Hyperspectral Data Processing: Algorithm Design and Analysis

13.9 Conclusions

This chapter presents a new approach to LSMA, referred to as FLSMA, which directly extends the well-known FLDA to LSMA in two different ways. One is called FVC-FLSMA that constrains the Fisher ratio-generated feature vectors to mutual orthogonal directions. Another is called AC-FLSMA that imposes the sum-to-one and non-negativity constraints on abundance fractions in the least squares sense. It has been shown that FVC-FLSMA operates in the same way as LCMV does, with the only difference that the data correlation matrix used in LCMV is replaced by the within-class scatter matrix in FLSMA. Because the within-class scatter matrix is a more effective measure than the data correlation matrix in pattern classification, FVC-FLSMA performs better than LCMV in mixed pixel classification. Additionally, it also shows that LCDA is essentially the same as FVC-FLSMA. There are also three types of AC-FLSMA that can be derived in parallel in the same fashion as three types of constrained least squares methods are developed for LSMA in Chang (2003a). They are called ASCLS-FLSMA, ANCLS-FLSMA, and AFCLS-FLSMA with their respective counterparts in the abundance-constrained least squares LSMA, SCLS, non-negativity constrained least squares (NCLS), and FCLS. Since the mixed pixel classification is performed by AC-FLSMA using Fisher's ratio as a classification measure and least squares error as an abundance estimation criterion, AC-FLSMA also performs better than abundance-constrained ...