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Least square regression (LSR) and its variants have been widely used for classification tasks. However, LSR-based methods ignore the local geometry structure of the data and the transformation matrix is not sparse or robust. In this paper, a novel linear regression (LR) framework is proposed for image classification. Two concrete algorithms are proposed under the framework, which are named manifold discriminant regression learning (MDRL) and robust manifold discriminant regression learning (RMDRL). MDRL introduces different norms for different purposes in the learning steps. MDRL introduces a within-class graph and between-class graph to compute an optimal subspace that can separate data points belonging to different class as far as possible and keep the data points from the same class closely. MDRL joints different norms constraints to generate sparse projections for feature extraction and …