Robust PCA in High-dimension: A Deterministic Approach

TL;DR

This paper introduces a deterministic high-dimensional robust PCA algorithm that is computationally efficient, robust to contamination, and theoretically sound, suitable for large-scale applications.

Contribution

It presents a deterministic approach to robust PCA in high dimensions with strong theoretical guarantees and improved computational efficiency over randomized methods.

Findings

Achieves a breakdown point of 50%

Exhibits better computational efficiency

Maintains theoretical robustness properties

Abstract

We consider principal component analysis for contaminated data-set in the high dimensional regime, where the dimensionality of each observation is comparable or even more than the number of observations. We propose a deterministic high-dimensional robust PCA algorithm which inherits all theoretical properties of its randomized counterpart, i.e., it is tractable, robust to contaminated points, easily kernelizable, asymptotic consistent and achieves maximal robustness -- a breakdown point of 50%. More importantly, the proposed method exhibits significantly better computational efficiency, which makes it suitable for large-scale real applications.