  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.
