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Discrete-time noise-tolerant Zhang neural network for dynamic matrix pseudoinversion

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Abstract

In this work, a discrete-time noise-tolerant Zhang neural network (DTNTZNN) model is proposed, developed, and investigated for dynamic matrix pseudoinversion. Theoretical analyses show that the proposed DTNTZNN model is inherently tolerant to noises and can simultaneously deal with different types of noise. For comparison, the discrete-time conventional Zhang neural network (DTCZNN) model is also presented and analyzed to solve the same dynamic problem. Numerical examples and results demonstrate the efficacy and superiority of the proposed DTNTZNN model for dynamic matrix pseudoinversion in the presence of various types of noise.

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References

  • Arqub OA (2017) Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditions. Comput Math Appl 73(6):1243–1261

    Article  MathSciNet  MATH  Google Scholar 

  • Arqub OA, Abo-Hammour Z (2014) Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm. Inf Sci 279(20):396–415

    Article  MathSciNet  MATH  Google Scholar 

  • Arqub OA, Momani S, Al-Mezel S, Kutbi M (2017) A novel iterative numerical algorithm for the solutions of systems of fuzzy initial value problems. Appl Math Inf Sci 11(4):1059–1074

    Article  Google Scholar 

  • Courrieu P (2005) Fast computation of Moore–Penrose inverse matrices. Neural Inf Process Lett Rev 8(2):25–29

    Google Scholar 

  • Cretu AM, Chagnon-Forget M, Payeur P (2017) Selectively densified 3D object modeling based on regions of interest detection using neural gas networks. Soft Comput 21(18):5443–5455

    Article  Google Scholar 

  • Feldkamp LA, Puskorius GV (1998) A signal processing framework based on dynamic neural networks with application to problem in adaptation, filtering, and classification. Proc IEEE 86(11):2259–2277

    Article  Google Scholar 

  • Guo W, Huang T (2010) Method of elementary transformation to compute Moore–Penrose inverse. Appl Math Comput 216(5):1614–1617

    MathSciNet  MATH  Google Scholar 

  • Guo D, Zhang Y (2014) Zhang neural network for online solution of time-varying linear matrix inequality aided with a equal conversion. IEEE Trans Neural Netw Learn Syst 25(2):370–382

    Article  Google Scholar 

  • Huang F, Zhang X (2006) An improved Newton iteration for the weighted Moore–Penrose inverse. Appl Math Comput 174(2):1460–1486

    MathSciNet  MATH  Google Scholar 

  • Jin L, Zhang Y (2014) Discrete-time Zhang neural network of \(O(\tau ^3)\) pattern for time-varying matrix pseudoinversion with application to manipulator motion generation. Neurocomputing 142(22):165–173

    Article  Google Scholar 

  • Jin L, Zhang Y, Li S (2016) Integration-enhanced Zhang neural network for real-time-varying matrix inversion in the presence of various kinds of noises. IEEE Trans Neural Netw Learn Syst 26(12):2615–2627

    Article  Google Scholar 

  • John M, Kurtis F (2004) Numerical methods using MATLAB, 4th edn. Prentice Hall, London

    Google Scholar 

  • Juang L, Wu M (2010) Image noise reduction using Wiener filtering with pseudo-inverse. Medsci 43(10):1649–1655

    Google Scholar 

  • Kang S (2017) Outgoing call recommendation using neural network. Soft Comput. https://doi.org/10.1007/s00500-017-2946-3

    Article  Google Scholar 

  • Liao B, Zhang Y (2014) From different ZFs to different ZNN models accelerated via Li activation functions to finite-time convergence for time-varying matrix pseudoinversion. Neurocomputing 133(10):512–522

    Article  Google Scholar 

  • Liu J, Chen S, Tan X, Zhang D (2007) Efficient pseudoinverse linear discriminant analysis and its nonlinear form for face recognition. Int J Pattern Recognit Artif Intell 21(8):1265–1278

    Article  Google Scholar 

  • Moon HM, Seo CH, Pan SB (2017) A face recognition system based on convolution neural network using multiple distance face. Soft Comput 21(17):4995–5002

