Існування та единість встановлених станів аналогової нейронної схеми визначення найбільших сигналів

2011;
: ст. 140 – 146
Authors: 

Тимощук П., Тимощук М.

П. Тимощук1, М. Тимощук2

  1. Національний університет «Львівська політехніка», кафедра систем автоматизованого проектування.
  2. Одеський національний політехнічний університет, кафедра ЕП.

Проаналізовано існування та єдиність усталених станів K-Winner-Take-All (KWTA) – нейронної схеми. Розглянуто час обробки схемою сигналів, властивість збереження впорядкованості сигналів, роздільну здатність і точність функціонування схеми. Наведено результати комп’ютерного моделювання, які підтверджують теоретичні передбачення і демонструють ефективність схеми.

1. R. P. Lippmann, B. Gold, and M. L. Malpass, A comparison of Hamming and Hopfield neural nets for pattern classification, MIT Lincoln Laboratory Technical Report, TR-769, 1987, pp. 1–37. 2. E. Majani, R. Erlanson and Y. Abu-Mostafa, On the K -winners-take-all network, in: D. S. Touretzky (Ed.), Advances in Neural Information Processing Systems, vol. I, Kaufmann, San Mateo, 1989, pp. 634–642. 3. P.Tymoshchuk and E.Kaszkurewicz, ”A Winner-take-all circuit based on second order Hopfield neural networks as building blocks”, in Proc. Int. Joint Conf. Neural Networks, vol. II, Portland, OR, 2003, pp. 891–896. 4. B. J. Jain and F. Wysotzki, A k-winner-takes-all classifier for structured data, in: Proceedings of 26th Annual German Conference on AI, Springer LNCS, vol. 2821, 2003, pp. 342–354. 5. T. M. Kwon and M. Zervakis, A parallel sorting network without comparators: A neural-network approach, in: Proceedings of the International Joint Conference on Neural Networks, vol. 1, 1992, pp. 701–706. 6. P. O. Pouliquen, A. G. Andreou and A. G., K. Strohbehn, Winner-takes-all associative memory: a hamming distance vector quantizer, Analogue Integrated Circuits and Signal Processing 13 (1997) 211–222. 7. K. Urahama and T. Nagao, K-Winner-take-all circuit with 0(n) complexity, IEEE Transactions on Neural Networks 6 (1995) 776–778. 8. J. C. Yen, J. I. Guo, and H. – C. Chen, A new k -Winners-take all neural network and its array architecture, IEEE Transactions on Neural Networks 9 (1998) 901–912. 9. L. N. Bihn and H. C. Chong, A neural-network contention controller for packet switching networks, IEEE Transactions on Neural Networks 6 (1995) 1402–1410. 10. U. Cilingiroglu and T. L. E. Dake, Rank-order filter design with a sampled-analogue multiple-winners-take-all core, IEEE Journal on Solid-State Circuits 37 (2002) 978–984. 11. A. Fish, D. Turchin, and O. Yadid-Pecht, An APS with 2-Dimensional winner-take-all selection employing adaptive spatial filtering and false alarm reduction, IEEE Transactions on Electron Devices 50 (2003) 159–165. 12. T. M. Kwon and M. Zervakis, KWTA networks and their applications, Multidimensional Systems and Signal Processing 6 (1995) 333–346. 13. R. Erlanson and Y. Abu-Mostafa, Analogue neural networks as decoders, in: D. S. Touretzky (Ed.), Advances in Neural Information Processing Systems, vol. 1, Kaufmann, San Mateo, 1991, pp. 585–588. 14. A. Fish, D. Akselrod, O. Yadid-Pecht, High precision image centroid computation via an adaptive k-winner-take-all circuit in conjunction with a dynamic element matching algorithm for star tracking applications, Analogue Integrated Circuits and Signal Processing 39 (2004) 251–266.15. A. K. J. Hertz and R. G. Palmer, Introduction to the Theory of Neural Computation, Addison-Wesley, Redwood City, 1991. 16. L. Itti, C. Koch and E. Niebur, A model of saliency-based visual attention for rapid scene analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence 20 (1998) 1254 – 1259. 17. D. Marr and T. Poggio, Cooperative computation of stereo disparity, Science 194 (1976) 283–287.18. B. J. Jain and F. Wysotzki, Central clustering of attributed graphs, Machine Learning 56 (2004) 169–207. 19. S. Liu and J. Wang, A simplified dual neural network for quadratic programming with its KWTA application, IEEE Transactions on Neural Networks, 17 (2006) 1500–1510. 20. G. N. de Souza and A. C. Zak, Vision for mobile robot navigation: a survey, IEEE Transactions on Pattern Analysis and Machine Intelligence 24 (2002) 237-267. 21. A. Yuille and D. Geiger, Winner-take-all networks, in: The Handbook of Brain Theory and Neural Networks, second ed., MIT, Cambridge, 2003, pp. 1228–1231. 22. D. Graupe, Principles of Artificial Neural Networks (2nd Edition), World Scientific Publishing Co., Singapore and River Edge, N.J., 2007. 23. B. D. Calvert and C. A. Marinov, Another K -winners-take-all analogue neural network, IEEE Transactions on Neural Networks 4 (2000) 829-838. 24. C. A. Marinov and B. D. Calvert, Performance analysis for a K -winners-take-all analogue neural network: basic theory, IEEE Transactions on Neural Networks 14 (2003) 766–780. 25. R. Perfetti, On the robust design of k-winners-take-all networks, IEEE Transactions on Circuits and Systems II: Analogue and Digital Signal Processing CAS-42 (1995) 55-58. 26. W. J. Wolfe, D. Mathis, C. Anderson, J. Rothman, M. Gotler, G. Bragy, R. Walker, G. Duane, and G. Alaghband, K-Winner networks, IEEE Transactions on Neural Networks 2 (1991) 310-315. 27. J. C. Yen and S. Chang, A new first- k -winners neural network, in: Proceedings of the ISANN, 1997, D-01-D-06. 28. J. J. Hopfield, Neurons with graded response have collective computational properties like those of twostate neurons, in: Proceedings of the National Academy of Sciences, vol. 81, USA, 1984, pp. 3088–3092. 29. P. V. Tymoshchuk, “A simplified continuous-time model of analogue K-winners-take-all neural circuit”, in Proc. XI Int. Conf. “The Experience of Designing and Application of CAD Systems in Microelectronics”, Polyana-Svalyava, Ukraine, February 23-25, 2011, pp. 121–125. 30. A. F. Filippov, Differential equations with discontinuous righthand sides, American Mathematical Society Translations 42 (1964) 199-231. 31. A. F. Filippov, Differential Equations with Discontinuous Righthand Sides, Kluwer, Dordrecht, 1988. 32. J. Wang, Analogue winner-take-all neural networks for determining maximum and minimum signals, International Journal of Electronics 77 (1994) 355–367. 33. O. Hajek, Discontinuous differential equations I, Differential Equations 32 (1979) 149–170. 34. E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955. 35. C. A. Marinov and B. D. Calvert, Performance analysis for a K -winnerstake-all analogue neural network: basic theory, IEEE Transactions on Neural Networks 14 (2003) 766-780. 36. C. A. Marinov and J. J. Hopfield, Stable computational dynamics for a class of circuits with 0(N) interconnections capable of KWTA and rank extractions, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 52 (2005) 949–959. 37. J. F. Yang, and C. M. Chen, A dynamic K -winners-take-all neural network, IEEE Transactions on Systems, Man and Cybernetics 27 (1997) 523–526.