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Discriminative least-squares regression (DLSR) has been shown to achieve promising performance in multiclass image classification tasks. Its key idea is to force the regression labels of different classes to move in opposite directions by means of the -dragging technique, yielding a discriminative regression model exhibiting wider margins. However, the -dragging technique ignores an important problem: its relaxation matrix is dynamically updated in optimization, which means the dragging values can also cause the labels from the same class to be uncorrelated. In order to learn a more powerful projection, as well as regression labels, we propose a Fisher regularized -dragging framework (Fisher- ) for image classification by constraining the relaxed labels using the Fisher criterion. On the one hand, the Fisher criterion improves the intraclass compactness of the relaxed labels during relaxation learning. On the other …