Management School, Hainan University, Haikou, 570228, PR China.
Management School, Hainan University, Haikou, 570228, PR China.
Neural Netw. 2021 Oct;142:73-91. doi: 10.1016/j.neunet.2021.04.030. Epub 2021 May 5.
Recent advances show that two-dimensional linear discriminant analysis (2DLDA) is a successful matrix based dimensionality reduction method. However, 2DLDA may encounter the singularity issue theoretically, and also is sensitive to outliers. In this paper, a generalized Lp-norm 2DLDA framework with regularization for an arbitrary p>0 is proposed, named G2DLDA. There are mainly two contributions of G2DLDA: one is G2DLDA model uses an arbitrary Lp-norm to measure the between-class and within-class scatter, and hence a proper p can be selected to achieve robustness. The other one is that the introduced regularization term makes G2DLDA enjoy better generalization performance and avoid singularity. In addition, an effective learning algorithm is designed for G2LDA, which can be solved through a series of convex problems with closed-form solutions. Its convergence can be guaranteed theoretically when 1≤p≤2. Preliminary experimental results on three contaminated human face databases show the effectiveness of the proposed G2DLDA.
最近的研究进展表明，二维线性判别分析（2DLDA）是一种成功的基于矩阵的降维方法。然而，2DLDA 在理论上可能会遇到奇异问题，并且对离群值也很敏感。在本文中，我们提出了一种广义 Lp-范数 2DLDA 框架，该框架具有正则化项，用于任意 p>0，称为 G2DLDA。G2DLDA 主要有两个贡献：一是 G2DLDA 模型使用任意 Lp-范数来度量类间和类内散布，因此可以选择适当的 p 值来实现鲁棒性。另一个是引入的正则化项使 G2DLDA 具有更好的泛化性能并避免奇异。此外，我们还为 G2LDA 设计了一种有效的学习算法，该算法可以通过一系列具有闭式解的凸问题来解决。当 1≤p≤2 时，理论上可以保证其收敛性。在三个受污染的人脸数据库上的初步实验结果表明了所提出的 G2DLDA 的有效性。
