This paper proposes an improved linear discriminant analysis called spectrally-corrected and regularized LDA (SRLDA). This method integrates the design ideas of the sample spectrally-corrected covariance matrix and the regularized discriminant analysis. With the support of a large-dimensional random matrix analysis framework, it is proved that SRLDA has a linear classification global optimal solution under the spiked model assumption. According to simulation data analysis, the SRLDA classifier performs better than RLDA and ILDA and is closer to the theoretical classifier. Experiments on different data sets show that the SRLDA algorithm performs better in classification and dimensionality reduction than currently used tools.

翻译：本文提出了一种改进的线性判别分析方法——光谱校正与正则化线性判别分析（SRLDA）。该方法融合了样本光谱校正协方差矩阵与正则化判别分析的设计思想。在大维随机矩阵分析框架的支持下，证明了SRLDA在尖峰模型假设下具有线性分类全局最优解。仿真数据分析表明，SRLDA分类器的性能优于RLDA和ILDA，且更接近理论分类器。在不同数据集上的实验结果显示，SRLDA算法在分类和降维方面的表现优于当前使用的工具。