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We propose a novel semi-supervised local discriminant analysis (SELD) method for feature extraction in hyperspectral remote sensing imagery. The proposed method combines a supervised method (Linear Discriminant Analysis (LDA)) and an unsupervised method (Neighborhood Preserving Embedding (NPE)) without any free parameters. The underlying idea is to design optimal projection vectors, which can discover the global discriminant structure of the available labeled samples while preserving the local neighborhood spatial structure of the unlabeled samples. Furthermore, in our approach the number of extracted feature bands is no longer limited by the number of classes, which is a disadvantage of LDA. Experimental results demonstrate that the proposed method outperforms consistently other related semi-supervised methods and that it is also much more stable when the percentage of the labeled samples changes.