Fisher´s linear spectral mixture analysis

Linear spectral mixture analysis (LSMA) has been widely used in subpixel analysis and mixed-pixel classification. One commonly used approach is based on either the least square error (LSE) criterion such as least squares LSMA or the signal-to-noise ratio (SNR) such as orthogonal subspace projection (OSP). Unfortunately, it is known that such criteria are not necessarily optimal for pattern classification. This paper presents a new and alternative approach to LSMA, called Fisher´s LSMA (FLSMA). It extends the well-known pure-pixel-based Fisher´s linear discriminant analysis to LSMA. Interestingly, what can be done for the LSMA can be also developed for the FLSMA. Of particular interest are two types of constraints imposed on the LSMA, target signature-constrained LSMA and target abundance-constrained LSMA, which can be also derived in parallel for the FLSMA, to be called feature-vector-constrained FLSMA (FVC-FLSMA) and abundance-constrained FLSMA (AC-FLSMA), respectively. Since Fisher´s ratio used by the FLSMA is a more appropriate classification criterion than the LSE or SNR used for the LSMA, the FVC-FLSMA improves over the classical least squares based LSMA and SNR-based OSP in mixed-pixel classification. Similarly, the AC-FLSMA also improves abundance-constrained least squares based LSMA in quantification of abundance fractions