A NOTE ON GREEDY ALGORITHM

  • Published : 2001.05.01

Abstract

We improve the greedy algorithm which is one of the general convergence criterion for certain iterative sequence in a given space by building a constructive greedy algorithm on a normed linear space using an arithmetic average of elements. We also show the degree of approximation order is still $Ο(1\sqrt{\n}$) by a bounded linear functional defined on a bounded subset of a normed linear space which offers a good approximation method for neural networks.

Keywords

References

  1. IEEE Trans. Information Theory v.39 Universal Approximation Bounds for Superposition of a Sigmoidal Function A. R. Barron
  2. Neural Networks v.10 Functional Emulation Using Radial Basis Function Networks S. V. Chakravarthy;J. Ghosh
  3. Brooks/Cole A Course in Approximation Theory E. W. Cheney;W. Light
  4. Adv. Comput. Math. v.5 Limitations of the Approximation Capabilities of Neural Networks with One Hidden Layer C. K. Chui;X. Li;H. N. Mhaskar
  5. J. Artificial Neural Networks with Applications in Speech and Vision v.1 Structural Adaptation and Generalization in Supervised Feedfordward Networks J. Ghosh;K. Tumer
  6. Mathematics of Control Signal and Systems v.2 Approximation by Superposition of Sigmoidal Functions G. Cybenko
  7. Bull. Austral. Math. Soc. v.59 Extension of localised approximation by neural networks N. Hahm;B. I. Hong
  8. Annals of Statistics v.20 A Simple Lemma on Greedy Approximation in Hilbert Space and Convergence Rates for Projection Pursuit Regression and Neural Network Training L. K. Jones
  9. Neural Networks v.6 Multilalyer Feedforward Networks with a Nonpolynomial Activation Function Can Approximate Any Function M. Leshno;V. Lin;A. Pinkus;S. Schocken
  10. IBM J. Research and Development v.38 Dimension-Independent Bounds on the Degree of Approximation by Neural Networks H.N. Mhaskar;C. A. Micchelli
  11. Neural Computation v.9 Neural Networks for Functional Approximation and System Identification H. N. Mhaskar;N. Hahm