Utilization of a best linear discriminant function for designing the binary decision tree†

Abstract

Abstract This paper describes an accurate and efficient method for supervised classification of multispectral images. First, a simple derivation of a best linear discriminant function (BLD) is presented through geometrical consideration on ellipses with equi-Mahalanobis distance. It is shown that the function satisfies the Minimax criterion, which implies the robustness with regard to prior probabilities. Then, the binary decision tree (BDT) is introduced in order to make the method efficient, where the BLD is utilized as a decision rule. Care is taken to prevent a decline in the classification accuracy during the process of constructing the BDT. In addition to the theoretical evaluation of the processing speed, the actual performance of the proposed method is shown by applying it to multispectral data of Landsat-5. It is shown that the BDT/BLD becomes more efficient than Fisher's linear discriminant function when the number of classes increases.