A Distributed Framework for Dimensionality Reduction and Denoising

With the recent upsurge in the amount of data transmission and use in networks, a lot of emphasis is placed on designing efficient methods to extract useful information by reducing the size of large data sets. A major approach in data dimensionality reduction relies on the estimation of the principal data covariance eigenspace. In this paper a distributed algorithmic framework is put forth for finding the principal eigenspace of spatially scattered sensor data. Toward this end, the standard principal component analysis framework is reformulated as a separable constrained minimization problem which is solved by utilizing coordinate descent techniques combined with the alternating direction method of multipliers. Computationally simple local updating recursions are obtained that involve only single-hop intersensor communications. The proposed distributed algorithm is shown to be robust even in the presence of inter-sensor communication noise and converge to the principal eigenspace when inter-sensor links are ideal. The proposed distributed framework is used in a data denoising setting, while extensive numerical tests using both synthetic and real data demonstrate a fast convergence rate, better steady-state performance of the novel algorithm over existing alternatives and communication noise resilience.