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Linear discriminant analysis (LDA) only considers the global Euclidean geometrical structure of data for dimensionality reduction. However, previous works have demonstrated that the local geometrical structure is effective for dimensionality reduction. In this paper, a novel approach is proposed, namely Joint Global and Local-structure Discriminant Analysis (JGLDA), for linear dimensionality reduction. To be specific, we construct two adjacency graphs to represent the local intrinsic structure, which characterizes both the similarity and diversity of data, and integrate the local intrinsic structure into Fisher linear discriminant analysis to build a stable discriminant objective function for dimensionality reduction. Experiments on several standard image databases demonstrate the effectiveness of our algorithm.