Modeling and estimating mixed memberships in weighted networks

We consider the problem of detecting latent community information of mixed membership weighted network in which nodes have mixed memberships and edges connecting between nodes can be finite real numbers. We propose a general mixed membership distribution-free model for this problem. The model has no distribution constraints of edges but only the expected values, and can be viewed as generalizations of some previous models. We use an efficient spectral algorithm to estimate community memberships under the model. We also derive the convergence rate of the proposed algorithm under the model using spectral analysis. We demonstrate the advantages of mixed membership distribution-free model and the algorithm with applications to a small scale of simulated networks when edges follow different distributions. We have also applied the algorithm to five real world weighted network data sets with encouraging results.