High-dimensional classification has challenges mainly due to the singularity issue of the sample covariance matrix. In this work, we propose a different approach to get a more reliable sample covariance matrix by adjusting the estimated eigenvalues. This procedure also brings us a nonsingular matrix as a by-product. We improve the optimization procedure to obtain a linear classifier by incorporating the adjusted sample covariance matrix and a shrinkage mean vector into the original optimization problem. We have shown that our proposed binary classification rule is better than some other rules in terms of the misclassification rate through most of various synthetic data and real data sets.

中文翻译：

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使用带有调整估计特征值的样本协方差矩阵的高维分类规则

高维分类的挑战主要是由于样本协方差矩阵的奇异性问题。在这项工作中，我们提出了一种不同的方法，通过调整估计的特征值来获得更可靠的样本协方差矩阵。这个过程也给我们带来了一个非奇异矩阵作为副产品。我们通过将调整后的样本协方差矩阵和收缩均值向量合并到原始优化问题中来改进优化程序以获得线性分类器。我们已经表明，我们提出的二元分类规则在大多数各种合成数据和真实数据集的误分类率方面优于其他一些规则。