Topology identification of undirected consensus networks via sparse inverse covariance estimation

We study the problem of identifying sparse interaction topology using sample covariance matrix of the state of the network. Specifically, we assume that the statistics are generated by a stochastically-forced undirected first-order consensus network with unknown topology. We propose a method for identifying the topology using a regularized Gaussian maximum likelihood framework where the ℓ
₁
regularizer is introduced as a means for inducing sparse network topology. The proposed algorithm employs a sequential quadratic approximation in which the Newton's direction is obtained using coordinate descent method. We provide several examples to demonstrate good practical performance of the method.