Linear discriminant analysis (LDA) is one of the important techniques for dimensionality reduction, machine learning, and pattern recognition. However, in many applications, applying the classical LDA often faces the following problems: (1) sensitivity to outliers, (2) absence of local geometric information, and (3) small sample size or matrix singularity that can result in weak robustness and efficiency. Although several researchers have attempted to address one or more of the problems, little work has been done to address all of them together to produce a more effective and efficient LDA algorithm. This article proposes 3E-LDA, an enhanced LDA algorithm, that deals with all three problems as an attempt to further improve LDA. It proposes to learn a weighted median rather than the mean of the samples to deal with (1), to embed both between-class and within-class local geometric information to deal with (2), and to calculate the projection vectors in the null space of the matrix to deal with (3). Experiments on six benchmark datasets show that these three enhancements enable 3E-LDA to markedly outperform state-of-the-art LDA baselines in both accuracy and efficiency.

中文翻译：

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3E-LDA

线性判别分析（LDA）是降维、机器学习和模式识别的重要技术之一。然而，在许多应用中，应用经典 LDA 经常面临以下问题：(1) 对异常值的敏感性，(2) 缺乏局部几何信息，以及 (3) 样本量小或矩阵奇异性会导致鲁棒性和效率较弱. 尽管一些研究人员试图解决一个或多个问题，但几乎没有做任何工作来解决所有这些问题以产生更有效和高效的 LDA 算法。本文提出3E-LDA，一种增强的LDA算法，处理所有三个问题，作为进一步改进LDA的尝试。它建议学习加权中位数而不是样本的平均值来处理（1），嵌入类间和类内局部几何信息来处理（2），并计算矩阵的零空间中的投影向量来处理（3）。在六个基准数据集上进行的实验表明，这三个增强功能使 3E-LDA 在准确性和效率方面都显着优于最先进的 LDA 基准。