TY - GEN
T1 - WAVELETS AS BASIS FUNCTIONS FOR LOCALIZED LEARNING IN A MULTI-RESOLUTION HIERARCHY
AU - Bakshi, Bhavik R.
AU - Stephanopoulos, George
N1 - Publisher Copyright:
© 1992 IEEE
PY - 1992
Y1 - 1992
N2 - A novel artificial neural network with one hidden layer of nodes, whose basis functions are drawn from a family of orthonormal wavelets, is developed in this paper. Wavelet Networks or Wave-Nets are based on firm theoretical foundations of functional analysis. The good localization characteristics of the basis functions, both in the input and frequency domains, allow hierarchical, multi-resolution learning of input-output maps from experimental data. Furthermore, Wave-Nets allow explicit estimation of global and local prediction error-bounds, and thus lend themselves to a rigorous and transparent design of the network. Computational complexity arguments prove that the training and adaptation efficiency of Wave-Nets is at least an order of magnitude better than other networks. This paper presents the mathematical framework for the development of Wave-Nets and discusses various aspects of their practical implementation. The problem of predicting a chaotic time-series is solved as an illustrative example.
AB - A novel artificial neural network with one hidden layer of nodes, whose basis functions are drawn from a family of orthonormal wavelets, is developed in this paper. Wavelet Networks or Wave-Nets are based on firm theoretical foundations of functional analysis. The good localization characteristics of the basis functions, both in the input and frequency domains, allow hierarchical, multi-resolution learning of input-output maps from experimental data. Furthermore, Wave-Nets allow explicit estimation of global and local prediction error-bounds, and thus lend themselves to a rigorous and transparent design of the network. Computational complexity arguments prove that the training and adaptation efficiency of Wave-Nets is at least an order of magnitude better than other networks. This paper presents the mathematical framework for the development of Wave-Nets and discusses various aspects of their practical implementation. The problem of predicting a chaotic time-series is solved as an illustrative example.
UR - http://www.scopus.com/inward/record.url?scp=0007736440&partnerID=8YFLogxK
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U2 - 10.1109/IJCNN.1992.227017
DO - 10.1109/IJCNN.1992.227017
M3 - Conference contribution
AN - SCOPUS:0007736440
T3 - Proceedings of the International Joint Conference on Neural Networks
SP - 140
EP - 145
BT - Proceedings - 1992 International Joint Conference on Neural Networks, IJCNN 1992
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 1992 International Joint Conference on Neural Networks, IJCNN 1992
Y2 - 7 June 1992 through 11 June 1992
ER -