Scale-Calibrated Median-of-Means for Robust Distributed Principal Component Analysis

ArXi:2605.20681v1 Announce Type: cross Distributed principal component analysis (PCA) produces node-level estimates of both a mean vector and a principal subspace. Robustly aggregating these heterogeneous objects requires a relative scale between mean error and subspace error. We study a scale-calibrated median-of-means estimator for this problem using the product geometry of Euclidean space and the Grassmann manifold. A node-level PCA expansion shows that the mean component has the usual linear influence, whereas the subspace component is an eigengap-weighted covariance perturbation.