Seeking Consensus on Subspaces in Federated Principal Component Analysis

Lei Wang (), Xin Liu () and Yin Zhang ()
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Lei Wang: The Hong Kong Polytechnic University
Xin Liu: Chinese Academy of Sciences and University of Chinese Academy of Sciences
Yin Zhang: The Chinese University of Hong Kong

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 1, No 20, 529-561

Abstract: Abstract 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, 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. We establish that the proposed algorithm can better protect data privacy than classic methods adapted to the federated PCA setting. We derive convergence results, including a worst-case complexity estimate, for the proposed ADMM-like algorithm in the presence of the nonlinear equality constraints. Extensive empirical results are presented to show that the new algorithm, while enhancing data privacy, requires far fewer rounds of communication than existing peer algorithms for federated PCA.

Keywords: Alternating direction method of multipliers; Federated learning; Principal component analysis; Orthogonality constraints; 15A18; 65F15; 65K05; 90C06; 90C26 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02523-1

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