Guo Jian, James Gareth, Levina Elizaveta, Michailidis George, Zhu Ji
Department of Statistics, University of Michigan, 269 West Hall, 1085 South University Avenue, Ann Arbor, MI 48109-1107.
Marshall School of Business, University of Southern California, Los Angeles, CA 90089-0809.
J Comput Graph Stat. 2010;19(4):930-946. doi: 10.1198/jcgs.2010.08127.
In this article, we propose a new method for principal component analysis (PCA), whose main objective is to capture natural "blocking" structures in the variables. Further, the method, beyond selecting different variables for different components, also encourages the loadings of highly correlated variables to have the same magnitude. These two features often help in interpreting the principal components. To achieve these goals, a fusion penalty is introduced and the resulting optimization problem solved by an alternating block optimization algorithm. The method is applied to a number of simulated and real datasets and it is shown that it achieves the stated objectives. The supplemental materials for this article are available online.
在本文中，我们提出了一种主成分分析（PCA）的新方法，其主要目标是捕捉变量中的自然“分组”结构。此外，该方法除了为不同成分选择不同变量外，还促使高度相关变量的载荷具有相同的大小。这两个特征通常有助于解释主成分。为实现这些目标，引入了融合惩罚项，并通过交替块优化算法解决由此产生的优化问题。该方法应用于多个模拟和真实数据集，结果表明它实现了既定目标。本文的补充材料可在线获取。
