Distributed Trace Ratio Optimization in Fully-Connected Sensor Networks

Abstract

The trace ratio optimization problem consists of maximizing a ratio between two trace operators and often appears in dimensionality reduction problems for denoising or discriminant analysis. In this paper, we propose a distributed and adaptive algorithm to solve the trace ratio optimization problem over network-wide covariance matrices, which capture the spatial correlation across sensors in a wireless sensor network. We focus on fully-connected network topologies, in which case the distributed algorithm reduces the communication bottleneck by only sharing a compressed version of the observed signals at each given node. Despite this compression, the algorithm can be shown to converge to the maximal trace ratio as if all nodes would have access to all signals in the network. We provide simulation results to demonstrate the convergence and optimality properties of the proposed algorithm.