Dimensionality reduction (DR) plays an important role in hyperspectral image processing. With enough efficient labeled samples, linear discriminant analysis (LDA) can find the optimal projections by maximizing the between-class scatter variance meanwhile minimizing the within-class scatter variance. However, LDA is not suitable for dimensional reduction of non-Gaussian data and will cause overfitting with insufficient samples. A semisupervised graph embedding and spatial neighbor-based discriminant analysis (SEGSA) method is proposed for DR. First, SEGSA constructs a similarity connected graph among samples without any parameter then uses the labeled samples to filter out valid unlabeled samples and assigns them weak labels. Second, SEGSA utilizes the label and weak label information of the samples to construct the interclass penalty weight graph and intraclass similarity weight graph, which uses different strategies to reduce the effect of weak labels’ inaccuracy. Finally, by mining the spatial neighbor information of samples, SEGSA constructs a spatial similarity graph and maintains the spatial neighbor structure while maximizing the interclass distance and minimizing the intraclass distance. Experimental results on hyperspectral images validate the advantage and effectiveness of the proposed method compared with other DR methods.