Distributed Adaptive Trace Ratio Optimization in Wireless Sensor Networks
Cem Ates Musluoglu, Alexander Bertrand · IEEE Transactions on Signal Processing · 2021
The trace ratio optimization (TRO) problem consists of finding an orthonormal basis for the discriminative subspace that maximizes the ratio of two trace operators on two covariance matrices corresponding to two distinctive classes or signal components. The TRO problem is encountered in various signal processing problems such as dimensionality reduction, signal enhancement, and discriminative analysis. In this paper, we propose a distributed and adaptive algorithm for solving the TRO problem in the context of wireless sensor networks (WSNs), where the two matrices involved in the trace ratio operators correspond to the (unknown) spatial correlation of the sensor signals across the nodes in the network. We first focus on fully-connected networks where every node can communicate with each other, but only compressed signals observations can be shared to reduce the communication cost. After showing convergence, we modify the algorithm to operate in WSNs with more general topologies. Simulation results are provided to validate and complement the theoretical results.