Linear spectral mixture models and support vector machines for remote sensing

Mixture modeling is becoming an increasingly important tool in the remote sensing community as researchers attempt to resolve subpixel, area information. This paper compares a well-established technique, linear spectral mixture models (LSMM), with a much newer idea based on data selection, support vector machines (SVM). It is shown that the constrained least squares LSMM is equivalent to the linear SVM, which relies on proving that the LSMM algorithm possesses the "maximum margin" property. This in turn shows that the LSMM algorithm can be derived from the same optimality conditions as the linear SVM, which provides important insights about the role of the bias term and rank deficiency in the pure pixel matrix within the LSMM algorithm. It also highlights one of the main advantages for using the linear SVM algorithm in that it performs automatic "pure pixel" selection from a much larger database. In addition, extensions to the basic SVM algorithm allow the technique to be applied to data sets that exhibit spectral confusion (overlapping sets of pure pixels) and to data sets that have nonlinear mixture regions. Several illustrative examples, based on an area-labeled Landsat dataset, are used to demonstrate the potential of this approach.