Skip to main content

Advances in Nonparametric Techniques of Statistical Pattern Classification

  • Conference paper
Pattern Recognition Theory and Applications

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 81))

Abstract

This paper is concerned with nonparametric statistical pattern recognition and focuses on some theoretical advances that have taken place since the previous NATO Advanced Study Institute on Pattern Recognition Theory and Applications held in Bandol, France, in 1975, [1]. In an article of this size, it is not feasible to cover the field exhaustively. Therefore, the aim of our selective discussion of topics is merely to give a limited perspective on how statistical theories of pattern classification have evolved during the last six years.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Fu, K.S., and Whinston, A.B., Eds., Pattern Recognition Theory and Applications, Leyden: Noordhoff, 1977.

    Google Scholar 

  2. Kanal, L., “Patterns in pattern recognition: 1968–1974”, IEEE Trans. Inf. Theory, vol. IT-20, pp. 697–722, Nov. 1974.

    Google Scholar 

  3. Stearns, S.D., “On selecting features for pattern classifiers”, in Proc. Third Int. Joint Conf. Pattern Recognition, Coronado, Ca., Nov. 1976, IEEE Computer Society, pp. 71–75,

    Google Scholar 

  4. Kittler, J., “Feature set search algorithms”, in Pattern Recognition and Signal Processing, C.H. Chen Ed., Alphen aan den Rijn: Sythoff & Noordhoff, 1978, pp. 41–60.

    Google Scholar 

  5. Elashoff, J.D., Elashoff, R.M., and Goldman, G.E., “On the choice of variables in classification problems with dichotomous variables”, Biometrika, vol. 54, pp. 668–670, 1967.

    MathSciNet  Google Scholar 

  6. Toussaint, G.T., “Note on the optimal selection of independent binary valued features for pattern recognition”, IEEE Trans. Inform. Theory, vol. IT-17, p. 618, Sept, 1971

    Google Scholar 

  7. Cover, T.M., “The best two independent measurements are not the two best”, IEEE Trans. Systems, Man and Cybernetics, vol. SMC-4, n° 1, pp, 116–117, Jan, 1974.

    Google Scholar 

  8. Cover, T.M,, and Van Campenhout, J.M., “On the possible orderings in the measurement selection problem”, IEEE Trans, Systems, Man and Cybernetics, vol, SMC-7, n° 9, pp. 657–661, Sept. 1977.

    Google Scholar 

  9. Kanal, L,N,, Preface to Pattern Recognition, L. Kanal Ed., Washington: Thompson Book Cy, 1968,

    Google Scholar 

  10. Narendra, P.M., and Fukunaga, K., “A Branch and Bound algorithm for feature subset selection”, IEEE Trans. Computer, vol. C-26, n° 9, pp. 917–922, Sept. 1977.

    Google Scholar 

  11. Kulkarni, A.V., Optimal and heuristic synthesis of hierarchical classifiers, Ph. D. Dissertation, Univ. of Maryland, Computer Science Tech. Rept. Series, TR-469, Aug. 1976.

    Google Scholar 

  12. Kulkarni, A.V., and Kanal, L.N., “Admissible strategies for parametric and nonparametric hierarchical classifiers”, in Proc. Fourth Int. Joint Conf. Pattern Recognition, Kyoto, Japan, Nov. 1978, pp. 238–245.

    Google Scholar 

  13. Van Campenhout, J.M., “On the peaking of the mean recognition accuracy: The resolution of an apparent paradox”, IEEE Trans. Systems, Man and Cybernetics, vol. SMC-8, n° 5, pp. 390–395, May 1978.

    Article  MathSciNet  Google Scholar 

  14. Duin, R.P.W., “On the possibility of avoiding peaking”, in Proc. Fifth Int. Conf. Pattern Recognition, Miami Beach, Fl., Dec. 1980, IEEE Computer Society, pp. 1375–1378.

    Google Scholar 

  15. Tounissoux, D., Processus sequential adaptatif de reconnaissance des formes pour l’aide au diagnostic, Doctoral Dissertation, Univ. Lyon I, June 1980

    Google Scholar 

  16. Fu, K.S., Sequential Methods in Pattern Recognition and Machine Learning, New York: Academic Press, 1968.

    Google Scholar 

  17. Terrenoire, M., and Tounissoux, D., “Sample size sensitive entropy”, in this volume.

    Google Scholar 

  18. Silverman, B.W., “Choosing the window width when estimating a density”, Biometrika, vol. 65, n° 1, 1–11, 1978.

    Google Scholar 

  19. Short, R.D., and Fukunaga, K., “A new nearest neighbor distance measure”, in Proc. Fifth Int. Conf. Pattern Recognition Miami Beach, Fl., Dec. 1980, IEEE Computer Society, pp. 81–86

    Google Scholar 

  20. Miyake, A., “On the Haar condition in algorithms for the optimum solution of linear inequalities”, in this volume.

    Google Scholar 

  21. Wassel, G.N., Training a linear classifier to minimize the error probability, Ph. D. Dissertation, Univ. of California, Irvine, Tech. Rep. TR-72-5, 1972.

    Google Scholar 

  22. Do Tu, H., and Installe, M., “Learning algorithm for optimum solution to the minimum error classification problem”, IEEE Trans. Computers, vol. C-27, n° 7, pp. 648–659, 1978.

