Skip to main content

Statistical Pattern Recognition of Binary Variables

  • Conference paper
Pattern Recognition Theory and Applications

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

Abstract

Many different methods for tackling binary variable pattern recognition problems have been proposed. The differences arise from the particular special needs of the individual problems as well as the background and orientation of the authors presenting the methods. This paper summarises these methods, beginning with the basic multinomial method and showing how other methods can be seen as different ways of tackling the shortcomings of the basic method by imposing different types of dependence structure on the data. The various merits and demerits of the methods are pointed out in the hope that this will aid in choice of method.

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. Aitchison, J. and Aikin, C.G.G. Multivariate Binary Discrimination by the Kernel Method. Biometrika 63, 413–420, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  2. Anderson, J.A. Separate Sample Logistic Discrimination. Biometrika 59, 19–35, 1972.

    Article  MathSciNet  MATH  Google Scholar 

  3. Bahadur, R.R. A Representation of the Joint Distribution of Responses to n Dichotomous Items. In Studies in Item Analysis and Prediction, ed. H. Solomon, 158–168, Stanford University Press, 1961.

    Google Scholar 

  4. Berkson, J. Application of Minimum Logit x2 Estimate to a Problem of Grizzle with a Notation on the Problem of fNo Interaction. Biometrics 24, 75–95, 1968.

    Article  Google Scholar 

  5. Birch, M.W. Maximum Likelihood in Three-Way Contingency Tables. Journal of the Royal Statistical Society B-25, 220–233, 1963.

    Google Scholar 

  6. Bishop, Y.M.M., Fienberg, S.E. and Holland, P.W. Discrete Multivariate Analysis. MIT Press, Cambridge, Mass., 1975.

    MATH  Google Scholar 

  7. Brown, D.T. A Note on Approximations to Discrete Probability Distributions. Information and Control 2, 386–392, 1959.

    Article  MathSciNet  MATH  Google Scholar 

  8. Brunk, H.D. and Pierce, D.A. Estimation of Discrete Multi¬variate Densities for Computer Aided Differential Diagnosis of Disease. Biometrika 61, 493–499, 1974.

    Article  MathSciNet  MATH  Google Scholar 

  9. Chow, C.K. and Liu, C.N. Approximating Discrete Probability Distributions with Dependence Trees. IEEE Transactions on Information Theory IT-14, 462–467, 1968.

    Google Scholar 

  10. Fielding, A. Latent Structure Models. In Exploring Data Structures, Vol. 1, eds. C.A. O’Muircheartaigh and C. Payne, 125–157, John Wiley and Sons, London, 1977.

    Google Scholar 

  11. Fienberg, S.E. and Holland, P.W. On the Choice of Flattening Constants for Estimating Multinomial Probabilities. Journal of Multivariate Analysis 2, 127–134, 1972.

    Article  MathSciNet  Google Scholar 

  12. Gilbert, E.S. On Discrimination Using Qualitative Variables. Journal of the American Statistical Association 63, 1399– 1412, 1968.

    Google Scholar 

  13. Good, I.J. A Bayesian Significance Test for Multinomial Distributions. Journal of the Royal Statistical Society B-29, 399–431, 1967.

    Google Scholar 

  14. Hilden, J. and Bjerregaard, B. Computer-Aided Diagnosis and the Atypical Case. In Decision Making and Medical Care, F.T. deDombal and F. Gremy, 365–378, North-Holland Publishing Co., 1976.

    Google Scholar 

  15. Hills, M. Discrimination and Allocation with Discrete Data. Applied Statistics 16, 237–250, 1967.

    Article  Google Scholar 

  16. Johnson, B.M. On the Admissible Estimators for Certain Fixed Sample Binomial Problems. Annals of Mathematical Statistics 42, 1579–1587, 1971.

    Article  MathSciNet  MATH  Google Scholar 

  17. Lancaster, H.O. The Chi-Squared Distribution, John-Wiley 5 Sons, New York, 1969.

    Google Scholar 

  18. Leonard, T. A Bayesian Approach to Some Multinomial Estimation and Pretesting Problems. Journal of the American Statistical Association 72, 869–874, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  19. Lewis, P.M. Approximating Probability Distributions to Reduce Storage Requirements. Information and Control 2, 214– 225, 1959.

    Google Scholar 

  20. Martin, D.C. and Bradley, R.A. Probability Models, Estimation, and Classification for Multivariate Dichotomous Populations. Biometrics 23, 203–221, 1972.

    Article  Google Scholar 

  21. Moore, D.H. Evaluation of Five Discrimination Procedures for Binary Variables. Journal of the Americal Statistical Association 68, 399–404, 1973.

    Article  Google Scholar 

  22. Neyman J. Contributions to the Theory of the x2 Test. In Proceedings of the first Berkeley Symposium on Mathematical Statistics and Probability. ed. J. Neyman, 230–273, University of California Press, Berkeley, 1949.

    Google Scholar 

  23. Ott, J. and Kronmal, R.A. Some Classification Procedures for Multivariate Binary Data Using Orthogonal Functions. Journal of the American Statistical Association 71, 391–399, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  24. Titterington, D.M. Analysis of Incomplete Multivariate Binary Data by the Kernel Method. Biometrika 64, 455–460, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  25. Titterington, D.M., Murray, G.D., Murray, L.S. Spiegelhalter, D.J., Skene, A.M., Habbema, J.D.F. and Gelpke, G.J. Comparison of Discrimination Techniques Applied to a Complex Set of Head Injured Patients. Journal of the Royal Statistical Society A-144, In Press, 1981.

    Google Scholar 

  26. Zentgraf, R. A Note on Lancaster’s Definition of Higher- Order Interactions. Biometrika 62, 375–378, 1975.

    Article  MathSciNet  MATH  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

Hand, D.J. (1982). Statistical Pattern Recognition of Binary Variables. 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_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-7772-3_2

  • 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