As a non-linear extension of the classic Linear Discriminant Analysis(LDA), Deep Linear Discriminant Analysis(DLDA) replaces the original Categorical Cross Entropy(CCE) loss function with eigenvalue-based loss function to make a deep neural network(DNN) able to learn linearly separable hidden representations. In this paper, we first point out DLDA focuses on training the cooperative discriminative ability of all the dimensions in the latent subspace, while put less emphasis on training the separable capacity of single dimension. To improve DLDA, a regularization method on within-class scatter matrix is proposed to strengthen the discriminative ability of each dimension, and also keep them complement each other. Experiment results on STL-10, CIFAR-10 and Pediatric Pneumonic Chest X-ray Dataset showed that our proposed regularization method Regularized Deep Linear Discriminant Analysis(RDLDA) outperformed DLDA and conventional neural network with CCE as objective. To further improve the discriminative ability of RDLDA in the local space, an algorithm named Subclass RDLDA is also proposed.

翻译：作为经典线性分辨分析(LDA)的非线性扩展,深海线性分辨分析(DLDA)将原分类跨子体损失功能替换为基于egenvalue的损耗功能,使深神经网络(DNN)能够学习线性分离的隐藏图象。在本文中,我们首先指出,DLDA侧重于培训潜潜藏子空间所有层面的合作性区别性能力,而较少强调培训单一层面的分解能力。为了改进DLDA,建议对类内散射矩阵采用一种正规化方法,以加强每个层面的区别性能力,并保持它们之间的互补。STL-10、CIFAR-10和Pediaric Pneumonic Chest X射线数据集的实验结果表明,我们提议的规范化方法(RDLDA)优于CE的DA和常规线性网络。为了进一步提高RDLDA在本地空间的区别性能力,还提出了一种名为RDA的子类。