Minimum fuel neural networks and their applications to overcomplete signal representations

Wang, Z.S.; Cheung, J.Y.; Xia, Yuqing; Chen, J.D.Z.

doi:10.1109/81.873870

Cited by 22 publications

(22 citation statements)

References 7 publications

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“…Reported results show that the cooperative modular neural networks can be well applied to classification and pattern recognition (Auda and Kamel 1997a, b, 1998a, b, 1999Zhang 2000;Lu and Ito 1999;Yang and Browne 2001;Oh and Suen 2002;Melin et al 2005;Fogelman-Soulie 1993;Hodge et al 1999;Kamel 1999;Alexandre et al 2001;Ozawa 1998;Islam et al 2003). Specially, in recent decade, as special one class of cooperative modular neural networks, cooperative recurrent modular neural networks for constrained optimization have been developed and well studied (Rodríguez-Vázquez et al 1990;Glazos et al 1998;Zhang and Constantinides 1992;He and Sun 2001;Tao and Fang 2000;Xia and Wang 1995, b, 2001, b, 2005Xia 1996aXia , b, 1997Xia , 2003Xia , 2004Xia et al 2002aXia et al , b, 2004aXia et al , b, 2005Xia et al , 2007Wang et al 2000;Tan et al 2000;Anguita and Boni 2002;Zhang et al 2003;Feng 2004, 2006;Kamel 2007a, b, c, d, 2008;Tao et al 2001;Leung et al 2001).…”

Section: Introductionmentioning

confidence: 99%

“…Theoretically, it was shown that under weaker condition than the conventional numerical methods, the cooperative recurrent neural networks can converge globally to the global optimal solution (Xia et al 2007). Moreover, they are successfully applied to classification, signal and image processing, system identification, and robot control (Wang et al 2000;Tan et al 2000;Anguita and Boni 2002;Wang 2001, 2004;Zhang et al 2003;Xia and Feng 2004;Xia et al 2002bXia et al , 2007Xia and Feng 2006;Kamel 2007a, b, c, d, 2008).…”

Section: Introductionmentioning

confidence: 99%

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Cooperative recurrent modular neural networks for constrained optimization: a survey of models and applications

Kamel

Xia

2008

Cogn Neurodyn

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Constrained optimization problems arise in a wide variety of scientific and engineering applications. Since several single recurrent neural networks when applied to solve constrained optimization problems for real-time engineering applications have shown some limitations, cooperative recurrent neural network approaches have been developed to overcome drawbacks of these single recurrent neural networks. This paper surveys in details work on cooperative recurrent neural networks for solving constrained optimization problems and their engineering applications, and points out their standing models from viewpoint of both convergence to the optimal solution and model complexity. We provide examples and comparisons to shown advantages of these models in the given applications.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cooperative recurrent modular neural networks for constrained optimization: a survey of models and applications

Kamel

Xia

2008

Cogn Neurodyn

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“…In such a circuit implementation, the projection operator of P Ω (·) is actually a simple limiter with a unit threshold. The matrix or vector multiplications are actually the synaptic weighting and summing operations, and hence, they can be implemented via a number of adders with a weighting function [1], [2], [11]- [13], [20]- [22], [31]- [33]. The rest are a number of simple integrators.…”

Section: Proofmentioning

confidence: 99%

“…These applications span the field of deconvolution, state estimation, blind source separation, system identification, parameter estimation, time-frequency analysis, and time-delay estimation [1]- [13]. The L 1 -norm solutions of systems of linear algebraic equations have certain properties not shared by the ordinary LS (L 2 -norm) solutions [1]- [13] as follows. 1) An L 1 -norm solution of an overdetermined system of linear equations always exists although the L 1 -norm solution is not necessarily unique in contrast to the L 2 -norm solution where the solution is always unique when matrix A is of full rank.…”

Section: Introductionmentioning

confidence: 99%

“…Hopfield and Tank first proposed to use an NN for solving linear programming problems [14], [15]. Their creative work has motivated many researchers to investigate alternative NNs for solving linear and nonlinear programming problems [1], [2], [11]- [13], [16]- [22] and for solving arbitrary roots of polynomials [23], [24]. For instance, Cichocki and Unbehauen proposed to use an NN for solving the unconstrained LAD problem [1].…”

Section: Introductionmentioning

confidence: 99%

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Constrained Least Absolute Deviation Neural Networks

Wang

Peterson

2008

IEEE Trans. Neural Netw.

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It is well known that least absolute deviation (LAD) criterion or L 1 -norm used for estimation of parameters is characterized by robustness, i.e., the estimated parameters are totally resistant (insensitive) to large changes in the sampled data. This is an extremely useful feature, especially, when the sampled data are known to be contaminated by occasionally occurring outliers or by spiky noise. In our previous works, we have proposed the least absolute deviation neural network (LADNN) to solve unconstrained LAD problems. The theoretical proofs and numerical simulations have shown that the LADNN is Lyapunov-stable and it can globally converge to the exact solution to a given unconstrained LAD problem. We have also demonstrated its excellent application value in timedelay estimation. More generally, a practical LAD application problem may contain some linear constraints, such as a set of equalities and/or inequalities, which is called constrained LAD problem, whereas the unconstrained LAD can be considered as a special form of the constrained LAD. In this paper, we present a new neural network called constrained least absolute deviation neural network (CLADNN) to solve general constrained LAD problems. Theoretical proofs and numerical simulations demonstrate that the proposed CLADNN is Lyapunov stable and globally converges to the exact solution to a given constrained LAD problem, independent of initial values. The numerical simulations have also illustrated that the proposed CLADNN can be used to robustly estimate parameters for nonlinear curve fitting, which is extensively used in signal and image processing.

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Neurodynamics

Kozma¹,

Wang²,

Zeng³

2015

Springer Handbook of Computational Intelligence

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This chapter introduces basic concepts, phenomena, and properties of neurodynamic systems. it consists of four sections with the first two on various neurodynamic behaviors of general neurodynamics and the last two on two types of specific neurodynamic systems. The neurodynamic behaviors discussed in the first two sections include attractivity, oscillation, synchronization, and chaos. The two specific neurodynamics systems are memrisitve neurodynamic systems and neurodynamic optimization systems.33.

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Minimum fuel neural networks and their applications to overcomplete signal representations

Cited by 22 publications

References 7 publications

Cooperative recurrent modular neural networks for constrained optimization: a survey of models and applications

Cooperative recurrent modular neural networks for constrained optimization: a survey of models and applications

Constrained Least Absolute Deviation Neural Networks

Neurodynamics

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