Lyapunov Theory-Based Multilayered Neural Network

This brief presents a Lyapunov theory-based weight adaptation scheme for a multilayered neural network (MLNN) mainly used to classify a multiple-input-multiple-output (MIMO) problem. Initially, the MLNN system is linearized using Taylor series expansion. Then, the weight adaptation scheme is designed based on the Lyapunov stability theory to iteratively update the weight. In the design, the Lyapunov function has to be well selected to construct an energy space with a single global minimum. Hence, the Lyapunov theory-based MLNN acts as a MIMO classifier for face recognition. Analysis and discussion on Lyapunov properties of the proposed classifier are included. The performance of the proposed technique is tested on the Olivetti Research Laboratory database for face classification, and some comparisons with existing conventional techniques are given. Simulation results have revealed that our proposed system achieved better performance.

[1]  Alexander S. Poznyak,et al.  Differential Neural Networks for Robust Nonlinear Control: Identification, State Estimation and Trajectory Tracking , 2001 .

[2]  Marimuthu Palaniswami,et al.  An adaptive tracking controller using neural networks for a class of nonlinear systems , 1998, IEEE Trans. Neural Networks.

[3]  S. Douglas,et al.  Linearized least-squares training of multilayer feedforward neural networks , 1991, IJCNN-91-Seattle International Joint Conference on Neural Networks.

[4]  M. Birgmeier,et al.  A fully Kalman-trained radial basis function network for nonlinear speech modeling , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[5]  Snehasis Mukhopadhyay,et al.  Adaptive control of nonlinear multivariable systems using neural networks , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[6]  Zhihong Man,et al.  Lyapunov stability-based adaptive backpropagation for discrete time system , 1999, ISSPA '99. Proceedings of the Fifth International Symposium on Signal Processing and its Applications (IEEE Cat. No.99EX359).

[7]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[8]  Zhihong Man,et al.  A New Adaptive Backpropagation Algorithm Based on Lyapunov Stability Theory for Neural Networks , 2006, IEEE Transactions on Neural Networks.

[9]  Zhihong Man,et al.  Nonlinear adaptive RBF neural filter with Lyapunov adaptation algorithm and its application to nonlinear channel equalization , 1999, ISSPA '99. Proceedings of the Fifth International Symposium on Signal Processing and its Applications (IEEE Cat. No.99EX359).

[10]  Zhihong Man,et al.  Lyapunov-theory-based radial basis function networks for adaptive filtering , 2002 .

[11]  Andrew Chi-Sing Leung,et al.  Two regularizers for recursive least squared algorithms in feedforward multilayered neural networks , 2001, IEEE Trans. Neural Networks.