Hyperspectral Data Processing: Algorithm Design and Analysis

13.1 Introduction

LSMA has been widely used in subpixel analysis and mixed pixel classification. Many algorithms have been developed for LSMA such as LS-LSMA, SNR-based OSP, and Mahalanobis distance-based Gaussian maximum likelihood estimation (GMLE). However, according to Juang and Katagiri (1992), LSE is not necessarily the best criterion to measure classification error and neither is SNR. Instead, FLDA is one of the major techniques widely used in pattern classification (Duda and Hart, 1973). It makes use of the so-called Fisher's ratio also known as Rayleigh quotient, which is the ratio of between-class scatter matrix to within-class scatter matrix, as a criterion to generate a set of feature vectors that constitute a feature space for better classification. A similar approach to FLDA was developed by Soltanian-Zadeh et al. (1996) who replaced Fisher's ratio with the ratio of interdistance to intradistance and aligned the generated feature vectors along mutual orthogonal directions. This approach has been shown to be successful in magnetic resonance (MR) image classification. Most recently, Soltanian-Zadeh et al.'s approach was further extended to linearly constrained discriminant analysis (LCDA) by Du and Chang for hyperspectral image classification to improve LSMA classification (Du and Chang, 2001a; Chang 2003b). Technically speaking, the feature vectors obtained by Soltanian-Zadeh et al. (1996) as well as those by Du and Chang (2001a) are not actually Fisher's feature vectors ...