Unsupervised constrained linear fisher's discriminant analysis for hyperspectral image classification

Fisher's linear discriminant analysis (FLDA) has been widely used in pattern classification due to its criterion, called Fisher's ratio, based on the ratio of between-class variance to within-class variance. Recently, a linear constrained discriminant analysis (LCDA) was developed for hyperspectral image classification where Fisher's ratio was replaced with the ratio of inter-distance to intra-distance and the target signatures were constrained to orthogonal directions. This paper directly extends the FLDA to constrained Fisher's linear discriminant analysis (CFLDA), which uses Fisher's ratio as a classification criterion. Since CFLDA is supervised which requires a set of training samples, this paper further extends the CFLDA to an unsupervised CFLDA (UCFLDA) by including a new unsupervised training sample generation algorithm to automatically produce a sample pool of training data to be used for CFLDA. In order to determine the number of classes, p, to be classified, a newly developed concept, called virtual dimensionality (VD) is used to estimate the p where a Neyman-Pearson-based eigen-analysis approach developed by Harsanyi, Farrand and Chang, called noise-whitened HFC (NWHFC)'s method, is implemented to find the VD. The experimental results have shown that the proposed UCFLDA perform effectively for HYDICE data and provides a promising unsupervised classification technique for hyperspectral imagery.