Improvement of CPU time of Linear Discriminant Functions based on MNM criterion by IP
نویسندگان
چکیده
Shinmura [12, 13, 14] proposes an optimal linear discriminant function (OLDF) using integer programming (IP) called as IP-OLDF based on the minimum number of misclassifications (MNM) criterion. It is defined on the data and discriminant coefficient spaces. We can understand the relation of a linear discriminant function (LDF) and NM clearly. This basic knowledge tells us several new facts of the discriminant theory. If data satisfies the Harr’s condition [1] or general position, IP-OLDF can obtain true MNM. But if data does not satisfy it, it may not choose the true MNM, because of the unresolved problem of the discriminant analysis that all LDFs cannot discriminate the cases xi on the discriminant hyperplane (f(xi) = 0) correctly. Therefore, Revised IP-OLDF [15, 16] is developed. However, it requires large elapsed runtime (CPU) because it is solved by IP. In this paper, we show how to reduce CPU time by Revised IPLPOLDF, NMs of which are good estimates of MNMs. It is evaluated whether NM of Revised IPLP-OLDF almost is as low as MNM by Revised IP-OLDF. And CPU time of Revised IPLP-OLDF is remarkably improved compared with Revised IP-OLDF. These results are examined by a total of 149 different discriminant functions using by real training samples and re-sampling validation samples.
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تاریخ انتشار 2015