A novel recurrent neural network with one neuron and finite-time convergence for k-winners-take-all operation

IEEE Transactions on Neural Networks

Volumn 21, Issue 7, 2010, Pages 1140-1148

  Liu, Qingshan ^a   Dang, Chuangyin ^b   Cao, Jinde ^a  

^a SOUTHEAST UNIVERSITY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

global convergence in finite time; k winners take all operation; Lyapunov function; recurrent neural network

Indexed keywords

FINITE-TIME CONVERGENCE; GLOBAL CONVERGENCE; K-WINNERS-TAKE-ALL OPERATION; LINEAR PROGRAMMING PROBLEM; NUMERICAL EXAMPLE; SIMPLE STRUCTURES; SIMULATION RESULT; TAKE-ALL;

DIFFERENTIAL EQUATIONS; LINEARIZATION; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; RECURRENT NEURAL NETWORKS;

COMPUTER SIMULATION;

ALGORITHM; ANIMAL; ARTICLE; ARTIFICIAL NEURAL NETWORK; BIOLOGICAL MODEL; FEEDBACK SYSTEM; GAME; NERVE CELL; PHYSIOLOGY; TIME;

ALGORITHMS; ANIMALS; FEEDBACK; GAME THEORY; MODELS, NEUROLOGICAL; NEURAL NETWORKS (COMPUTER); NEURONS; TIME FACTORS;

EID: 77954561082     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2010.2050781     Document Type: Article

References (38)

