Bias of error rates in linear discriminant analysis caused by feature selection and sample size

Proceedings - International Conference on Pattern Recognition

Volumn 15, Issue 2, 2000, Pages 372-377

  Schulerud, Helene ^a,b  

^a UNIVERSITY OF OSLO   (Norway)

^b OSLO UNIVERSITY HOSPITAL   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRIMINANT ANALYSIS; ERRORS; INTELLIGENT SYSTEMS; MONTE CARLO METHODS; NORMAL DISTRIBUTION;

BIASED ESTIMATES; LEAVE ONE OUT ERRORS; LINEAR DISCRIMINANT ANALYSIS; MAHALANOBIS DISTANCES; MULTI-VARIATE NORMAL DISTRIBUTIONS; SAMPLE SIZES; SMALL DATA SET; UNBIASED ESTIMATES;

FEATURE EXTRACTION;

EID: 0347458021     PISSN: 10514651     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Article

References (26)

1. R. Duda and P. Hart. Pattern classification and scene analysis. A Wiley-interscience publication, first edition, 1973.
2. B. Efron. Estimating the error rate of a prediction rule: Improvement on cross-validation. J. Am. Stat. Assoc, 78(382):316-331, 1983.
3. D. Foley. Considerations of sample and feature size. IEEE Trans Inf Theory, 18:618-626, 1972.
4. K. Fu, P. Min, and T. Li. Feature selection in pattern recognition. IEEE Trans on Syst Science and Cybern - Part C, 6(1):33-39, 1970.
5. K. Fukunaga and R. Hayes. Estimation of classifier performance. IEEE Trans Pattern Anal Mach Intell, 11(10):1087-101, 1989.
6. S. Ganeshanandam and W. Krzanowski. On selecting variables and assessing their performance in linear discriminant analysis. Aust J Stat, 31(3):433-447, 1989.
7. D. Hand. Recent advances in error rate estimation. Pattern Recogn Lett, 4(5):335-346, 1986.
8. W. Highleyman. The design and analysis of pattern recognition experiments. Bell Sys Tech J, 41:723-744, 1962.
9. A. Jain and D. Zongker. Feature selection: Evaluation, application, and small sample performance. IEEE Trans Pattern Anal Mach Intell, 19(2):153-158, 1997.
10. L.Kanal. Patterns in pattern recognition: 1968-1974. IEEE Trans Inf Theory, 20:697-722, 1974.
11. L. Kanal and B. Chandrasekaran. On dimensionality and sample size in statistical pattern classification. Pattern Recogn, 3:225-234, 1971.
12. W. R. Klecka. Discriminant analysis. Sage Publications, Beverly Hills: 07-019, 1980.
13. P. Lachenbruch. On expected probabilities of misclassification in discriminant analysis, necessary sample size, and a relation with the mulitple correlation coefficient. Biometrics, 24:823-834, 1968.
14. P. Lachenbruch. Discriminant analysis. New York: Hafner Press, first edition, 1975.
15. P. Lachenbruch and M. Mickey. Estimation of error rates in discriminant analysis. Techometrics, 10(1):1-11, 1968.
16. L. Larsen, D. Walter, J. McNew, and W. Adey. On the problem of bias in error rate estimation for discriminant analysis. Pattern Recogn, 3:217-223, 1971.
17. N. Le Roux, S. Steel, and N. Louw. Variable selection and error rate estimation in discriminant analysis. J Stat Comput Simulation, 59(3): 195-219, 1997.
18. G. Murray. A cautionary note on selection of variables in discriminant analysis. Appl. Statist., 26(3):246-250, 1977.
19. J. Piper. Variability and bias in experimentally measured classifier error rates. Pat Rec Let, 13:685-692, 1992.
20. S. Raudys and A. Jain. Small sample size effects in statistical pattern recognition: recommendations for practitioners. IEEE Trans Pattern Anal Mach Intell, 13:252-264, 1991.
21. S. Raudys and V. Pikelis. On dimensionality, sample size, classification error, and complexity of classification algorithm in pattern recognition. IEEE Trans Pattern Anal Mach Intell, PAMI-2(3):242-252, 1980.
22. A. Rencher and S. Larson. Bias in Wilks' lambda in stepwise discriminant analysis. Technometrics, 22(3):349-356, 1980.
23. C. Rutter, V. Flack, and P. Lachenbruch. Bias in error rate estimates in discriminant analysis when setpwise variable selection is employed. Commun. Stat., Simulation Comput, 20(1):1-22, 1991.
24. C. Smith. Some examples of discrimination. Ann. Eugen., 18:272-273, 1947.
25. S. Snapinn and J. Knoke. Estimation of error rates in discriminant analysis with selection of variables. Biometrics, 45(1):289-299, 1989.
26. G. Toussaint. Bibliography on estimation of misclassification. IEEE Trans Inf Theory, 20(4):472-479, 1974.