A distributed EM algorithm to estimate the parameters of a finite mixture of components

In this paper, a distributed expectation maximization (DEM) algorithm is first introduced in a general form for estimating the parameters of a finite mixture of components. This algorithm is used for density estimation and clustering of data distributed over nodes of a network. Then, a distributed incremental EM algorithm (DIEM) with a higher convergence rate is proposed. After a full derivation of distributed EM algorithms, convergence of these algorithms is analyzed based on the negative free energy concept used in statistical physics. An analytical approach is also developed for evaluating the convergence rate of both incremental and distributed incremental EM algorithms. It is analytically shown that the convergence rate of DIEM is much faster than that of the DEM algorithm. Finally, simulation results approve that DIEM remarkably outperforms DEM for both synthetic and real data sets.