Regularized class-specific subspace classifier

In this paper, we mainly focus on how to achieve the translated subspace representation for each class, which could simultaneously indicate the distribution of the associated class and the differences from its complementary classes. By virtue of the reconstruction problem, the class-specific subspace classifier (CSSC) problem could be represented as a series of biobjective optimization problems, which minimize and maximize the reconstruction errors of the related class and its complementary classes, respectively. Besides, the regularization term is specifically introduced to ensure the whole system's stability. Accordingly, a regularized class-specific subspace classifier (RCSSC) method can be further proposed based on solving a general quadratic ratio problem. The proposed RCSSC method consistently converges to the global optimal subspace and translation under the variations of the regularization parameter. Furthermore, the proposed RCSSC method could be extended to the unregularized case, which is known as unregularized CSSC (UCSSC) method via orthogonal decomposition technique. As a result, the effectiveness and the superiority of both proposed RCSSC and UCSSC methods can be verified analytically and experimentally.