Spectral Unmixing Model Based on Least Squares Support Vector Machine With Unmixing Residue Constraints

Spectral unmixing has been an important technique for hyperspectral imagery processing. In traditional spectral unmixing methods that are based on the linear spectral mixture model (LSMM), unmixing accuracy is limited by the inherent deficiency of the model. It was shown that the support vector machine (SVM) can be extended for spectral unmixing, based on the advantage that the SVM model can accommodate the variations within a relative pure class by using multiple pure samples instead of a single endmember for one class. In the SVM model, class label errors are considered in constraints. However, the errors concerned in spectral unmixing are the unmixing residue instead of the class label ones. This letter presents a method of imposing unmixing residue constraints on the least squares SVM unmixing model. The related problems, including deducing the closed-form solution and substituting the single endmember for multiple ones, were studied together. Experiments showed that the new SVM model was superior to the original SVM as well as the traditional LSMM in terms of unmixing residue, fractional abundance, and confused matrix criterions.