MOP/GP models for machine learning

Techniques for machine learning have been extensively studied in recent years as effective tools in data mining. Although there have been several approaches to machine learning, we focus on the mathematical programming (in particular, multi-objective and goal programming; MOP/GP) approaches in this paper. Among them, Support Vector Machine (SVM) is gaining much popularity recently. In pattern classification problems with two class sets, its idea is to find a maximal margin separating hyperplane which gives the greatest separation between the classes in a high dimensional feature space. This task is performed by solving a quadratic programming problem in a traditional formulation, and can be reduced to solving a linear programming in another formulation. However, the idea of maximal margin separation is not quite new: in the 1960s the multi-surface method was suggested by Mangasarian. In the 1980s, linear classifiers using goal programming were developed extensively. This paper presents an overview on how effectively MOP/GP techniques can be applied to machine learning such as SVM, and discusses their problems.