Fisher Discriminative Least Squares Regression for Image Classification

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 proposed the joint use of the $\epsilon$-draggings technique, yielding discriminative regression model exhibiting wider margins, and the Fisher criterion. The $\epsilon$-draggings technique ignores an important problem: its non-negative 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 discriminative projection, as well as regression labels, we propose a Fisher regularized DLSR (FDLSR) framework 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 $\epsilon$-draggings technique. FDLSR for the first time ever attempts to integrate the Fisher discriminant criterion and $\epsilon$-draggings technique into one unified model because they are absolutely complementary in learning discriminative projection. Extensive experiments on various datasets demonstrate that the proposed FDLSR method achieves performance that is superior to other state-of-the-art classification methods. The Matlab codes of this paper are available at https://github.com/chenzhe207/FDLSR.