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Graph-embedding along with its linearization and kernelization provides a general framework that unifies most traditional dimensionality reduction algorithms. From this framework, we propose a new manifold learning technique called discriminant locally linear embedding (DLLE), in which the local geometric properties within each class are preserved according to the locally linear embedding (LLE) criterion, and the separability between different classes is enforced by maximizing margins between point pairs on different classes. To deal with the out-of-sample problem in visual recognition with vector input, the linear version of DLLE, i.e., linearization of DLLE (DLLE/L), is directly proposed through the graph-embedding framework. Moreover, we propose its multilinear version, i.e., tensorization of DLLE, for the out-of-sample problem with high-order tensor input. Based on DLLE, a procedure for gait recognition is described. We conduct comprehensive experiments on both gait and face recognition, and observe that: 1) DLLE along its linearization and tensorization outperforms the related versions of linear discriminant analysis, and DLLE/L demonstrates greater effectiveness than the linearization of LLE; 2) algorithms based on tensor representations are generally superior to linear algorithms when dealing with intrinsically high-order data; and 3) for human gait recognition, DLLE/L generally obtains higher accuracy than state-of-the-art gait recognition algorithms on the standard University of South Florida gait database.