Distributed EM algorithms for density estimation in sensor networks

The paper considers the problem of density estimation and clustering in distributed sensor networks. It is assumed that each node in the network senses an environment that can be described as a mixture of some elementary conditions. The measurements are thus statistically modeled with a mixture of Gaussians, each Gaussian component corresponding to one of the elementary conditions. A distributed EM algorithm is developed for estimating the Gaussian components, which are common to the environment and sensor network as a whole, as well as the mixing probabilities which may vary from node to node. The algorithm produces an estimate (in terms of a Gaussian mixture approximation) of the density of the sensor data without requiring the data to be transmitted to and processed at a central location. Alternatively, the algorithm can be viewed as a distributed processing strategy for clustering the sensor data into components corresponding to predominant environmental features sensed by the network. The convergence of the distributed EM algorithm is discussed, and simulations demonstrate the potential of this approach to sensor network data analysis.