Abstract
In this paper, a discrete-time recurrent neural network with one neuron and global convergence is proposed for k-winners-take-all (kWTA) operation. Comparing with the existing kWTA networks, the proposed network has simpler structure with only one neuron. The global convergence of the network can be guaranteed for kWTA operation. Simulation results are provided to show that the outputs vector of the network is globally convergent to the solution of the kWTA operation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Andreou, A., Boahen, K., Pouliquen, P., Pavasovic, A., Jenkins, R., Strohbehn, K.: Current-mode subthreshold mos circuits for analog vlsi neural systems. IEEE Trans. Neural Networks 2, 205–213 (1991)
Hertz, J., Krogh, A., Palmer, R.: Introduction to the Theory of Neural Computing. Addison-Wesley, Massachusetts (1991)
Marr, D., Poggio, T.: Cooperative computation of stereo disparity. Science 194, 283–287 (1976)
Wolfe, W., Mathis, D., Anderson, C., Rothman, J., Gottler, M., Brady, G., Walker, R., Duane, G., Alaghband, G.: K-winner networks. IEEE Trans. Neural Networks 2, 310–315 (1991)
Wang, J.: Analogue winner-take-all neural networks for determining maximum and minimum signals. Int. J. Electron 77, 355–367 (1994)
Urahama, K., Nagao, T.: K-winners-take-all circuit with o(n) complexity. IEEE Trans. Neural Networks 6, 776–778 (1995)
Sekerkiran, B., Cilingiroglu, U.: A cmos k-winners-take-all circuit with o(n) complexity. IEEE Trans. Circuits and Systems-II 46, 1–5 (1999)
Maass, W.: Neural computation with winner-take-all as the only nonlinear operation. Advances in Neural Information Processing Systems 12, 293–299 (1999)
Marinov, C., Calvert, B.: Performance analysis for a k-winners-take-all analog neural network: basic theory. IEEE Trans. Neural Networks 14, 766–780 (2003)
Liu, S., Wang, J.: A simplified dual neural network for quadratic programming with its kwta application. IEEE Trans. Neural Networks 17, 1500–1510 (2006)
Liu, Q., Wang, J.: Two k-winners-take-all networks with discontinuous activation functions. Neural Networks 21, 406–413 (2008)
Hu, X., Wang, J.: An improved dual neural network for solving a class of quadratic programming problems and its k-winners-take-all application. IEEE Trans. Neural Networks 19, 2022–2031 (2008)
Bazaraa, M., Sherali, H., Shetty, C.: Nonlinear Programming: Theory and Algorithms, 2nd edn. John Wiley, New York (1993)
Marinov, C., Hopfield, J.: Stable computational dynamics for a class of circuits with o(n) interconnections capable of kwta and rank extractions. IEEE Trans. Circuits and Systems-I 52, 949–959 (2005)
Kinderlehrer, D., Stampacchia, G.: An Introduction to Variational Inequalities and Their Applications. Academic, New York (1982)
LaSalle, J.: The Stability of Dynamical Systems. Society for Industrial Mathematics (1976)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liu, Q., Cao, J., Liang, J. (2009). A Discrete-Time Recurrent Neural Network with One Neuron for k-Winners-Take-All Operation. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01507-6_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-01507-6_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01506-9
Online ISBN: 978-3-642-01507-6
eBook Packages: Computer ScienceComputer Science (R0)