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Linear discriminant analysis (LDA) is a popular statistical approach for dimensionality reduction. LDA captures the global geometric structure of the data by simultaneously maximizing the between-class distance and minimizing the within-class distance. However, local geometric structure has recently been shown to be effective for dimensionality reduction. In this paper, a novel dimensionality reduction algorithm is proposed, which integrates both global and local structures. The main contributions of this paper include: (1) We present a least squares formulation for dimensionality reduction, which facilities the integration of global and local structures; (2) We design an efficient model selection scheme for the optimal integration, which balances the tradeoff between the global and local structures; and (3) We present a detailed theoretical analysis on the intrinsic relationship between the proposed framework and LDA …