Efficient Robust Graph Learning Based on Minimax Concave Penalty and ?-Cross Entropy

This paper presents an efficient robust method to learn sparse graphs from contaminated data. Specifically, the convex-analytic approach using the minimax concave penalty is formulated using the so-called ?-lasso which exploits the ?-cross entropy. We devise a weighting technique which designs the data weights based on the l₁ distance in addition to the Mahalanobis distance for avoiding possible failures of outlier rejection due to the combinatorial graph Laplacian structure. Numerical examples show that the proposed method significantly outperforms ?-lasso and t-lasso as well as the existing non-robust graph learning methods in contaminated situations.