A Semi-Supervised Feature Extraction based on Supervised and Fuzzy-based Linear Discriminant Analysis for Hyperspectral Image Classification

Linear discriminant analysis (LDA) is a commonly used feature extraction method to resolve the Hughes phenomenon for classification. Moreover, many studies show that the spatia l information can greatly improve the classification perfor mance. Hence, for hyperspectral image classification, it is not only neces sary to use the available spectral information but also to ex ploit the spatial information. Recently, we proposed a fuzzy-based LDA (FLDA), an unsupervised feature extraction, and used it for clust ering problem. However, it is hard to apply in the image segmentation because the optimization problem is nonlinear and non-convex and the number of membership values, the product of the number of clusters and the number of pixels in the image, is too large. In this paper, a semi- supervised feature extraction method which is based on the scatter matrices of LDA and FLDA (FLDA) is proposed. The unknown samples and their membership values which are determined by the posteriors after applying the classifier are used to form the within- and between-cluster scatter matrices of FLDA. The experimental results on two hyperspectral images, the Washington DC Mall and the Indian Pine Site, show that the proposed method can yield a better classification performance than LDA in the small sam pling size problem.