Distributed principal components analysis in sensor networks

Estimation of the principal eigenspace of a data covariance matrix is instrumental in applications such as data dimensionality reduction and denoising. In sensor networks the acquired data are spatially scattered which further calls for the development of distributed principal subspace estimation algorithms. 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 inter-sensor communications and allow sensors to estimate the principal covariance eigenspace in a distributed fashion. Adaptive implementations are also considered that allow online information processing. Numerical tests demonstrate that the novel algorithm has the potential to achieve a considerably faster convergence rate and better steady-state estimation performance compared to existing alternatives.