ARTMAP Neural Network in Pattern Classification, 137: 77-107.
Sasu, L; Andonie, R. (2012); The Bayesian ARTMAP for Regression, under review.
Izquierdo, J.M.C.; Dimitriadis, Y.A.; Coronado, J.L. (1997); Proceedings of the Sixth IEEE International Conference on Fuzzy Systems, FasBack: matching-error based learning for automatic generation of fuzzy logic systems, 3: 1561 -1566.
Bellman, R.E. (1961), Rand Corporation Research studies, Adaptive control processes: a guided tour.
Andonie, R. (1997); Dealing with Complexity: A Neural Network Approach, The Psychological Limits of Neural Computation, 252-263.
Duda, R.O.; Hart, P.E.; David G.S (2000); Pattern Classification, 2nd edition.
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