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The paper propose a new non-linear dimensionality reduction algorithm based on locally linear embedding called supervised locally linear embedding in tensor space (SLLE/T), in which the local manifold structure within same class are preserved and the separability between different classes is enforced by maximizing distance of each point with its neighbors. To keep structure of data, we introduce tensor representation and reduce SLLE/T into the optimization problem based on HOSVD which is desirable to solve the out of sample problem. We also prove SLLE/T can be united in the graph embedding framework. The comparison experiments on face recognition indicate that SLLE/T outperform most popular dimensionality reduction algorithms both vectorization and tensor version.