    Article  Google Scholar 

  • Nadeem M, Banka H, Venugopal R (2018) A neural network-based approach for steady-state modelling and simulation of continuous balling process. Soft Comput 22(3):873–887

    Article  Google Scholar 

  • Nemec B, Zlajpah L (2000) Null space velocity control with dynamically consistent pseudo-inverse. Robotica 18(5):513–518

    Article  Google Scholar 

  • Perković MD, Stanimirović PS (2011) Iterative method for computing the Moore–Penrose inverse based on Penrose equations. J Comput Appl Math 235(6):1604–1613

    Article  MathSciNet  MATH  Google Scholar 

  • Tasić MB, Stanimirović PS, Petković MD (2007) Symbolic computation of weighted Moore–Penrose inverse using partitioning method. Appl Math Comput 189(1):615–640

    MathSciNet  MATH  Google Scholar 

  • Wang J (1997) Recurrent neural networks for computing pseudoinverses of rank-deficient matrices. SIAM J Sci Comput 18(5):1479–1493

    Article  MathSciNet  MATH  Google Scholar 

  • Wang J, Jeong J (2017) Wavelet-content-adaptive BP neural network-based deinterlacing algorithm. Soft Comput. https://doi.org/10.1007/s00500-017-2968-x

    Article  Google Scholar 

  • Wang H, Li J, Liu H (2006) Practical limitations of an algorithm for the singular value decomposition as applied to redundant manipulators. In: Proceedings of IEEE conference on robotics, automation and mechatronics. pp 1–6

  • Wei Y (2000) Recurrent neural networks for computing weighted Moore–Penrose inverse. Appl Math Comput 116(3):279–287

    MathSciNet  MATH  Google Scholar 

  • Wei Y, Wu H, Wei J (2000) Successive matrix squaring algorithm for parallel computing the weighted generalized inverse \(A^{+}_{MN}\). Appl Math Comput 116(3):289–296

    MathSciNet  MATH  Google Scholar 

  • Wei Y, Cai J, Michael KN (2004) Computing Moore–Penrose inverses of Toeplitz matrices by Newtons iteration. Math Comput Model 40(1–2):181–191

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang Y, Leithead WE (2005) Exploiting Hessian matrix and trust-region algorithm in hyperparameters estimation of Gaussian process. Appl Math Comput 171(2):1264–1281

    MathSciNet  MATH  Google Scholar 

  • Zhang BL, Zhang H, Ge SS (2004) Face recognition by applying wavelet subband representation and kernel associative memory. IEEE Trans Neural Netw 15(1):166–177

    Article  Google Scholar 

  • Zhang Y, Li Z, Guo D, Ke Z, Chen P (2013) Discrete-time ZD, GD and NI for solving nonlinear time-varying equations. Numer Algorithms 64(4):721–740

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang Z, Li Z, Zhang Y, Luo Y, Li Y (2015) Neural dynamic method based dual arm CMG scheme with time-varying constraints applied to humanoid robots. IEEE Trans Neural Netw Learn Syst 26(12):3251–3262

    Article  MathSciNet  Google Scholar 

  • Zhang Y, Jin L, Guo D, Yin Y, Chou Y (2015) Taylor-type 1-step-ahead numerical differentiation rule for first-order derivative approximation and ZNN discretization. J Comput Appl Math 273:29–40

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou J, Zhu Y, Li X, You Z (2002) Variants of the Greville formula with applications to exact recursive least squares. SIAM J Matrix Anal Appl 24(1):150–164

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (with numbers 61563017 and 61503152), by the Hunan Natural Science Foundation of China (with numbers 2017JJ3258 and 2017JJ3257), by the Research Foundation of Education Bureau of Hunan Province, China (with numbers 17B215 and 17C1299)).

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Correspondence to Bolin Liao.

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Communicated by A. Di Nola.

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Xiang, Q., Liao, B., Xiao, L. et al. Discrete-time noise-tolerant Zhang neural network for dynamic matrix pseudoinversion. Soft Comput 23, 755–766 (2019). https://doi.org/10.1007/s00500-018-3119-8

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