Robust PCA in High-dimension: A Deterministic Approach
This work addresses robust PCA for high-dimensional data, offering a deterministic method with strong theoretical guarantees and practical speed-ups, though it is incremental as it builds on existing randomized approaches.
The authors tackled robust principal component analysis for contaminated high-dimensional data by proposing a deterministic algorithm that achieves a 50% breakdown point and significantly improves computational efficiency for large-scale applications.
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.