Modified Fisher's Linear Discriminant Analysis for Hyperspectral Imagery

In this letter, we present a modified Fisher's linear discriminant analysis (MFLDA) for dimension reduction in hyperspectral remote sensing imagery. The basic idea of the Fisher's linear discriminant analysis (FLDA) is to design an optimal transform, which can maximize the ratio of between-class to within-class scatter matrices so that the classes can be well separated in the low-dimensional space. The practical difficulty of applying FLDA to hyperspectral images includes the unavailability of enough training samples and unknown information for all the classes present. So the original FLDA is modified to avoid the requirements of training samples and complete class knowledge. The MFLDA requires the desired class signatures only. The classification result using the MFLDA-transformed data shows that the desired class information is well preserved and they can be easily separated in the low-dimensional space.