Decentralized Singular Value Decomposition for Large-scale Distributed Sensor Networks

This article studies the problem of decentralized Singular Value Decomposition (d-SVD), which is fundamental in various signal processing applications. Two scenarios are considered depending on the availability of the data matrix under consideration. In the first scenario, the matrix of interest is row-wisely available in each local node in the network. In the second scenario, the matrix of interest implicitly forms an outer product from two different series of measurements. By combining the lightweight local rational function approximation approach with parallel averaging consensus algorithms, two d-SVD algorithms are proposed to cope with the two aforementioned scenarios. We evaluate the proposed algorithms using two application examples: decentralized sensor localization via low-rank matrix completion and decentralized passive radar detection. Moreover, a novel and non-trivial truncation technique, which employs a representative vector that is orthonormal to the principal signal subspace, is proposed to further reduce the communication cost associated with the d-SVD algorithms. Simulation results show that the proposed d-SVD algorithms converge to the centralized solution with reduced communication cost compared to those facilitated with the state-of-the-art decentralized power method.