A Trivial Linear Discriminant Function
In this paper, we focus on the new model selection procedure of the discriminant analysis. Combining re-sampling technique with k-fold cross validation, we develop a k-fold cross validation for small sample method. By this breakthrough, we obtain the mean error rate in the validation samples (M2) and the 95\% confidence interval (CI) of discriminant coefficient. Moreover, we propose the model selection procedure in which the model having a minimum M2 was chosen to the best model. We apply this new method and procedure to the pass/ fail determination of exam scores. In this case, we fix the constant =1 for seven linear discriminant functions (LDFs) and several good results were obtained as follows: 1) M2 of Fisher's LDF are over 4.6\% worse than Revised IP-OLDF. 2) A soft-margin SVM for penalty c=1 (SVM1) is worse than another mathematical programming (MP) based LDFs and logistic regression . 3) The 95\% CI of the best discriminant coefficients was obtained. Seven LDFs except for Fisher's LDF are almost the same as a trivial LDF for the linear separable model. Furthermore, if we choose the median of the coefficient of seven LDFs except for Fisher's LDF, those are almost the same as the trivial LDF for the linear separable model.
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