Distributed EM Algorithm for Gaussian Mixtures in Sensor Networks

This paper presents a distributed expectation-maximization (EM) algorithm over sensor networks. In the E-step of this algorithm, each sensor node independently calculates local sufficient statistics by using local observations. A consensus filter is used to diffuse local sufficient statistics to neighbors and estimate global sufficient statistics in each node. By using this consensus filter, each node can gradually diffuse its local information over the entire network and asymptotically the estimate of global sufficient statistics is obtained. In the M-step of this algorithm, each sensor node uses the estimated global sufficient statistics to update model parameters of the Gaussian mixtures, which can maximize the log-likelihood in the same way as in the standard EM algorithm. Because the consensus filter only requires that each node communicate with its neighbors, the distributed EM algorithm is scalable and robust. It is also shown that the distributed EM algorithm is a stochastic approximation to the standard EM algorithm. Thus, it converges to a local maximum of the log-likelihood. Several simulations of sensor networks are given to verify the proposed algorithm.