Learning Graph Laplacian with MCP
This work addresses graph learning for sparsity promotion, which is incremental as it applies a non-convex penalty to an existing framework.
The paper tackles the problem of learning a graph under Laplacian constraints using the minimax concave penalty (MCP) to promote sparsity, and it demonstrates that their method is more efficient and reliable than existing state-of-the-art approaches.
We consider the problem of learning a graph under the Laplacian constraint with a non-convex penalty: minimax concave penalty (MCP). For solving the MCP penalized graphical model, we design an inexact proximal difference-of-convex algorithm (DCA) and prove its convergence to critical points. We note that each subproblem of the proximal DCA enjoys the nice property that the objective function in its dual problem is continuously differentiable with a semismooth gradient. Therefore, we apply an efficient semismooth Newton method to subproblems of the proximal DCA. Numerical experiments on various synthetic and real data sets demonstrate the effectiveness of the non-convex penalty MCP in promoting sparsity. Compared with the existing state-of-the-art method, our method is demonstrated to be more efficient and reliable for learning graph Laplacian with MCP.