マルチカテゴリパターン分類のための区分的線形識別関数の一構成法

概要

論文の詳細を見る
This paper presents a method for determining piecewise-linear discriminant function for multicategory pattern classification and the sufficient condition for linear-separability of the given pattern set. The piecewise-linear discriminant function can be constituted of the minimum number of the linear discriminant functions under a certain condition. The linear discriminant function determined by the present method can be separated the largest number of the patterns in one category from any pattern belonging to the other categories. The problem of determining the piecewise-linear discriminant function, which divides a set of patterns into subclasses, is formulated here as a 0-1 integer programming problem called "set covering problem". Therefore, the piecewise-linear discriminant function obtained here is optimal in the sense of minimizing the number of linear discriminant functions. This method proposed here is useful in such a case that the given pattern set has unknown statistic property or the sample patterns belonging to the given set have a very complex distribution. Furthermore some advantages of the present method are that the algorithm finding the linear discriminant function is very simple and the number of parameters characterizing the piece-wise-linear discriminant function is not necessary to be given beforehand.
東海大学の論文