# Robust Orthogonal Complement Principal Component Analysis

arXiv: https://arxiv.org/abs/1410.1173 · HTML: https://mlsanity.com/paper/1410.1173/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2014.

## Built on by (most cited first, 3 of 3)

- [Robust SVD Made Easy: A fast and reliable algorithm for large-scale data analysis](https://mlsanity.com/paper/2402.09754/) (2024)
- [Robust factored principal component analysis for matrix-valued outlier accommodation and detection](https://mlsanity.com/paper/2112.06760/) (2021)
- [Robust bilinear factor analysis based on the matrix-variate t distribution](https://mlsanity.com/paper/2401.02203/) (2024)

## Abstract (arXiv)

Recently, the robustification of principal component analysis 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 non-asymptotic 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 paper also points out a pitfall of a common practice of SVD reduction in robust PCA. Experiments show the effectiveness and efficiency of ROC-PCA in both synthetic and real data.