Abstract
In this paper, a novel method for the determination of the position of the maxima among the M members of a set of positive real numbers S that stem from a finite discrete domain is proposed. The method does not follow the competitive spirit of the winner-take-all methods. It involves neither recursion nor comparisons between the members of S. Instead, a threshold T less than but arbitrarily close to the maximum value of S is directly calculated, with the contribution of all members of S and then each member of S is compared with it. Also, it is shown how the proposed method can be applied to the associative memory problem. In addition, arguments are given showing that, in principle, there are versions of the proposed method that are significantly faster than other well established methods for determining the position of the maximum in a set S of numbers.
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References
W. T. Chen K. R. Hsieh (1993) ArticleTitleA neural sorting network with O(1) complexity Information Processing Letters 45 IssueID6 309–313 Occurrence Handle10.1016/0020-0190(93)90042-8 Occurrence HandleMR1216941
C.-M. Chen M.-H. Hsu T.-Y. Wang (2002) ArticleTitleA fast winner-take-all neural network with the dynamic ratio Journal of Information Science and Engineering 18 211–222
Floreen, P.: The convergence of the hamming memory networks, IEEE Transactions on Neural Networks 2(4) (1991).
H. K. Hartline F. Ratliff (1957) ArticleTitleInhibitory interaction of receptor units in the eye of the Limulus Journal of General Physiology 40 357–376 Occurrence Handle10.1085/jgp.40.3.357 Occurrence Handle13398569
K. Koutroumbas N. Kalouptsidis (1994) ArticleTitleQualitative analysis of the parallel and asynchronous modes of the hamming network IEEE Transactions on Neural Networks 5 IssueID3 380–391 Occurrence Handle10.1109/72.286910
K. Koutroumbas N. Kalouptsidis (1998) ArticleTitleNeural networks architectures for selecting the maximum input International Journal of Computer Mathematics 67 25–32 Occurrence HandleMR1676712
H.-T. Ku M.-C. Ku X.-M. Zhang (1999) ArticleTitleGeneralized power meansand interpolating inequalities Proceedings of the American Mathematical Society 8 IssueID1 145–154 Occurrence Handle10.1090/S0002-9939-99-04845-5
H. K. Kwan (1992) ArticleTitleOne-layer feedforward neural network for fast maximum/minimum determination Electronics Letters 28 IssueID17 1583–15850
S. S. Lin S. H. Hsu (1996) ArticleTitleA low-cost neural sorting network with O(1) time complexity Neurocomputing – An International Journal 14 289–299 Occurrence Handle10.1016/S0925-2312(96)00040-9
Lippmann, R. P.: An introduction to computing with neural nets, IEEE ASSP Magazine 4(2) (1987).
Lippmann, R. P., Bold, B. and Malpass, M. L.: A comparison of Hamming and Hopfield neural nets for pattern classification, Technical Report 769, Lincoln Laboratory, MIT, 1987.
I. Melijson E. Ruppin M. Sipper (1995) ArticleTitleA single-iteration threshold Hamming network IEEE Transactions on Neural Networks 6 261–266 Occurrence Handle10.1109/72.363428
M. Skbrek (1999) ArticleTitleFast neural network implementation Neural Processing World 5 375–391
Sum, J. and Tam, P. K. S.: Note on the maxnet dynamics, Neural Computation 8(3) (1996).
Y. H. Tseng J. L. Wu (1995) ArticleTitleOn a constant-time, low-complexity winner-take-all neural network IEEE Transactions on Computers 44 IssueID4 601–604 Occurrence Handle10.1109/12.376175
K. Urahama T. Nagao (1995) ArticleTitlek-winners-take-all circuit with O(N) complexity IEEE Transactions on Neural Networks 6 IssueID3 776–778 Occurrence Handle10.1109/72.377986
Witkowski, A.: A new proof of the monotonicity of power means, Journal of Inequalities in Pure and Applied Mathematics 5(1) (2004).
W. J. Wolfe C. MathisD. Anderson J. Rothman M. Gottler G. Brady R. Walker G. Duace G. Alaghband (1991) ArticleTitlek-winner networks IEEE Transactions on Neural Networks 2 IssueID2 310–315 Occurrence Handle10.1109/72.80342
O. Yadid-Pecht M. Gur (1995) ArticleTitleA biologically-inspired improved Maxnet IEEE Transactions on Neural Networks 6 IssueID3 757–759 Occurrence Handle10.1109/72.377981
J. F. Yang C. M. Chen W. C. Wang J. Y. Lee (1995) ArticleTitleA general mean based iteration winner-take-all neural network IEEE Transactions on Neural Networks 6 IssueID1 14–24 Occurrence Handle10.1109/72.363454
J. F. Yang C. M. Chen (2000) ArticleTitleWinner-take-all neural networks using the highest threshold IEEE Transactions on Neural Networks 11 IssueID1 194–199 Occurrence Handle10.1109/72.839016
Yen, J. C. and Chang, S.: Improved winner-take-all neural network, Electronics Letters (1992), 662–664.
J. C. Yen F. J. Chang S. Chang (1994) ArticleTitleA new winners-take-all architecture in artificial neural networks IEEE Transactions on Neural Networks 5 IssueID5 838–843 Occurrence Handle10.1109/72.317736
J. C. Yen J. I. Guo H. C. Chen (1998) ArticleTitleA new k-winners-take-all neural network and its array architecture IEEE Transactions on Neural Networks 9 IssueID5 901–912 Occurrence Handle10.1109/72.712163
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Koutroumbas, K. COMAX: A Cooperative Method for Determining the Position of the Maxima. Neural Process Lett 22, 205–221 (2005). https://doi.org/10.1007/s11063-005-5541-z
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DOI: https://doi.org/10.1007/s11063-005-5541-z