MAXIMUM TOLERANCE AND MAXIMUM GREATEST TOLERANCE - Weights and Threshold of Strict Separating Systems

J. Freixas, X. Molinero

Abstract

An important consideration when applying neural networks is the sensitivity to weights and threshold in strict separating systems representing a linearly separable function. Two parameters have been introduced to measure the relative errors in weights and threshold of strict separating systems: the tolerance and the greatest tolerance. Given an arbitrary separating system we study which is the equivalent separating system that provides maximum tolerance or/and maximum greatest tolerance.

References

  1. Beiu, V., Quintana, J. M., and Avedillo, M. J. (2003). Vlsi implementation of threshold logic-a comprehensive survey. IEEE Transactions on Neural Networks, 14(5):1217-1243.
  2. Elgot, C. C. (1961). Truth functions realizable by single threshold organs. In AIEE Conference Paper 60-1311 (October), revised November 1960; paper presented at IEEE Symposium on Switching Circuit Theory and Logical Design.
  3. Elizondo, D. (2004). Searching for linearly separable subsets using the class of linear separability method. In Proceedings of the 2004 International Joint Conference on Neural Networks (IJCNN 04), volume 2 of IEEE, pages 955-959.
  4. Elizondo, D. (2006). The linear separability problem: some testing methods. IEEE Transactions on Neural Networks, 17(2):330-344.
  5. Freixas, J. and Molinero, X. (2008a). The greatest allowed relative error in weights and threshold of strict separating systems. IEEE Transactions on Neural Networks, 19(5).
  6. Freixas, J. and Molinero, X. (2008b). On the existence of a minimum integer representation for weighted voting systems. Annals of Operations Research, 166(1):243- 260.
  7. Hu, S. T. (1960). Linearly separable switching functions. Technical report, Technical report, LMSC, Technical Document, LMSD-703024.
  8. Hu, S. T. (1965). Threshold Logic. Univ. of California Press. xiv + 338 pp. Let xx, x2.
  9. Myhill, J. and Kautz, W. H. (1961). On the size of weights required for linear-input switching functions. IRETransactions, EC-10.
  10. Ozdemir, H., Kepkep, A., Pamir, B., Leblebici, Y., and Cilingiroglu, U. (1996). A capacitive threshold logic gate. IEEE J. Solid-State Circuits, 31.
  11. Picton, P. D. (1991). Neural Networks. Palgrave, second edition.
  12. Roychowdhury, V., Siu, K., and (Eds.), A. O. (1994). Theoretical Advances in Neural Computation and Learning. Kluwer Academic Publishers, Stanford, USA.
  13. Sang-Hoon, O. and Lee, Y. (1995). Sensitivity analysis of single hidden-layer neural networks with threshold functions. IEEE Trans. Computers, 6(4):1005-1007.
  14. Siu, K., Roychowdhury, V., and Kailath, T. (1995). Discrete Neural Computation: A Theoretical Foundation. Prentice Hall, New Jersey, USA.
  15. Winder, R. O. (1962). Threshold logic. PhD thesis, Department of Mathematics, Princeton University.
  16. Yao, S. S. and Ostapko, D. L. (1968). Realization of a class switching functions by threshold-logic networks. IEEE Transactions on Computers, C-17(4):391-399.
Download


Paper Citation


in Harvard Style

Freixas J. and Molinero X. (2010). MAXIMUM TOLERANCE AND MAXIMUM GREATEST TOLERANCE - Weights and Threshold of Strict Separating Systems . In Proceedings of the 2nd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART, ISBN 978-989-674-021-4, pages 511-514. DOI: 10.5220/0002706905110514


in Bibtex Style

@conference{icaart10,
author={J. Freixas and X. Molinero},
title={MAXIMUM TOLERANCE AND MAXIMUM GREATEST TOLERANCE - Weights and Threshold of Strict Separating Systems},
booktitle={Proceedings of the 2nd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},
year={2010},
pages={511-514},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002706905110514},
isbn={978-989-674-021-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 2nd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,
TI - MAXIMUM TOLERANCE AND MAXIMUM GREATEST TOLERANCE - Weights and Threshold of Strict Separating Systems
SN - 978-989-674-021-4
AU - Freixas J.
AU - Molinero X.
PY - 2010
SP - 511
EP - 514
DO - 10.5220/0002706905110514