通过案例加权和单元加权实现稳健主成分
Robust Principal Components by Casewise and Cellwise Weighting
AI总结：
提出 cellPCA 方法，通过结合两种稳健损失函数和迭代重加权最小二乘算法，同时处理案例异常值、单元异常值和缺失数据，实现稳健的主成分分析。
摘要：
主成分分析（PCA）是分析多元数据的基本工具。这里关注的是降维到主子空间，其特征由投影矩阵表示。经典的主子空间可能受到异常值的强烈影响。传统的稳健方法考虑案例异常值，即由与干净案例不同的未指定异常分布生成的案例。但也可能存在单元异常值，即可能出现在数据矩阵中任何位置的可疑条目。另一个常见问题是某些单元格可能缺失。本文提出了一种新的稳健PCA方法，称为cellPCA，它可以同时处理案例异常值、单元异常值和缺失单元格。其单一目标函数结合了两个稳健损失函数，共同减轻案例和单元异常值的影响。目标函数通过迭代重加权最小二乘（IRLS）算法最小化。提出了残差单元格图和增强异常值图用于异常值检测。推导了主子空间的案例和单元影响函数，并得到了其渐近分布。广泛的模拟和两个真实数据示例说明了cellPCA的性能。
英文摘要：
Principal component analysis (PCA) is a fundamental tool for analyzing multivariate data. Here the focus is on dimension reduction to the principal subspace, characterized by its projection matrix. The classical principal subspace can be strongly affected by the presence of outliers. Traditional robust approaches consider casewise outliers, that is, cases generated by an unspecified outlier distribution that differs from that of the clean cases. But there may also be cellwise outliers, which are suspicious entries that can occur anywhere in the data matrix. Another common issue is that some cells may be missing. This paper proposes a new robust PCA method, called cellPCA, that can simultaneously deal with casewise outliers, cellwise outliers, and missing cells. Its single objective function combines two robust loss functions, that together mitigate the effect of casewise and cellwise outliers. The objective function is minimized by an iteratively reweighted least squares (IRLS) algorithm. Residual cellmaps and enhanced outlier maps are proposed for outlier detection. The casewise and cellwise influence functions of the principal subspace are derived, and its asymptotic distribution is obtained. Extensive simulations and two real data examples illustrate the performance of cellPCA.
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。
