Advertisement

Pattern Class Representation Related to the Karhunen-Loeve Expansion

  • Th. Van der Pyl
Conference paper
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 81)

Abstract

We propose an algebraic study of the subspace methods. General theorems allow us to extend the results relative to the Karhunen-Loeve expansion and thus to give another point of view related to the measure theory on the closed subspaces of a Hilbert space.

Keywords

Hilbert Space Orthonormal Basis Closed Subspace Subspace Method Pattern Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Anderson, T.W. An Introduction to Multivariate Statistical Analysis. Wiley (1957).Google Scholar
  2. [2]
    Berman, A., Plemmons, R.J. Non-Negative Matrices in Mathematical Sciences, Academic Press (1979).Google Scholar
  3. [3]
    Fukunaga, K, Koontz, W.L.G. Application of the Karhunen- Loeve Expansion to Feature Selection and Ordering. IEEE Trans, on comp. vol. C-19, Nov. 4, April 1970.Google Scholar
  4. [4]
    Kittler, J. Feature Selection Methods Based on the Karhunen- Loeve Expansion, in Pattern Recognition Theory and Application, ed. D.S. Fu and A.B. Whinston, 61–74, Noordhoff-Leyden (1977).Google Scholar
  5. [5]
    Noguchi, Y. Subsp. Meth. and Proj. Oper. Trans. 5th IJCPR Miami Beach, Florida, Dec. 1–4, 1980.Google Scholar
  6. [6]
    Ostrowski, A. Sur Quelques Applications des Fonctions Con- vexes et Concaves au Sens de I.Schur, J. Math. Pure Appl. 31, 257–292 (1952).MathSciNetGoogle Scholar
  7. [7]
    Ozeki, K. A Coorinate-Free th. of Eigenvalue Anal. Related to the Meth. of Princ. Compon. and the Karhunen-Loeve Expansion. Inf. and Contr. 42, 38–59, (1979).CrossRefGoogle Scholar
  8. [8]
    Parthasarathy, M. Probability th. on Closed Subspaces of a Hilbert Space, in Coll. CNRS, Prob. sur les struc. alg. Clermont-Ferrand, 30th June-5th July 1969, ed. CNRS (1970).Google Scholar
  9. [9]
    Sallantin, J. Representation d’Observations dans le Contexte de la Theorie de l’Information, These d’Etat, Publ. CNRS, GR22, No. 8 (1979).Google Scholar
  10. [10]
    Simon, J.C., Backer, E., Sallantin, J. A Structural Approach of P.R. Signal Processing 2 (1980), 5–22.CrossRefGoogle Scholar
  11. [11]
    Strang, G. Linear Algebra and its Applications. Academic Press (1980).Google Scholar
  12. [12]
    Van der Pyl, Th. Axiomatique de l’Information d’Ordre a et de Type ß. C.R.A.S., Paris, t.282, Serie A, 1031–1033 (1976).Google Scholar
  13. [13]
    Van der Pyl, Th. Produit Scalaire, Changement de Base et Expansion de Karhunen-Loeve. Journees Mancelles Information et Questionnaires, Le Mans 15–17 Sept. 1980. Publications C.N.R.S. GR 22, No. 18.Google Scholar
  14. Van der Pyl, Th. Mesure, Produit Scalaire et Expansion de Karhunen-Loeve. C.R.A.S. (soumis)Google Scholar
  15. Watanabe, S. Knowing and Guessing. Wiley (1969).Google Scholar

Copyright information

© D. Reidel Publishing Company 1982

Authors and Affiliations

  • Th. Van der Pyl
    • 1
  1. 1.Structures de l’InformationTour 45, Universite Paris VIParis Cedex 05France

Personalised recommendations