Unsupervised distributed estimation of Gaussian mixtures in sensor networks

This paper presents a new unsupervised distributed Expectation-Maximization (EM) algorithm for estimating parameters of Gaussian mixture models in sensor networks. Using the proposed algorithm, a challenging problem is solved: selection of the proper number of components. The algorithm starts with a large number of initialized components. In the E-step of this algorithm, each sensor node calculates local sufficient statistics and also a new quantity which will be used to determine irrelevant components. In the next step a Peer-to-Peer algorithm is used to diffuse local sufficient statistics to neighboring nodes and estimate global sufficient statistics in each node. In the M-step, using the value calculated in the E-step, irrelevant components are determined and discarded. Then the remaining components´ parameters are estimated using global sufficient statistics. The new distributed unsupervised algorithm is robust and scalable. It estimates the parameters of mixtures and simultaneously selects the number of components. Simulation results show good performance of the proposed method.