Advertisement

Automation and Remote Control

, Volume 68, Issue 5, pp 912–921 | Cite as

Parallel computations and committee constructions

  • V. D. Mazurov
  • M. Yu. Khachai
Topical Issue

Abstract

The paper reviewed the results bearing out the deep-seated relation between the parallel computations and learning procedures for the laminated neural networks one of whose formalizations is represented by the theory of committee constructions. Additionally, consideration was given to two combinatorial problems concerned with learning pattern recognition in the class of affine committees—the problem of verifying existence of a three-element affine separating committee and that of element-minimal affine separating committee. The first problem was shown to be N P-complete, whereas the second problem is N P-hard and does not belong to the Apx class.

PACS numbers

02.10.Ox 02.60.-x 89.20.Ff 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Mazurov, Vl.D., On the Committee of a System of Convex Inequalities, in Proc. Int. Math. Congr., Moscow: Mosk. Gos. Univ., 1966, no. 14, p. 41.Google Scholar
  2. 2.
    Mazurov, Vl.D., Metod komitetov v zadachakh optimizatsii i klassifikatsii (Method of Committees in the Problems of Optimization and Classification), Moscow: Nauka, 1990.zbMATHGoogle Scholar
  3. 3.
    Mazurov, Vl.D., Consistent Completion of Systems of Algorithms to Committee Technologies, Pattern Recognit. Image Anal., 1998, vol. 8, no. 4, pp. 501–506.MathSciNetGoogle Scholar
  4. 4.
    Ablow, C.M. and Kaylor, D.J., Inconsistent Homogeneous Linear Inequalities, Bull. Am. Math. Soc., 1965, vol. 71, no. 5, p. 724.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Judd, J.S., Neural Network Design and Complexity of Learning, New York: MIT Press, 1990.Google Scholar
  6. 6.
    Lin, J.H. and Vitter, J.S., Complexity Results on Learning by Neural Nets, Machine Learning, 1991, vol. 6, pp. 211–230.Google Scholar
  7. 7.
    Blum, A.L. and Rivest, R.L., Training a 3-node Neural Network is NP-complete, Neural Networks, 1992, vol. 5, pp. 117–127.CrossRefGoogle Scholar
  8. 8.
    Mazurov, Vl.D., Committees of Inequality Systems and the Problem of Recognition, Kibernetika, 1971, no. 3, pp. 140–146.MathSciNetGoogle Scholar
  9. 9.
    Khachai, M.Yu., On Computational Complexity of the Minimal Committee and Related Problems, Dokl. Ross. Akad. Nauk, 2006, vol. 406, no. 6, pp. 742–745.MathSciNetGoogle Scholar
  10. 10.
    Hastad, J., Clique is Hard to Approximate within n 1−ε, Acta Mathematica, 1999, vol. 182, no. 13, pp. 105–142.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Dinur, I., Regev, O., and Smyth, C., The Hardness of 3-uniform Hypergraph Coloring, in Proc. 43rd Ann. IEEE Sympos. Foundat. Comput. Sci., 2002.Google Scholar
  12. 12.
    Khachai, M.Yu., On the Computational and Approximational Complexity of the Problem of Minimal Separating Committee, Tavrich. Vest. Informatiki i Mat., 2006, no. 1, pp. 34–43.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  • V. D. Mazurov
    • 1
    • 2
  • M. Yu. Khachai
    • 1
    • 2
  1. 1.Ural State UniversityYekaterinburgRussia
  2. 2.Institute of Mathematics and Mechanics, Ural BranchRussian Academy of SciencesYekaterinburgRussia

Personalised recommendations