Abstract
From 1997, I proposed several different kinds of discriminant functions using by mathematical programming in my research. At first, IP-OLDF and LP-OLDF are proposed. IP-OLDF is linear discriminant function based on MMN (Minimum Misclassification Number) criteria. This model is defined on both data and discriminant coefficient spaces. So, new facts about discriminant analysis are obtained: 1) relationship about discriminant coefficients and MMN, 2) MMN decreases monotonously on the models selected by forward stepwise method. 3) Misclassification numbers of different discriminant models are regressed by MMN. And different models are evaluated by these regression lines. But, IP-OLDF needs huge computational power because it uses integer programming. In addition to this, it rarely looks for wrong solution if data isn't in general position. LP-OLDF is derived from IP-OLDF by minor modification of decision variables. This model is one of L_1 norm discriminant model that is very popular in these researches. In 2003, faster algorithm of IP-OLDF is proposed. Firstly, data is analyzed by LP-OLDF. Secondly, classified cases are fixed and IP-OLDF is applied for misclassified cases. This algorism is evaluated by several data and obtained good results. After 2005, Revised IP-OLDF is proposed. This model can find MMN correctly, even though data is not in general position. So, I can evaluate Revised IP-OLDF with other discriminate models, especially SVM. In this research, new algorithm of soft margin maximization SVM is found. This model obtained good result compared with soft margin SVM. Sometimes, it can find MMN.
