Hyperspectral Data Processing: Algorithm Design and Analysis

33.5 Support Vector Machines and Kernel-Based Approaches

In remote sensing image classification, one of most widely used techniques is maximum likelihood classifier (MLC), which is based on Mahalanobis distance. Since MLC is essentially a weighted distance measure with the weighting matrix specified by sample covariance matrix, it is not particularly designed for classification. Consequently, it does not necessarily yield the best classification. It has been shown in pattern classification that Fisher's linear discriminant analysis (FLDA) is one of best classifiers due to the fact that the Fisher's ratio used by FLDA as a criterion is specifically to be designed for classification where the Fisher ratio is defined by a ratio of the between-class scatter matrix to the within-class scatter matrix. In both cases, these two classifiers require second-order statistics to calculate the weighting matrix for MLC and scatter matrices for FLDA. Accordingly, MLC or FLDA may not work effectively if either data statistics cannot be well characterized by second-order statistics or the second-order statistics used to characterize the data are not reliable. In the former case, classifiers must go beyond second-order statistics such as high-order statistics-based classifiers, projection pursuit, neural networks, etc. As for the latter case, two circumstances may occur. One is that the used training samples are not appropriately selected. The other is that the pool of selected training samples is ...