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

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1 Author(s)
Schulerud, H. ; Dept. of Inf., Oslo Univ., Norway

The holdout and leave-one-out error estimates for a two-class problem with multivariate normal distributions and common covariance are derived as a function of the number of feature candidates, classifier dimensionality, sample size and Mahalanobis distance, using Monte Carlo simulations. It is demonstrated that the leave-one-out error rate is a highly biased estimate of the true error if feature selection is performed on the same data before error estimation. This problem is especially pronounced when analyzing many features on a small data set. The holdout error is an almost unbiased estimate of the true error independent of the number of feature candidates

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Pattern Recognition, 2000. Proceedings. 15th International Conference on  (Volume:2 )

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