A linear constrained distance-based discriminant analysis for hyperspectral image classification

Abstract Fisher's linear discriminant analysis (LDA) is a widely used technique for pattern classification problems. It employs Fisher's ratio, ratio of between-class scatter matrix to within-class scatter matrix to derive a set of feature vectors by which high-dimensional data can be projected onto a low-dimensional feature space in the sense of maximizing class separability. This paper presents a linear constrained distance-based discriminant analysis (LCDA) that uses a criterion for optimality derived from Fisher's ratio criterion. It not only maximizes the ratio of inter-distance between classes to intra-distance within classes but also imposes a constraint that all class centers must be aligned along predetermined directions. When these desired directions are orthogonal, the resulting classifier turns out to have the same operation form as the classifier derived by the orthogonal subspace projection (OSP) approach recently developed for hyperspectral image classification. Because of that, LCDA can be viewed as a constrained version of OSP. In order to demonstrate its performance in hyperspectral image classification, Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and HYperspectral Digital Imagery Collection Experiment (HYDICE) data are used for experiments.