Many high dimensional classification techniques have been proposed in the literature based on sparse linear discriminant analysis (LDA). To efficiently use them, sparsity of linear classifiers is a prerequisite. However, this might not be readily available in many applications, and rotations of data are required to create the needed sparsity. In this paper, we propose a family of rotations to create the required sparsity. The basic idea is to use the principal components of the sample covariance matrix of the pooled samples and its variants to rotate the data first and to then apply an existing high dimensional classifier. This rotate-and-solve procedure can be combined with any existing classifiers, and is robust against the sparsity level of the true model. We show that these rotations do create the sparsity needed for high dimensional classifications and provide theoretical understanding why such a rotation works empirically. The effectiveness of the proposed method is demonstrated by a number of simulated and real data examples, and the improvements of our method over some popular high dimensional classification rules are clearly shown.

中文翻译：

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通过旋转稀疏Fisher线性判别式。

基于稀疏线性判别分析（LDA）的文献已经提出了许多高维分类技术。为了有效地使用它们，线性分类器的稀疏性是先决条件。但是，这在许多应用程序中可能并不容易获得，并且需要轮换数据以创建所需的稀疏性。在本文中，我们提出了一系列轮换以创建所需的稀疏性。基本思想是使用合并样本及其变体的样本协方差矩阵的主要成分来首先旋转数据，然后应用现有的高维分类器。该旋转和求解过程可以与任何现有分类器组合，并且对于真实模型的稀疏性级别具有鲁棒性。我们表明，这些旋转确实产生了高维分类所需的稀疏性，并提供了理论上的理解，为什么这种旋转凭经验起作用。通过大量的模拟和真实数据实例证明了该方法的有效性，并且清楚地表明了我们的方法对一些流行的高维分类规则的改进。