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Title: Global convergence of GHA learning algorithm with nonzero-approaching adaptive learning rates
Authors: Lv, J.C.
Yi, Z.
Tan, K.K. 
Keywords: Deterministic discrete-time (DDT) equation
Generalized Hebbian algorithm (GHA)
Global convergence
Neural networks (NNs)
Principal component analysis (PCA)
Issue Date: Nov-2007
Citation: Lv, J.C., Yi, Z., Tan, K.K. (2007-11). Global convergence of GHA learning algorithm with nonzero-approaching adaptive learning rates. IEEE Transactions on Neural Networks 18 (6) : 1557-1571. ScholarBank@NUS Repository.
Abstract: The generalized Hebbian algorithm (GHA) is one of the most widely used principal component analysis (PCA) neural network (NN) learning algorithms. Learning rates of GHA play important roles in convergence of the algorithm for applications. Traditionally, the learning rates of GHA are required to converge to zero so that its convergence can be analyzed by studying the corresponding deterministic continuous-time (DCT) equations. However, the requirement for learning rates to approach zero is not a practical one in applications due to computational roundoff limitations and tracking requirements. In this paper, nonzero-approaching adaptive learning rates are proposed to overcome this problem. These proposed adaptive learning rates converge to some positive constants, which not only speed up the algorithm evolution considerably, but also guarantee global convergence of the GHA algorithm. The convergence is studied in detail by analyzing the corresponding deterministic discrete-time (DDT) equations. Extensive simulations are carried out to illustrate the theory. © 2007 IEEE.
Source Title: IEEE Transactions on Neural Networks
ISSN: 10459227
DOI: 10.1109/TNN.2007.895824
Appears in Collections:Staff Publications

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