Abstract We introduce a new method of performing high-dimensional discriminant analysis (DA), which we call multiDA. Starting from multiclass diagonal DA classifiers which avoid the problem of high-dimensional covariance estimation we construct a hybrid model that seamlessly integrates feature selection components. Our feature selection component naturally simplifies to weights which are simple functions of likelihood ratio test statistics allowing natural comparisons with traditional hypothesis testing methods. We provide heuristic arguments suggesting desirable asymptotic properties of our algorithm with regard to feature selection. We compare our method with several other approaches, showing marked improvements in regard to prediction accuracy, interpretability of chosen features, and fast run time. We demonstrate such strengths of our model by showing strong classification performance on publicly available high-dimensional datasets, as well as through multiple simulation studies. We make an R package available implementing our approach. Supplementary materials for this article are available online.

中文翻译：

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对高维数据进行特征选择的对角线判别分析

摘要 我们介绍了一种执行高维判别分析 (DA) 的新方法，我们称之为 multiDA。从避免高维协方差估计问题的多类对角 DA 分类器开始，我们构建了一个无缝集成特征选择组件的混合模型。我们的特征选择组件自然地简化为权重，权重是似然比检验统计的简单函数，允许与传统假设检验方法进行自然比较。我们提供启发式参数，表明我们的算法在特征选择方面的理想渐近特性。我们将我们的方法与其他几种方法进行了比较，在预测准确性、所选特征的可解释性和快速运行时间方面显示出显着改进。我们通过在公开可用的高维数据集上展示强大的分类性能以及通过多次模拟研究来证明我们模型的这种优势。我们提供了一个 R 包来实现我们的方法。本文的补充材料可在线获取。