1. A. Andreou, K. Boahen, P. Pouliquen, A. Pavasovic, R. Jenkins, and K. Strohbehn, "Current-mode subthreshold MOS circuits for analog VLSI neural systems," IEEE Trans. Neural Netw., vol.2, no.2, pp. 205-213, Mar. 1991.
2. J. Aubin and A. Cellina, Differential Inclusions: Set-Valued Maps and Viability Theory. New York: Springer-Verlag, 1984.
3. M. Bazaraa, H. Sherali, and C. Shetty, Nonlinear Programming: Theory and Algorithms, 3rd ed. Hoboken, NJ: Wiley, 2006.
4. L. Binh and H. Chong, "A neural-network contention controller for packet switching networks," IEEE Trans. Neural Netw., vol.6, no.6, pp. 1402-1410, Nov. 1995.
5. B. Calvert and C. Marinov, "Another k-winners-take-all analog neural network," IEEE Trans. Neural Netw., vol.11, no.4, pp. 829-838, Jul. 2000.
6. F. Clarke, Optimization and Nonsmooth Analysis. New York: Wiley, 1983.
7. C. Dang, Y. Leung, X. Gao, and K. Chen, "Neural networks for nonlinear and mixed complementarity problems and their applications," Neural Netw., vol.17, no.2, pp. 271-283, 2004.
8. A. Filippov, Differential Equations With Discontinuous Righthand Sides (Mathematics and Its Applications, Soviet Series). Boston, MA: Kluwer, 1988.
9. M. Forti, P. Nistri, and M. Quincampoix, "Generalized neural network for nonsmooth nonlinear programming problems," IEEE Trans. Circuits Syst. I, vol.51, no.9, pp. 1741-1754, Sep. 2004.
10. J. Hertz, A. Krogh, and R. Palmer, Introduction to the Theory of Neural Computing. Reading, MA: Addison-Wesley, 1991.
11. J. Hopfield and D. Tank, "Computing with neural circuits: A model," Science, vol.233, no.4764, pp. 625-633, 1986.
12. S. Hu and J. Wang, "Global robust stability of a class of discrete-time interval neural networks," IEEE Trans. Circuits Syst. I, vol.53, no.1, pp. 129-138, Jan. 2006.
13. X. Hu and J. Wang, "An improved dual neural network for solving a class of quadratic programming problems and its k-winners-take-all application," IEEE Trans. Neural Netw., vol.19, no.12, pp. 2022-2031, Dec. 2008.
14. X. Hu and B. Zhang, "A new recurrent neural network for solving convex quadratic programming problems with an application to the k-winnerstake- all problem," IEEE Trans. Neural Netw., vol.20, no.4, pp. 654-664, Apr. 2009.
15. Jayadeva and S. Rahman, "A neural network with O(N) neurons for ranking n numbers in O(1/N) time," IEEE Trans. Circuits Syst. I, vol.51, no.10, pp. 2044-2051, Oct. 2004.
16. M. Kennedy and L. Chua, "Neural networks for nonlinear programming," IEEE Trans. Circuits Syst., vol.35, no.5, pp. 554-562, May 1988.
17. M. Lemmon and B. Kumar, "Competitive learning with generalized winner-take-all activation," IEEE Trans. Neural Netw., vol.3, no.2, pp. 167-175, Mar. 1992.
18. D. Liu, S. Hu, and J. Wang, "Global output convergence of a class of continuous-time recurrent neural networks with time-varying thresholds," IEEE Trans. Circuits Syst. II, vol.51, no.4, pp. 161-167, Apr. 2004.
19. Q. Liu, J. Cao, and J. Liang, "A discrete-time recurrent neural network with one neuron for k-winners-take-all operation," in Proc. 6th ISNN, Jun. 2009, pp. 272-278.
20. Q. Liu and J.Wang, "A one-layer recurrent neural network with a discontinuous hard-limiting activation function for quadratic programming," IEEE Trans. Neural Netw., vol.19, no.4, pp. 558-570, Apr. 2008.
21. Q. Liu and J. Wang, "Two k-winners-take-all networks with discontinuous activation functions," Neural Netw., vol.21, nos. 2-3, pp. 406-413, 2008.
22. S. Liu and J. Wang, "A simplified dual neural network for quadratic programming with its KWTA application," IEEE Trans. Neural Netw., vol.17, no.6, pp. 1500-1510, Nov. 2006.
23. W. Maass, "On the computational power of winner-take-all," Neural Comput., vol.12, no.11, pp. 2519-2535, 2000.
24. D. Mandic, "Data-reusing recurrent neural adaptive filters," Neural Comput., vol.14, no.11, pp. 2693-2707, 2002.
25. D. Mandic and J. Chambers, Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures, and Stability. New York: Wiley, 2001.
26. C. Marinov and J. Hopfield, "Stable computational dynamics for a class of circuits with O(N) interconnections capable of KWTA and rank extractions," IEEE Trans. Circuits Syst. I, vol.52, no.5, pp. 949-959, May 2005.
27. D. Marr and T. Poggio, "Cooperative computation of stereo disparity," Science, vol.194, no.4262, pp. 283-287, 1976.
28. B. Sekerkiran and U. Cilingiroglu, "A CMOS k-winners-take-all circuit with O(n) complexity," IEEE Trans. Circuits Syst. II, vol.46, no.1, pp. 1-5, Jan. 1999.
29. D. Tank and J. Hopfield, "Simple neural optimization networks: An A/D converter, signal decision circuit, and a linear programming cir cuit," IEEE Trans. Circuits Syst., vol.33, no.5, pp. 533-541, May 1986.
30. K. Urahama and T. Nagao, "K-winners-take-all circuit with O(N) complexity," IEEE Trans. Neural Netw., vol.6, no.3, pp. 776-778, May 1995.
31. J. Wang, "Analysis and design of a recurrent neural network for linear programming," IEEE Trans. Circuits Syst. I, vol.40, no.9, pp. 613-618, Sep. 1993.
32. W. Wolfe, D. Mathis, C. Anderson, J. Rothman, M. Gottler, G. Brady, R. Walker, G. Duane, and G. Alaghband, "K-winner networks," IEEE Trans. Neural Netw., vol.2, no.2, pp. 310-315, Mar. 1991.
33. Y. Xia and J. Wang, "A general projection neural network for solving monotone variational inequalities and related optimization problems," IEEE Trans. Neural Netw., vol.15, no.2, pp. 318-328, Mar. 2004.
34. J. Yen, J. Guo, and H. Chen, "A new k-winners-take-all neural network and its array architecture," IEEE Trans. Neural Netw., vol.9, no.5, pp. 901-912, Sep. 1998.
35. Z. Yi, J. Lv, and L. Zhang, "Output convergence analysis for a class of delayed recurrent neural networks with time-varying inputs," IEEE Trans. Syst., Man, Cybernet. B, vol.36, no.1, pp. 87-95, Feb. 2006.
36. A. Yuille and D. Geiger, "Winner-take-all networks," in The Handbook of Brain Theory and Neural Networks, 2nd ed. Cambridge, MA: MIT Press, 2003, pp. 1228-1231.
37. H. Zhang, Z. Liu, G. Huang, and Z. Wang, "Novel weighting-delaybased stability criteria for recurrent neural networks with time-varying delay," IEEE Trans. Neural Netw., vol.21, no.1, pp. 91-106, Jan. 2010.
38. H. Zhang, Z. Wang, and D. Liu, "Global asymptotic stability of recurrent neural networks with multiple time-varying delays," IEEE Trans. Neural Netw., vol.19, no.5, pp. 855-873, May 2008.