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Dimensionality reduction is an important task in the analysis of hyperspectral image data. While traditional dimensionality reduction methods use class labels as prior information, this letter presents a general semisupervised dimensionality reduction framework for hyperspectral image classification based on new prior information, i.e., pairwise constraints which specify whether a pair of examples belongs to the same class or not. The proposed semisupervised dimensionality reduction framework contains two terms: 1) a discrimination term that assesses the separability between classes; and 2) a regularization term that characterizes some property of the original data set. Furthermore, a novel semisupervised dimensionality reduction method is derived from the framework based on sparse representation. Experimental results on two hyperspectral image data sets show that the proposed algorithms are remarkably effective in comparison to traditional dimensionality reduction methods.