新型递归神经网络求解时变矩阵Moore-Penrose逆

doi:10.3969/j.cnki.jdxb.2017.03.007

吉首大学学报（自然科学版）

新型递归神经网络求解时变矩阵Moore-Penrose逆

向秋红,廖柏林,马川

（1.吉首大学数学与统计学院，湖南吉首 416000；2.吉首大学信息科学与工程学院，湖南吉首 416000）

出版日期:2017-05-25 发布日期:2017-06-19
通讯作者: 廖柏林（1981—），男，湖南衡阳人，吉首大学信息科学与工程学院副教授，博士，硕士生导师，主要从事神经网络和智能计算研究.
作者简介:向秋红（1990—），女，湖南湘西人，吉首大学数学与统计学院硕士研究生，主要从事神经计算研究
基金资助:
国家自然科学基金资助项目（61563017，61503152）;吉首大学校级科研项目（JDY16007）;锰锌钒产业技术协同创新中心研究生科研创新项目

Novel Neural Network for Dynamic Matrix Moore-Penrose Inverse

XIANG Qiuhong,LIAO Bolin,MA Chuan

(1.College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China;2.College ofInformation Science and Engineering,Jishou University,Jishou 416000,Hunan China)

Online:2017-05-25 Published:2017-06-19

摘要/Abstract

摘要：

将传统梯度神经网络（GNN）与张神经网络（ZNN）巧妙结合，提出了一种新型的神经网络（NNN）模型.在相同的条件下，采用NNN，GNN，ZNN模型求解时变矩阵M-P逆，从理论上证明了NNN模型的有效性和优越性.计算机仿真结果表明NNN模型在有噪声的条件下求解矩阵M-P逆具鲁棒性.

关键词： 梯度神经网络, 张神经网络, 矩阵Moore-Penrose逆

Abstract:

A novel neural network model (termed NNN model) is proposed,which is composed of a conventional gradient neural network (GNN) and the recently proposed Zhang neural network (ZNN).In the same conditions,NNN,GNN and ZNN are applied for solving the dynamic matrix Moore-Penrose (M-P) inverse.The theoretical analyses demonstrate the efficacy and superiority of the proposed NNN model,and the computer-simulation results show that the NNN model has good robustness against noise.

Key words: gradient neural network, Zhang neural network, Moore-Penrose (M-P) inverse

向秋红,廖柏林,马川. 新型递归神经网络求解时变矩阵Moore-Penrose逆[J]. 吉首大学学报（自然科学版）, DOI: 10.3969/j.cnki.jdxb.2017.03.007.

XIANG Qiuhong,LIAO Bolin,MA Chuan. Novel Neural Network for Dynamic Matrix Moore-Penrose Inverse[J]. Journal of Jishou University（Natural Sciences Edition), DOI: 10.3969/j.cnki.jdxb.2017.03.007.

参考文献

[1] NEMEC BO JAN,ZLAJPAH LEON.Null Space Velocity Control with Dynamically Consistent Pseudo-Inverse[J].Robotica,2000,18(5):513-518.
[2] BAUSCHKE HEINZ H,BORWEIN JONATHAN M,WANG Xianfu.Fitzpatrick Functions and Continuous Linear Monotone Operators[J].Siam Journal and Optimization,2007,18(3):789-809.
[3] HARTMANN WOLFGAN M,HARTWIG ROBERT E.Computing the Moore-Penrose Inverse for the Covariance Matrix in Constrained Nonlinear Estimation[J].Siam Journal and optimization,1996,6(3):727-747.
[4] KOHONEN TEUVO,BARNA GYORGY,CHRISLRY RONALD.Statistical Pattern Recognition with Neural Networks：Benchmarking Studies[C].IEEE International Conference on Neural Networks,1988,1(2)：61-68.
[5] ZHANG Bailin,ZHANG Hanhong,SAM GE SUZHI.Face Recognition by Applying Wavelet Subband Representation and Kernel Associative Memory[J].IEEE Transactions on Neural Networks,2004,15(1):166-77.
[6] ZHOU Jie,ZHU Yunmin,LI Xirong,et al.Variants of the Greville Formula with Applications to Exact Recursive Least Squares[J].Siam Journal on Matrix Analysis and Applications,2002,24(1):150-164.
[7] WANG Hanlei,LI Jiawei,LIU Hong.Practical Limitations of an Algorithm for the Singular Value Decomposition as Applied to Redundant Manipulators[C].IEEE Conference on Robotics,Automation and Mecha,2006,63(9):1-6.
[8] ZHANG Yunong,YI Chenfu.Zhang Neural Networks and Neural -Dynamic Method[M].New York：Nova Science Publishers,2011.
[9] 张雨浓,黎卫兵,郭东生，等.基于前向和中间差分的离散ＺＮＮ的定常矩阵求逆方法[J].中国科学技术大学学报,2013,43(4):259-264.
[10] ZHANG Yunong,YI Chenfu,MA Weimu.Simulation and Verification of Zhang Neural Network for Online Time-Varying Matrix Inversion[J].Simulation Modeling Practice and Theory,2009,17(10)：1 603-1 617.
[11] ZHANG Yunong,YANG Yiwen,TAN Ning,et al.Zhang Neural Network Solving for Time-Varying Full-Rank Matrix Moore-Penrose Inverse[J].Computing,2011,92(2):97-121.
[12] LIAO Bolin,ZHANG Yunong.From Different ZFs to Different ZNN Models Accelerated via Li Activation Functions to Finite-Time Convergence for Time-Varying Matrix Pseudoinversion[J].Neurocomputing 2014,133(8):512-522.
[13] WANG Jun.Recurrent Neural Networks for Computing Pseudoinverses of Rank-Deficient Matrix[J].Siam Journal on Scientific Computing,1997,18 (5):1 479-1 493.
[14] 肖林,皮赛男,孟凡斌.梯度神经网络在p次方根求解中的应用[J].吉首大学学报（自然科学版）,2015,36(3):15-18.
[15] 汪思成，肖林，严慧玲.基于不同误差函数的神经网经求解线性方程组[J].吉首大学学报（自然科学版）,2016,37(6):26-28.

新型递归神经网络求解时变矩阵Moore-Penrose逆

Novel Neural Network for Dynamic Matrix Moore-Penrose Inverse

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[1]	汪思成，肖林，严慧玲. 基于不同误差函数的神经网络求解线性方程组[J]. 吉首大学学报（自然科学版）, 2016, 37(6): 26-28.
[2]	肖林, 皮赛男, 孟凡斌. 梯度神经网络在p次方根求解中的应用[J]. journal6, 2015, 36(3): 15-18.