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In this paper, we propose a method for the dimensionality reduction (DR) of spectral-spatial features in hyperspectral images (HSIs), under the umbrella of multilinear algebra, i.e., the algebra of tensors. The proposed approach is a tensor extension of conventional supervised manifold-learning-based DR. In particular, we define a tensor organization scheme for representing a pixel's spectral-spatial feature and develop tensor discriminative locality alignment (TDLA) for removing redundant information for subsequent classification. The optimal solution of TDLA is obtained by alternately optimizing each mode of the input tensors. The methods are tested on three public real HSI data sets collected by hyperspectral digital imagery collection experiment, reflective optics system imaging spectrometer, and airborne visible/infrared imaging spectrometer. The classification results show significant improvements in classification accuracies while using a small number of features.