<i>Fisher</i> Regularized ε-Dragging for Image Classification
Zhe Chen, Xiao‐Jun Wu, Josef Kittler
Abstract
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> -dragging technique, yielding a discriminative regression model exhibiting wider margins. However, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> -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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> -dragging framework (Fisher- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> ) 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 hand, it is expected further to enhance the interclass separability of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> -dragging. Fisher- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> for the first time ever attempts to integrate the Fisher criterion and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> -dragging technique into a unified model because they are complementary in learning discriminative projection. Extensive experiments on various data sets demonstrate that the proposed Fisher- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> method achieves performance that is superior to other state-of-the-art classification methods. The MATLAB codes are available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/chenzhe207/Fisher-epsilon</uri> .