Graph Learning from Data under Structural and Laplacian Constraints

Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i) formulation of various graph learning problems, (ii) their probabilistic interpretations and (iii) efficient algorithms to solve them. We specifically focus on graph learning problems where the goal is to estimate a graph Laplacian matrix from some observed data under given structural constraints (e.g., graph connectivity and sparsity). Our experimental results demonstrate that the proposed algorithms outperform the current state-of-the-art methods in terms of graph learning performance.