 Local Geometric Structure Fisher Analysis, LGSFA, is a novel dimensionality reduction technique, designed specifically for hyperspectral imaging, HSI. It takes advantage of the intrinsic structure of HSI data by using interclass reconstructions of neighboring points to improve the intrinsic manifold structure and interclass separability. This allows for more accurate classification of HSI data compared to existing techniques. This article was authored by Fulin Luo, Honghuang, Yilduan, and others.