Switching Linear Discriminant Using Fuzzy Clustering

Abstract

Linear discriminant analysis by R.A.Fisher is based on the single linear projection of the whole data set, that provides a convenient index for classification. If the data set to be classified has a region where the data of the different classes overlap and has nonlinear decision boundaries, Fisher's linear discriminant analysis may not be able to demonstrate good classification performance. In this paper, we propose a new linear discriminant approach(switching linear discriminant)which derives the linear discriminant function for each cluster obtained by a fuzzy clustering algorithm which takes local nonlinearity into consideration. The fuzzy clustering algorithm locates cluster centers around the nonlinear boundaries for the switching linear discriminant, which thus provides several indices for classification in a form of simplified rules. The effectiveness of our method is shown in the numerical examples.