Distributed MAXVAR: Identifying Common Signal Components across the Nodes of a Sensor Network

A wireless sensor network (WSN) consists of a collection of sensor nodes, which are equipped with processing and wireless communication facilities to share data between each other. In some WSN applications, it would be relevant for each node to identify which signal components it shares with other nodes in the network. However, this is hard to realize in a distributed context, in particular between node pairs that do not share a direct wireless link. In this paper, we introduce a distributed algorithm for estimating the signal subspace that (on average) is closest to the pairwise intersections between any two of the per-node sensor signal subspaces. In order to facilitate an efficient data fusion, we assume the WSN has (or can be pruned to) a tree-topology. As opposed to a centralized algorithm where all the sensor signals are transmitted to a fusion center (FC), the per-node bandwidth and processing requirements are independent of the network-size and only depend on the number of neighbors per node and a chosen compression parameter. By construction, our algorithm converges to the solution of the so-called “maximum variance” (MAXVAR) formulation of the generalized canonical correlation anlalysis (GCCA) problem in which observations of every node act as a separate “view” in the GCCA formulation. Therefore, even though our work is formalized within a WSN context, it can be used as a generic distributed MAXVAR algorithm in other application contexts as well.