Fisher线性判别式的旋转稀疏化
Sparsifying the Fisher Linear Discriminant by Rotation
摘要：
基于稀疏线性判别分析（LDA）的高维分类技术已经在文献中提出了许多。为了有效地使用它们，线性分类器的稀疏性是一个先决条件。然而，这在许多应用程序中可能并不容易获得，并且需要数据的旋转来创建所需的稀疏性。在本文中，我们提出了一个家庭的旋转创建所需的稀疏性。其基本思想是利用合并样本的样本协方差阵的主成分及其变量来旋转数据，然后应用现有的高维分类器。这种旋转和求解过程可以与任何现有的分类器相结合，并且对真实模型的稀疏程度具有鲁棒性。我们发现，这些旋转确实创造了高维分类所需的稀疏性，并提供了理论上的理解，为什么这样的旋转工程经验。大量的模拟和真实数据的例子证明了所提出的方法的有效性，我们的方法的改进，一些流行的高维分类规则清楚地显示。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