    Google Scholar 

  23. Dasarathy, B.V., and Sheela, B.V., “Visiting nearest neighbors”, in Proc. 1977 IEEE Int. Conf. Cybernetics and Society, Washington D.C., Sept. 1977, pp. 630–634.

    Google Scholar 

  24. Devijver, P.A., “An overview of asymptotic properties of nearest neighbor rules”, in Pattern Recognition in Practice, E.S. Gelsema, and L.N. Kanal Eds., Amsterdam: North Holland, 1980, pp. 343–350.

    Google Scholar 

  25. Cover, T.M., and hart, P.E., “Nearest neighbor pattern classification”, IEEE Trans. Inform. Theory, vol. IT-13, pp.21–27, Jan. 1967

    Google Scholar 

  26. Stone, C.J., “Consistent nonparametric regression”, Ann. Statist., vol. 5, pp. 595–645, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  27. 27]Devroye, L., “On the inequality of Cover and Hart in nearest neighbor discrimination”, IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-3, n° 1, pp. 75–78, Jan. 1981.

    Article  MathSciNet  Google Scholar 

  28. Devijver, P.A., “A note on ties in voting with the k-NN rule”, Pattern Recognition, vol. 10, pp. 297–298, 1978.

    Article  MathSciNet  Google Scholar 

  29. Györfi, L., and Györfi, Z., “An upper bound on the asymptotic error probability of the k-nearest neighbor rule for multiple classes”, IEEE Trans. Inform. Theory, vol, IT-24, pp. 512–514, July 1978.

    Google Scholar 

  30. Devijver, P.A., “New error bounds with the nearest neighbor rule”, IEEE Trans. Inform. Theory, vol, IT-25, n° 6, pp. 749–753, Nov. 1979.

    Google Scholar 

  31. Devroye, L., “Some properties of the nearest neighbor rule”, in Proc. Fifth Int. Conf. Pattern Recognition, Miami Beach, Fl., Dec, 1980, IEEE Computer Society, pp. 103–105.

    Google Scholar 

  32. Devijver, P.A,, “Decision theoretic and related approaches to pattern classification”, in Pattern Recognition Theory and Application, K.S, Fu and A.B, Whinston Eds., Leyden: Noordhoff, 1977, pp. 1–34.

    Google Scholar 

  33. Devijver, P.A., Reconnaissance des formes par la methode des plus proches voisins, Doctoral Dissertation, Univ. Paris VI, June 1977, also available as MBLE Res. Rept. R-346, April 1977.

    Google Scholar 

  34. Devijver, P.A., “Error and reject tradeoff for nearest neighbor decision rules”, in Aspects of Signal Processing, Part 2, G. Tacconi Ed., Dordrecht: Reidel, 1977, pp. 525–538.

    Google Scholar 

  35. Devijver, P.A. and Dekesel, M, M., “A nonparametric, self-orga- nizing pattern classification system with automatic performance control, Part 2: System implementation”, PRLB Tech. Note N-137, 72 pp., May 1980.

    Google Scholar 

  36. Devijver, P.A. and Kittler J., “On the edited nearest neighbor rule”, in Proc. Fifth Int. Conf. Pattern Recognition, Miami Beach, Fl., Dec. 1980, IEEE Comp. Soc., pp.72–80.

    Google Scholar 

  37. Wilson, D.L,, “Asymptotic properties of nearest neighbor rules using edited data”, IEEE Trans. Systems, Man, and Cybernetics, vol, SMC-2, pp. 408–420, July 1972.

    Google Scholar 

  38. Penrod, C.S., and Wagner, T,J., “Another look at the edited nearest neighbor rule”, IEEE Trans. System, Man, and Cybernetics, vol. SMC-7, pp. 92–94, Feb. 1977.

    Google Scholar 

  39. Hart, P.E., “The condensed nearest neighbor rule”, IEEE Trans. Inform. Theory, vol. IT-14, pp. 515–516, May 1968.

    Google Scholar 

  40. Gowda, K.C., and Krishna, G., “The condensed nearest neighbor rule using the concept of mutual nearest neighborhood”, IEEE Trans. Inform. Theory, vol. IT-25, pp. 480–490, July 1979.

    Google Scholar 

  41. Toussaint, G.T., Battacharyya, B.K., and Poulsen, R.S., “Graph theoretic methods for edited nearest neighbor decision rules”, (Abstract), in Proc. 1981 IEEE Symp. Information Theory, Santa Monica, Ca., Jan. 1981, pp. 66–67.

    Google Scholar 

  42. Toussaint, G.T., “Computational geometric problems in pattern recognition”, in this volume, p. 73.

    Google Scholar 

  43. Devijver, P.A., and Dekesel, M.M,, “Insert and delete algorithms for maintaining dynamic Voronoi tessellations”, Memo, n° 13, Philips Res. Lab., June 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1982 D. Reidel Publishing Company

About this paper

Cite this paper

Devijver, P.A. (1982). Advances in Nonparametric Techniques of Statistical Pattern Classification. In: Kittler, J., Fu, K.S., Pau, LF. (eds) Pattern Recognition Theory and Applications. NATO Advanced Study Institutes Series, vol 81. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7772-3_1

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-7772-3_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-7774-7

  • Online ISBN: 978-94-009-7772-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics