Support vector machines for optimal classification and spectral unmixing

Abstract

Mixture modelling is becoming an increasingly important tool in the remote sensing community as researchers attempt to resolve the sub-pixel, mixture information, which arises from the overlapping land cover types within the pixel’s instantaneous field of view. This paper describes an approach based on a relatively new technique, support vector machines (SVMs), and contrasts this with more established algorithms such as linear spectral mixture models (LSMM) and artificial neural networks (ANN). In the simplest case, it is shown that the mixture regions formed by the linear support vector machine and the linear spectral mixture model are equivalent; however, the support vector machine automatically selects the relevant pure pixels. When non-linear algorithms are considered it can be shown that the non-linear support vector machines have model spaces which contain many of the conventional neural networks, multi-layer perceptrons and radial basis functions. However, the non-linear support vector machines automatically determine the relevant set of basis functions (nodes) from the performance constraints specified via the loss function and in doing so select only the data points which are important for making a decision. In practice, it has been found that only about 5% of the training exemplars are used to form the decision boundary region, which represents a considerable compression of the data and also means that validation effort can be concentrated on just those important data points.