Robust Orthogonal Complement Principal Component Analysis

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

11 Scopus Citations
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Original languageEnglish
Pages (from-to)763-771
Journal / PublicationJournal of the American Statistical Association
Issue number514
Publication statusPublished - 2 Apr 2016
Externally publishedYes


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 subspace 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-wise 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.

Research Area(s)

  • Low-rank approximation, Manifold optimization, Oracle inequalities, Outliers, Sparsity

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Citation Format(s)

Robust Orthogonal Complement Principal Component Analysis. / She, Yiyuan; Li, Shijie; Wu, Dapeng.
In: Journal of the American Statistical Association, Vol. 111, No. 514, 02.04.2016, p. 763-771.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review