Decentralized Subspace Projection for Asymmetric Sensor Networks

A large number of applications in Wireless Sensor Networks include projecting a vector of noisy observations onto a subspace dictated by prior information about the field being monitored. In general, accomplishing such a task in a centralized fashion, entails a large power consumption, congestion at certain nodes and suffers from robustness issues against possible node failures. Computing such projections in a decentralized fashion is an alternative solution that solves these issues. Recent works have shown that this task can be done via the so-called graph filters where only local inter-node communication is performed in a distributed manner using a graph shift operator. Most of the existing methods have focused on the design of graph filters for symmetric topologies to compute an exact subspace projection. However, in this paper, motivated by the asymmetric communications in Wireless Sensor Networks, we analyze the design of graph shift operators to perform decentralized subspace projection for asymmetric topologies. we first characterize the existence of solutions and then we present a convex optimization problem that considers also the efficiency of the graph filtering, with an ADMM-based solver.