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Laplacian support vector machine (LapSVM), as a benchmark method, which includes an additional regularization term with graph Laplacian, has been successfully applied to remote sensing image classification. However, using the Euclidean distance to construct weights, the graph in LapSVM may not really represent the inherent distribution of the data. In this paper, optimized LapSVMs are developed for semisupervised hyperspectral image classification, by introducing distance metric learning instead of the traditional Euclidean distance which is used in the existing LapSVM. In the procedure of constructing graph with distance metric learning, equivalence and non-equivalence pairwise constraints are imposed for better capturing similarity of samples from different classes. In this way, two new optimization problems are reformulated for building LapSVM with normalized and unnormalized graph Laplacian respectively. Experiments are conducted on two real hyperspectral datasets. Corresponding results obtained with low number of labeled training samples demonstrate the effectiveness of our proposed methods for hyperspectral image classification.