Topology identification via growing a Chow-Liu tree network

We study the problem of sparse interaction topology identification using sample covariance matrix of the states of the network. We postulate that the statistics are generated by a stochastically-forced undirected consensus network with unknown topology in which some of the nodes may have access to their own states. We first propose a method for topology identification using a regularized Gaussian maximum likelihood framework where the l(1) regularizer is introduced as a means for inducing sparse network topology. We also develop a method based on growing a Chow-Liu tree that is well-suited for identifying the underlying structure of large-scale systems. We apply this technique to resting-state functional MRI (FMRI) data as well as synthetic datasets to illustrate the effectiveness of the proposed approach.