School of Computer Science and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi'an, P. R. China.
Center for OPTical IMagery Analysis and Learning (OPTIMAL), State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an, P. R. China.
IEEE Trans Neural Netw Learn Syst. 2017 Nov;28(11):2738-2747. doi: 10.1109/TNNLS.2016.2598744.
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.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.
本文主要关注如何为每个类别实现翻译子空间表示，该表示能够同时指示相关类别的分布以及与其互补类别之间的差异。借助于重构问题，可以将类别特定子空间分类器（CSSC）问题表示为一系列双目标优化问题，分别最小化和最大化相关类别及其互补类别的重构误差。此外，特别引入正则化项以确保整个系统的稳定性。因此，可以进一步基于求解一般二次比问题提出正则化类别特定子空间分类器（RCSSC）方法。所提出的 RCSSC 方法在正则化参数变化下一致收敛到全局最优子空间和平移。此外，所提出的 RCSSC 方法可以通过正交分解技术扩展到无正则化情况，即无正则化 CSSC（UCSSC）方法。因此，可以从理论和实验上验证所提出的 RCSSC 和 UCSSC 方法的有效性和优越性。
