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Discriminative least squares regression (DLSR) aims to learn relaxed regression labels to replace strict zero-one labels. However, the distance of the labels from the same class can also be enlarged while using the ε-draggings technique to force the labels of different classes to move in the opposite directions, and roughly persuing relaxed labels may lead to the problem of overfitting. To solve above problems, we propose a low-rank discriminative least squares regression model (LRDLSR) for multi-class image classification. Specifically, LRDLSR class-wisely imposes low-rank constraint on the relaxed labels obtained by non-negative relaxation matrix to improve its within-class compactness and similarity. Moreover, LRDLSR introduces an additional regularization term on the learned labels to avoid the problem of overfitting. We show that these two improvements help to learn a more discriminative projection for …