Graph Learning with Laplacian Constraints: Modeling Attractive Gaussian Markov Random Fields

Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. This paper proposes a novel framework for learning graphs from data. The proposed framework (i) poses the graph learning problem as estimation of generalized graph Laplacian matrices and (ii) develops an efficient algorithm. Under specific statistical assumptions, the proposed formulation leads to modeling attractive Gaussian Markov random fields. Our experimental results show that the proposed algorithm outperforms sparse inverse covariance estimation methods in terms of graph learning performance.