Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.neucom.2006.01.003
Title: Convergence analysis of Xu's LMSER learning algorithm via deterministic discrete time system method
Authors: Cheng Lv, Jian
Yi, Zhang
Tan, K.K. 
Keywords: Deterministic discrete time system
Oja's learning algorithm
Principal component analysis
Xu's learning algorithm
Issue Date: Dec-2006
Source: Cheng Lv, Jian, Yi, Zhang, Tan, K.K. (2006-12). Convergence analysis of Xu's LMSER learning algorithm via deterministic discrete time system method. Neurocomputing 70 (1-3) : 362-372. ScholarBank@NUS Repository. https://doi.org/10.1016/j.neucom.2006.01.003
Abstract: The convergence of Xu's LMSER algorithm with a constant learning rate, which is in the one unit case, is interpreted by analyzing an associated deterministic discrete time (DDT) system. Some convergent results relating to the Xu's DDT system are obtained. An invariant set and an ultimate bound are identified so that the non-divergence of the system can be guaranteed. It is rigorously proven that all trajectories of the system from points in this invariant set will converge exponentially to a unit eigenvector associated with the largest eigenvalue of the correlation matrix. By comparing Xu's algorithm with Oja's algorithm, it can be observed, on the whole, the Xu's algorithm evolves faster at a cost of larger computational complexity. Extensive simulations will be carried out to illustrate the theory. © 2006 Elsevier B.V. All rights reserved.
Source Title: Neurocomputing
URI: http://scholarbank.nus.edu.sg/handle/10635/55434
ISSN: 09252312
DOI: 10.1016/j.neucom.2006.01.003
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