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This paper presents a new dimensionality reduction algorithm for multi-dimensional data based on the tensor rank-one decomposition and graph preserving criterion. Through finding proper rank-one tensors, the algorithm effectively enhances the pairwise inter-class margins and meanwhile preserves the intra-class local manifold structure. In the algorithm, a novel marginal neighboring graph is devised to describe the pairwise inter-class boundaries, and a differential formed objective function is adopted to ensure convergence. Furthermore, the algorithm has less computation in comparison with the vector representation based and the tensor-to-tensor projection based algorithms. The experiments for the basic facial expressions recognition show its effectiveness, especially when it is followed by a neural network classifier.