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In this paper, a new tensor dimensionality reduction algorithm is proposed based on graph preserving criterion and tensor rank-one projections. In the algorithm, a novel, effective and converged orthogonalization process is given based on a differential-form objective function. A set of orthogonal rank-one basis tensors are obtained to preserve the intra-class local manifolds and enhance the inter-class margins. The algorithm is evaluated by applying to the basic facial expressions recognition.