Wang Yulong, Tan Yap-Peng, Tang Yuan Yan, Chen Hong, Zou Cuiming, Li Luoqing
IEEE Trans Cybern. 2022 May;52(5):2675-2686. doi: 10.1109/TCYB.2020.3021712. Epub 2022 May 19.
This article presents a generalized collaborative representation-based classification (GCRC) framework, which includes many existing representation-based classification (RC) methods, such as collaborative RC (CRC) and sparse RC (SRC) as special cases. This article also advances the GCRC theory by exploring theoretical conditions on the general regularization matrix. A key drawback of CRC and SRC is that they fail to use the label information of training data and are essentially unsupervised in computing the representation vector. This largely compromises the discriminative ability of the learned representation vector and impedes the classification performance. Guided by the GCRC theory, we propose a novel RC method referred to as discriminative RC (DRC). The proposed DRC method has the following three desirable properties: 1) discriminability: DRC can leverage the label information of training data and is supervised in both representation and classification, thus improving the discriminative ability of the representation vector; 2) efficiency: it has a closed-form solution and is efficient in computing the representation vector and performing classification; and 3) theory: it also has theoretical guarantees for classification. Experimental results on benchmark databases demonstrate both the efficacy and efficiency of DRC for multiclass classification.
本文提出了一种基于广义协同表示的分类（GCRC）框架，该框架包含许多现有的基于表示的分类（RC）方法，例如协同RC（CRC）和稀疏RC（SRC）作为其特殊情况。本文还通过探索一般正则化矩阵的理论条件推进了GCRC理论。CRC和SRC的一个关键缺点是它们未能利用训练数据的标签信息，并且在计算表示向量时本质上是无监督的。这在很大程度上损害了所学习的表示向量的判别能力，并阻碍了分类性能。在GCRC理论的指导下，我们提出了一种新颖的RC方法，称为判别式RC（DRC）。所提出的DRC方法具有以下三个理想特性：1）可判别性：DRC可以利用训练数据的标签信息，并且在表示和分类方面都是有监督的，从而提高了表示向量的判别能力；2）效率：它具有闭式解，并且在计算表示向量和执行分类方面效率很高；3）理论性：它在分类方面也具有理论保证。在基准数据库上的实验结果证明了DRC在多类分类中的有效性和效率。
