Discriminant Analysis with graph learning for hyperspectral image classification

Linear Discriminant Analysis (LDA) is a widely-used technique for dimensionality reduction, and has been applied in many practical applications, such as hyperspectral image classification. Traditional LDA assumes that the data obeys the Gaussian distribution. However, in real-world situations, the high-dimensional data may be with various kinds of distributions, which restricts the performance of LDA. To reduce this problem, we propose the Discriminant Analysis with Graph Learning (DAGL) method in this paper. Without any assumption on the data distribution, the proposed method learns the local data relationship adaptively during the optimization. The main contributions of this research are threefold: (1) the local data manifold is captured by learning the data graph adaptively in the subspace; (2) the spatial information within the hyperspectral image is utilized with a regularization term; and (3) an efficient algorithm is designed to optimize the proposed problem with proved convergence. Experimental results on hyperspectral image datasets show that promising performance of the proposed method, and validates its superiority over the state-of-the-art.