Pattern Classification by Linear Goal Programming and its Applications

Abstract

For pattern classification, the multi-surface method proposed by Mangasarian is attracting much attention, because it can provide an exact discrimination function even for highly nonlinear problems without any assumption on the data distribution. However, the method produces often too complicated discrimination surfaces, which cause poor generalization ability.

In this paper, several trials in order to overcome this difficulty of the multi-surface method will be suggested: One of them is the utilization of the goal programming in which the auxiliary linear programming problem is formulated as a goal programming in order to get as simple discrimination curve as possible. Another one is to apply the fuzzy programming by which we can get fuzzy discrimination curves with gray zones. In addition, using the suggested methods, the additional learning can be easily made. These features of the methods make the discrimination more realistic. The effectiveness of the methods are shown on the basis of some applications.