Generalized two-dimensional linear discriminant analysis with regularization
Generalized two-dimensional linear discriminant analysis with regularization
复制标题
正则化广义二维线性判别分析
DOI：
10.1016/j.neunet.2021.04.030
复制
发表时间：
2021-05-10
期刊：
影响因子：
7.8
通讯作者：
Deng, Nai-Yang
中科院分区：
文献类型：
--
作者：
Li, Chun-Na;Shao, Yuan-Hai;Deng, Nai-Yang
最近的进步表明，二维线性判别分析（2DLDA）是一种基于矩阵的成功降低方法。但是，从理论上讲，2DLDA可能会遇到奇异性问题，并且对异常值也很敏感。在本文中，提出了一个通用的LP-NORM 2DLDA框架，并提出了带有任意p> 0的正则化，称为G2DLDA。 G2DLDA的主要有两个贡献：一个是G2DLDA模型使用任意的LP-NORM来测量阶级和阶级散布的阶段，因此可以选择适当的P来实现稳健性。另一个是引入的正规化术语使G2DLDA享有更好的概括性能并避免奇异性。此外，有效的学习算法是为G2LDA设计的，可以通过一系列具有封闭式溶液的凸问题来解决。当1时，可以从理论上保证其收敛性
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