Robust Orthogonal Complement Principal Component Analysis

• 成果类型: Article
• 署名作者: She, Yiyuan; Li, Shijie; Wu, Dapeng
• 署名单位: State University System of Florida; Florida State University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2015.1042107
• 发表日期: 2016
• 页码: 763-771
• 关键词: VARIABLE SELECTION; model selection; Consistency; algorithm; barzilai

摘要

Recently, the robustification of principal component analysis (PCA) has attracted lots of attention from statisticians, engineers, and computer scientists. In this work, we study the type of outliers that are not necessarily apparent in the original observation space but can seriously affect the principal sub-space estimation. Based on a mathematical formulation of such transformed outliers, a novel robust orthogonal complement principal component analysis (ROC-PCA) is proposed. The framework combines the popular sparsity-enforcing and low-rank regularization techniques to deal with row-wise outliers as well as element-wisp outliers. A nonasymptotic oracle inequality guarantees the accuracy and high breakdown performance of ROC-PCA in finite samples. To tackle the computational challenges, an efficient algorithm is developed on the basis of Stiefel manifold optimization and iterative thresholding. Furthermore, a batch variant is proposed to significantly reduce the cost in ultra high dimensions. The article also points out a pitfall of a common practice of singular value decomposition (SVD) reduction in robust PCA. Experiments show the effectiveness and, efficiency of ROC-PCA in both synthetic and real data. Supplementary materials for this article are available online.