A synthesis method based on stability analysis for complex-valued Hopfield neural network

This paper discusses the synthesis problem for a class of discrete time complex-valued Hopfield neural network. To be an associative memory, each memory pattern of the network should be stable and attractive. For this reason, this paper firstly analysis the stability of network, where a generalized Hamming distance defined in complex-valued domain is used to be Lyapunov function. Thus a stable criterion about network parameters is derived and utilized to decide whether the network synthesized by equilibrium equations is local asymptotically stable. If not, then the gain of activation function is regulated until the stable criterion is satisfied. Compared with commonly used Hebb rule, the proposed complex-valued network synthesis method need not orthogonal relations between the set of memory patterns, or the symmetric assumption for the interconnection matrix, but can guarantee each desired memory pattern is attractive.

[1]  B. Widrow,et al.  The complex LMS algorithm , 1975, Proceedings of the IEEE.

[2]  A. Michel,et al.  Analysis and synthesis of a class of neural networks: linear systems operating on a closed hypercube , 1989 .

[3]  Anthony N. Michel,et al.  Analysis and synthesis techniques for Hopfield type synchronous discrete time neural networks with application to associative memory , 1990 .

[4]  John J. Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities , 1999 .

[5]  Donq-Liang Lee Improving the capacity of complex-valued neural networks with a modified gradient descent learning rule , 2001, IEEE Trans. Neural Networks.

[6]  Donq-Liang Lee,et al.  Relaxation of the stability condition of the complex-valued neural networks , 2001, IEEE Trans. Neural Networks.

[7]  Yasuaki Kuroe,et al.  On energy function for complex-valued neural networks and its applications , 2002, Proceedings of the 9th International Conference on Neural Information Processing, 2002. ICONIP '02..

[8]  Jacek M. Zurada,et al.  A new design method for the complex-valued multistate Hopfield associative memory , 2003, IEEE Trans. Neural Networks.

[9]  C. Guzelis,et al.  Construction of energy landscape for discrete Hopfield associative memory with guaranteed error correction capability , 2003, First International IEEE EMBS Conference on Neural Engineering, 2003. Conference Proceedings..

[10]  Akira Hirose,et al.  Complex-Valued Neural Networks: Theories and Applications , 2003 .

[11]  Yasuaki Kuroe,et al.  Models of Self-correlation Type Complex-Valued Associative Memories and Their Dynamics , 2005, ICANN.