2010 Volume 22 Issue 1 Pages 37-57
Revised IP-OLDF (optimal linear discriminant function using integer programming) is a linear discriminant function used to obtain the minimum number of misclassifications (MNM) of training data using integer programming. However, integer programming requires a large computation time. Therefore, we aim to reduce the computation time using linear programming. In the first phase, Revised LP-OLDF (optimal linear discriminant function using linear programming) is applied to the data, and the data are categorized into two groups: those classified correctly and those not classified by support vectors. In the second phase, Revised IP-OLDF is applied to the misclassified data. This method is called Revised IPLP-OLDF. In this sturdy, we devise a method to reduce the computation time by using Revised IPLP-OLDF. In addition, it is evaluated whether the number of misclassifications obtained using Revised IPLP-OLDF is equals to the MNM. Four types of real data, namely, data pertaining to students, irises, Swiss bank-notes, and medicine, are used as training data. Four types of re-sampling data generated from the real data are used as the evaluation data. In these evaluation data, there are a total of 149 models for all combinations of explanatory variables. The numbers of misclassifications and calculation times of the 149 models are compared using Revised IPLP-OLDF and Revised IP-OLDF. The following results are obtained: 1. Revised IPLP-OLDF considerably reduces the computation time. 2. In the case of training data, the number of misclassifications obtained for all 149 models using Revised IPLP-OLDF is equal to the MNM obtained using Revised IP-OLDF. 3. In the case of the evaluation data, for most of the models, the numbers of misclassifications obtained using Revised IPLP-OLDF is equal to that obtained using Revised IP-OLDF. 4. It is concluded that the generalization abilities of both methods are high, because the difference between the probability of misclassifications of training and evaluation data is almost within 2%. Therefore, it is concluded that Revised IPLP-OLDF can be applied to real problems in lieu of Revised IP-OLDF.
