33.3 Linear Spectral Mixture Analysis

Linear spectral mixture analysis (LSMA) is a theory developed for sub-sample and mixed sample analysis discussed in Chapter 2, whereas LSU is a technique to carry out LSMA to unmix data sample vectors via a linear mixing model into a number of basic constituent spectra assumed to make up the entire data sample vectors with appropriate abundance fractions of these constituent spectra. In spite of this distinction, these two terminologies have been used interchangeably in the literature. Depending on whether or not the signature knowledge is available, LSMA can be carried out by supervised LSMA (SLSMA) or ULSMA.

There are three crucial differences between LSMA and classification. One is that the spectral unmixing performed by LSMA produces abundance fractional maps considered as soft decisions as opposed to classification, which produces classification maps considered as hard decisions. Another difference is that LSMA only requires signature knowledge to form a linear mixture model and does not need training samples as required by classification. Even for ULSMA, the signature knowledge can be obtained by endmember extraction algorithms or unsupervised virtual signature finding algorithms (UVSFAs) developed in Chapter 17 where the only training samples are endmembers or virtual signatures themselves. So, the cross-validation used by classification via a set of training samples to evaluate performance is not applicable to LSMA. A third difference ...

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