Distributed density estimation in sensor networks based on variational approximations

Abstract

This article presents a peer-to-peer (P2P) distributed variational Bayesian (P2PDVB) algorithm for density estimation and clustering in sensor networks. It is assumed that measurements of the nodes can be statistically modelled by a common Gaussian mixture model. The variational approach allows the simultaneous estimate of the component parameters and the model complexity. In this algorithm, each node independently calculates local sufficient statistics first by using local observations. A P2P averaging approach is then used to diffuse local sufficient statistics to neighbours and estimate global sufficient statistics in each node. Finally, each sensor node uses the estimated global sufficient statistics to estimate the model order as well as the parameters of this model. Because the P2P averaging approach only requires that each node communicate with its neighbours, the P2PDVB algorithm is scalable and robust. Diffusion speed and convergence of the proposed algorithm are also studied. Finally, simulated and real data sets are used to verify the remarkable performance of proposed algorithm.