Semi-supervised local discriminant analysis with nearest neighbors for hyperspectral image classification

Feature extraction can overcome the Hughes phenomenon for hyperspectral image classification. Linear discriminant analysis (LDA) is a basic supervised feature extraction method. However, LDA only cannot extract features more than number of classes. The semi-supervised local discriminant analysis (SELD) was proposed to solve the above problem by combing the scatter matrices of LDA and the neighborhood preserving embedding (NPE). Some unlabeled samples were used to form the scatter matrices of NPE. It can preserve the local geometric property according to the used unlabeled samples. Moreover, the between-class scatter matrix of SELD is nonsingular, and more features can be extracted by applying SELD. However, in SELD, the unlabeled sample were randomly selected. The local geometric property around the training samples cannot be preserved due to the randomly selection. In this study, the concept of the Voronoi diagram is used to determine the regions according to the training samples, and the unlabeled samples are chosen in the regions based on the nearest neighbors. Experimental results on the Indian Pine Site dataset show that the proposed method outperforms SELD with less number of unlabeled samples on the small sample size problem.