Robust Method for Network Topology Identification Under Structural Equation Model

We present a robust method to infer network topology in the presence of outliers from given observations at nodes under the structural equation model. We introduce auxiliary matrices modeling Gaussian noise and sparse outliers. The topology identification task is cast as a minimization problem of the sum of three terms under constraints involving a bilinear form: (i) the squared Frobenius norm of the noise matrix, (ii) the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{1}$</tex> norm of the adjacency matrix, and (iii) a weakly-convex sparsity-promoting function (the minimax concave penalty) of the outlier matrix. The problem is reformulated into an unconstrained optimization problem by introducing a linear operator, and an efficient alternating minimization method is presented. Simulation results show remarkable robustness of the proposed method.