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In this paper a new tensor dimensionality reduction algorithm is proposed based on graph embedding and orthogonal tensor rank one decomposition. In the algorithm, both the intra- class local manifold structure and the inter-class margins are enhanced by projecting the original tensors onto a group of orthogonal rank-one tensors, and a novel and effective orthogonalization process is given. In the experiments the algorithm is used for the facial expression recognition and achieves accelerant results.