Distributed algorithms to determine eigenvectors of matrices on spatially distributed networks

Abstract

Eigenvectors of matrices on a network have been used for understanding influence of a vertex and spectral clustering. For matrices with small geodesic-width and their given eigenvalues, we propose preconditioned gradient descent algorithms in this paper to find eigenvectors. We also consider synchronous implementation of the proposed algorithms at vertex/agent level in a spatially distributed network in which each agent has limited data processing capability and confined communication range.