Abstract
Discriminative least squares regression (DLSR) has been shown to achieve promising performance in multi-class image classification tasks. Its key idea is to force the regression labels of different classes to move in opposite directions by means of the ε-dragging technique, yielding discriminative regression model exhibiting wider margins. However, the ε-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 ε-dragging framework (Fisher-ε) for image classification by constraining the relaxed labels using the Fisher criterion. On one hand, the Fisher criterion improves the intra-class compactness of the relaxed labels during relaxation learning. On the other hand, it is expected further to enhance the inter-class separability of ε-dragging. Fisher-ε for the first time ever attempts to integrate the Fisher criterion and ε-dragging technique into a unified model because they are complementary in learning discriminative projection. Extensive experiments on various datasets demonstrate that the proposed Fisher-ε method achieves performance that is superior to other state-of-the-art classification methods. The Matlab codes are available at https://github.com/chenzhe207/Fisher-epsilon.