One-Shot Distributed Generalized Eigenvalue Problem (DGEP): Concept, Algorithm and Experiments

Abstract

This paper focuses on the design of a distributed algorithm for generalized eigenvalue problems (GEPs) in one-shot communication. Since existing distributed methods for eigenvalue decomposition cannot be applied to GEP, a general one-shot distributed GEP framework is proposed. The theoretical analysis of the approximation error reveals its relation to the divergence of the data covariance, the eigenvalues of the empirical data covariance, and the number of local servers. If the symmetric data covariance has repeated eigenvalues in GEP, e.g., in canonical component analysis, we further modify the method for better convergence and prove the necessity experimentally. Numerical experiments validate the effectiveness of the proposed algorithms both on synthetic and real-world datasets.