Fast Distributed Subspace Projection via Graph Filters

A significant number of linear inference problems in wireless sensor networks can be solved by projecting the observed signal onto a given subspace. Decentralized approaches avoid the need for performing such an operation at a central processor, thereby reducing congestion and increasing the robustness and the scalability of the network. Unfortunately, existing decentralized approaches either confine themselves to a reduced family of subspace projection tasks or need an infinite number of iterations to obtain the exact projection. To remedy these limitations, this paper develops a framework for computing a wide class of subspace projections in a decentralized fashion by relying on the notion of graph filtering. To this end, a methodology to obtain the shift matrix and the corresponding filter coefficients that provide exact subspace projection in a nearly minimal number of iterations is proposed. Numerical experiments corroborate the merits of the proposed approach.