Abstract
Shinmura (1998) proposed Optimal Linear Discriminant Function using integer programming (IP-OLDF). Although IP-OLDF enters the black hall of explosion of calculation, it reveals some new facts about discriminant analysis by the optimal convex polyhedron and MMN. But, IP-OLDF has weakness when it is applied for the tiny data that violates Haar condition. In this paper, Revised IP-OLDF is proposed. This method can find true MMN for the data that violate Haar condition. And it can resolve several following problems. 1) it can find minimum linearly separable feature space, 2) it can obtain optimal discriminant function by one step, although IP-OLDF needs two steps, 3) it can examine evaluation data using by this optimal discriminant hyperplane. Swiss bank notes data is used as training data. Twenty thousand random numbers that have as same means and variance-covariance matrices as this data are generated for evaluation data. Revised IP-OLDF, LDF and nominal logistic model are applied for this data, and 63 discriminate functions are obtained for all combinations of independent variables. Next, these models are applied for evaluation data.
