# Mean-Shift PCA by Knockoff Mean

arXiv: https://arxiv.org/abs/2605.25460 · HTML: https://mlsanity.com/paper/2605.25460/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 25 May 2026.

## Builds on (most cited first, 8 of 8)

- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [Non-convex Robust PCA](https://mlsanity.com/paper/1410.7660/) (2014)
- [Robust Sub-Gaussian Principal Component Analysis and Width-Independent Schatten Packing](https://mlsanity.com/paper/2006.06980/) (2020)
- [Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection](https://mlsanity.com/paper/2110.05649/) (2021)
- [Accelerated Alternating Projections for Robust Principal Component Analysis](https://mlsanity.com/paper/1711.05519/) (2017)
- [Optimal Algorithms for L1-subspace Signal Processing](https://mlsanity.com/paper/1405.6785/) (2014)
- [Efficient L1-Norm Principal-Component Analysis via Bit Flipping](https://mlsanity.com/paper/1610.01959/) (2016)
- [Robust Principal Component Analysis: A Median of Means Approach](https://mlsanity.com/paper/2102.03403/) (2021)

## Abstract (arXiv)

Removing noise is difficult, but adding noise is easy. In this work, we show how to eliminate mean-shift noisy components from PCA by deliberately introducing knockoff mean-shift perturbation. Standard PCA is highly sensitive to shifts in the sample mean: a small fraction of samples from a shifted distribution can cause large deviations in the leading principal components. In high-dimensional regimes, existing Robust PCA approaches cannot handle the mean-shift contamination structure inherent in the mixture model. Using tools from Random Matrix Theory, we prove that the mean-shift spikes are spectrally separable from the stable eigenvalues of the original covariance. Furthermore, the original eigenspace remains asymptotically invariant to the contamination, independent of the mixture weight. Exploiting this spectral stability, we propose a simple, two-stage PCA algorithm by adding knockoff mean that identifies and removes the mean-shift component using only standard PCA operations.