Seeking Consensus on Subspaces in Federated Principal Component Analysis

Understand

In this paper, we develop an algorithm for federated principal component analysis (PCA) with emphases on both communication efficiency and data privacy.

• Generally speaking, federated PCA algorithms based on direct adaptations of classic iterative methods, such as simultaneous subspace iterations (SSI), are unable to preserve data privacy, while algorithms based on variable-splitting and consensus-seeking, such as alternating direction methods of multipliers (ADMM), lack in communication-efficiency.
• In this work, we propose a novel consensus-seeking formulation by equalizing subspaces spanned by splitting variables instead of equalizing variables themselves, thus greatly relaxing feasibility restrictions and allowing much faster convergence.
• Then we develop an ADMM-like algorithm with several special features to make it practically efficient, including a low-rank multiplier formula and techniques for treating subproblems.