Diffusion scheme of distributed EM algorithm for Gaussian mixtures over random networks

This paper presents a distributed EM algorithm for Gaussian mixtures based on diffusion scheme over random sensor networks. In the E-step of this method, sensor nodes compute the local statistics by using local observation data and parameters estimated at last iterative step. A diffusion step is implemented over the time-varying communication networks after E-step. In this step, the communication network is modeled as a random graph, and each node exchanges local information only with its current neighbors. In the M-step, the sensor nodes compute the estimation of parameter using the updated local statistics by the D-step at this iterative step. Compared with the existing distributed EM algorithms, our proposed method can extensively reduce communication for each sensor node while maintains the estimation performance. In addition, we show that the proposed distributed diffusion EM (DDEM) algorithm can be considered as a stochastic approximation method to find the maximum likelihood estimation for Gaussian Mixture. Simulation shows the performance of our method.