The nonnegative representation-based classification only imposes an overall nonnegative constraint on the representation coefficients but fails to apply differentiated penalties on the coefficients of different classes, which inevitably limits its effectiveness. In response, this article proposes a dual flexible competitive nonnegative representation method, which introduces two competitive mechanisms: mean competition and inter-class competition. Mean competition relies on the class-wise mean of training samples as the competitive target, encouraging the representation coefficients to accurately capture the unique features of each class and enhancing the discriminability between the representation coefficients. Inter-class competition fully considers the intrinsic relationship between the overall representation and the class representations, strengthening the competitive representation between the true class and all remaining classes, thereby improving classification performance. Meanwhile, flexible factors are ingeniously incorporated into both competitive terms to effectively reduce interference from incorrect classes in the classification decision. The alternating direction method of multipliers is employed to solve the dual flexible competitive nonnegative representation problem, with a comprehensive explanation of the iterative procedure provided. Experimental findings indicate that the dual flexible competitive nonnegative representation method demonstrates significant advantages in face recognition tasks. The source code will be made available upon the acceptance of this article at https://github.com/li-zi-qi/DFCNR .
Guo et al. (Thu,) studied this question.