 Local Geometric Structure Fisher Analysis, LGSFA, is a novel dimensionality reduction, DR, method for hyperspectral image, HSI, classification. It first constructs an intrinsic graph and a penalty graph from the interclass, and interclass properties of neighboring points in the HSI, respectively. The reconstruction points of these points are then used to enhance the interclass manifold compactness and the interclass manifold separability. This DR method has been shown to be effective in revealing the intrinsic manifold structure of HSI and achieving better classification results than other state-of-the-art methods. This article was authored by Fulin Luo, Hong Huang, Yilduan, and others.