A continuous-time K-winners-take-all (KWTA) neural network (NN) which is capable of identifying the largest K of N inputs, where a command signal has presented. The network is described by a state equation with a discontinuous right-hand side and by an output equation. The state equation contains an impulse train defined by a sum of Dirac delta functions. The main advantage of the network is not subject to the intrinsic convergence speed limitations of comparable designs. Application of the network for parallel rank-order filtering has described. Theoretical results are derived and illustrated with computer simulation example that demonstrates the network’s performance.

- Majani E., Erlanson R., and Abu-Mostafa Y. On the k-winners-take-all network G// in Advances in Neural Information Processing Systems 1, R. P. Lippmann, J. E. Moody, and D. S. Touretzky, Eds. San Mateo, CA: Morgan Kaufmann, 1989, pp. 634–642.
- Tymoshchuk P. A dynamic K-winners take all analog neural circuit, in Proc. IV th Int. Conf. "Perspective technologies and methods in MEMS design", Lviv-Polyana, Ukraine, 2008, pp. 13–18.
- Wang J. Analysis and design of a k-winners-take-all network with a single state variable and the Heaviside step activation function, IEEE Trans. Neural Netw., vol. 21, no. 9, P. 1496–1506, Sept. 2010.
- Lippmann R. P. An introduction to computing with neural nets, IEEE Acoustics, Speech and Signal Processing Magazine, vol. 3, no. 4, pp. 4–22, Apr. 1987.
- Tymoshchuk P. and Kaszkurewicz E. A winner-take all circuit using neural networks as building blocks, Neurocomputing, vol. 64, pp. 375–396, Mar. 2005.
- Wunsch D. C. The cellular simultaneous recurrent network adaptive critic design for the generalized maze problem has a simple closed-form solution, in Proc. Int. Joint Conf. Neural Netw., Jul. 2000, P. 79–82.
- Atkins M. Sorting by Hopfield nets, in Proc. Int. Joint Conf. Neural Netw., Jun. 1989, P. 65–68.
- Binh L. N. and Chong H. C. A neural-network contention controller for packet switching networks, IEEE Trans. Neural Netw. vol. 6, no. 6, P. 1402–1410, Nov. 1995.
- Itti L., Koch C., and Niebur E. A network of saliency-based visual attention for rapid scene analysis, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 11, P. 1254 – 1259,Nov. 1998.
- Cilingiroglu U. and Dake T. L. E. Rank-order filter design with a sampled-analog multiplewinners-take-all core, IEEE J. Solid-State Circuits, vol. 37, no. 2, pp. 978-984, Aug. 2002.
- Erlanson R. and Abu-Mostafa Y. Analog neural networks as decoders, in Advances in Neural Information Processing Systems, vol. 1, R. P. Lippmann, J. E. Moody, and D. S. Touretzky, Eds. San Mateo, CA: Morgan Kaufmann, 1991.
- Fish A., Akselrod D., and Yadid-Pecht O. 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, Analog Integrated Circuits and Signal Processing, vol. 39, no. 3, P. 251–266, Jun. 2004.
- Jain B. J. and Wysotzki F. Central clustering of attributed graphs, Machine Learning, vol. 56, no. 1, pp. 169–207, Jul. 2004.
- Chartier S., Giguere G., Langlois D. and Sioufi R. Bidirectional associative memories, self-organizing maps and k-winners-take-all; uniting feature extraction and topological principles, in Proc. Int. Joint Conf. Neural Netw., Jun. 2009, pp. 503–510.
- G. N. DeSouza and A. C. Zak, "Vision for mobile robot navigation: a survey," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 2, r. 237–267, Feb. 2002.
- O’Reilly R. C. and Munakata Y. Computational Explorations in Cognitive Neuroscience: Understanding the Mind by Simulating the Brain. Cambridge, MA: MIT Press, 2000.
- Lazzaro J., Ryckebusch S., Mahowald M. A., and Mead C. A. Winner-take-all networks of O (N) complexity, in Advances in Neural Information Processing Systems 1, R. P. Lippmann, J. E. Moody, and D. S. Touretzky, Eds. San Mateo, CA: Morgan Kaufmann,1989, pp. 703-711.
- Sekerkiran B. and Cilingiroglu U. A CMOS K-winners-take-all circuits with 0(N) complexity, IEEE Trans. Circuits Syst. II, vol. 46, no. 1, r. 1–5, Jan. 1999.
- Maass W. Neural computation with winner-take-all as the only nonlinear operation, in Advances in Information Processing Systems, vol. 12, S. A. Solla, T. K. Leen, and K.-R. Mueller, Eds. Cambridge, MA: MIT Press, 2000, pp.293–299.
- Calvert B. D. and Marinov C. A. Another K-winners-take-all analog neural network, IEEE Trans. Neural Netw., vol. 4, no. 1, P. 829–838, Jul. 2000.
- Wang J. Analogue winner-take-all neural networks for determining maximum and minimum signals," Int. J. Electron., vol. 77, no. 3, r. 355–367,Mar. 1994.
- Cichocki A. and Unbehauen R. Neural Networks for Optimization and Signal Processing. New York, NY, USA: Wiley, 1993.