Discrete-Time Recurrent Neural Networks With Complex-Valued Linear Threshold Neurons

This brief discusses a class of discrete-time recurrent neural networks with complex-valued linear threshold neurons. It addresses the boundedness, global attractivity, and complete stability of such networks. Some conditions for those properties are also derived. Examples and simulation results are used to illustrate the theory.

[1]  Akira Hirose Complex-Valued Neural Networks , 2006, Studies in Computational Intelligence.

[2]  Igor N. Aizenberg,et al.  Solving the XOR and parity N problems using a single universal binary neuron , 2007, Soft Comput..

[3]  Lisheng Wang,et al.  Sufficient and necessary conditions for global exponential stability of discrete-time recurrent neural networks , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  Richard Hans Robert Hahnloser,et al.  Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit , 2000, Nature.

[5]  Heiko Wersing,et al.  A Competitive-Layer Model for Feature Binding and Sensory Segmentation , 2001, Neural Computation.

[6]  Zhang Yi,et al.  Multistability Analysis for Recurrent Neural Networks with Unsaturating Piecewise Linear Transfer Functions , 2003, Neural Computation.

[7]  Claudio Moraga,et al.  Multilayer Feedforward Neural Network Based on Multi-valued Neurons (MLMVN) and a Backpropagation Learning Algorithm , 2006, Soft Comput..

[8]  Zhang Yi,et al.  A Modified Oja–Xu MCA Learning Algorithm and Its Convergence Analysis , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[9]  S. L. Goh,et al.  An Augmented Extended Kalman Filter Algorithm for Complex-Valued Recurrent Neural Networks , 2007, Neural Computation.

[10]  Richard H. R. Hahnloser,et al.  On the piecewise analysis of networks of linear threshold neurons , 1998, Neural Networks.

[11]  Constantine Butakoff,et al.  Image processing using cellular neural networks based on multi-valued and universal binary neurons , 2002, J. VLSI Signal Process..

[12]  Jacek M. Zurada,et al.  Blur Identification by Multilayer Neural Network Based on Multivalued Neurons , 2008, IEEE Transactions on Neural Networks.

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

[14]  Qiankun Song,et al.  Passivity analysis of discrete-time stochastic neural networks with time-varying delays , 2009, Neurocomputing.

[15]  Joos Vandewalle,et al.  Multi-Valued and Universal Binary Neurons , 2000 .

[16]  Zidong Wang,et al.  A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays , 2007 .

[17]  Joos Vandewalle,et al.  Multi-Valued and Universal Binary Neurons: Theory, Learning and Applications , 2012 .

[18]  Jacek M. Zurada,et al.  Complex-valued multistate neural associative memory , 1996, IEEE Trans. Neural Networks.

[19]  Naum N. Aizenberg,et al.  Cellular neural networks and computational intelligence in medical image processing , 2001, Image Vis. Comput..

[20]  Zhang Yi,et al.  Multistability of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions , 2004, IEEE Transactions on Neural Networks.

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

[22]  Naum N. Aizenberg,et al.  CNN based on multi-valued neuron as a model of associative memory for grey scale images , 1992, CNNA '92 Proceedings Second International Workshop on Cellular Neural Networks and Their Applications.

[23]  Pheng-Ann Heng,et al.  Winner-take-all discrete recurrent neural networks , 2000 .

[24]  Kay Chen Tan,et al.  Analysis of Cyclic Dynamics for Networks of Linear Threshold Neurons , 2005, Neural Computation.

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

[26]  Jinde Cao,et al.  Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses , 2008, J. Frankl. Inst..

[27]  Danilo P. Mandic,et al.  A Complex-Valued RTRL Algorithm for Recurrent Neural Networks , 2004, Neural Computation.

[28]  Kay Chen Tan,et al.  Dynamics analysis and analog associative memory of networks with LT neurons , 2006, IEEE Transactions on Neural Networks.