A1843
Title: Mean-shift PCA by knockoff mean
Authors: Zeng Li - Southern University of Science and Technology (China) [presenting]
Abstract: Removing noise is difficult, but adding noise is easy. The aim is to 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 models. Using tools from Random Matrix Theory, it is proven 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, a simple, two-stage PCA algorithm is proposed by adding knockoff mean that identifies and removes the mean-shift component using only standard PCA operations.
