| Paper ID | SPTM-16.5 |
| Paper Title |
A Graph Learning Algorithm Based on Gaussian Markov Random Fields and Minimax Concave Penalty |
| Authors |
Tatsuya Koyakumaru, Masahiro Yukawa, Keio University, Japan; Eduardo Pavez, Antonio Ortega, University of Southern California, United States |
| Session | SPTM-16: Graph Topology Inference |
| Location | Gather.Town |
| Session Time: | Thursday, 10 June, 14:00 - 14:45 |
| Presentation Time: | Thursday, 10 June, 14:00 - 14:45 |
| Presentation |
Poster
|
| Topic |
Signal Processing Theory and Methods: [SIPG] Signal and Information Processing over Graphs |
| IEEE Xplore Open Preview |
Click here to view in IEEE Xplore |
| Virtual Presentation |
Click here to watch in the Virtual Conference |
| Abstract |
This paper presents a graph learning framework to produce sparse and accurate graphs from network data. While our formulation is inspired by the graphical lasso, a key difference is the use of a nonconvex alternative of the $\ell_1$ norm as well as a quadratic term to ensure overall convexity. Specifically, the weakly-convex minimax concave penalty (MCP) is used, which is given by subtracting the Huber function from the $\ell_1$ norm, inducing a less-biased sparse solution than $\ell_1$. In our framework, the graph Laplacian is represented by a linear transform of the vector corresponding to its upper triangular part. Via a reformulation relying on the Moreau decomposition, the problem can be solved by the primal-dual splitting method. An admissible choice of parameters for provable convergence is presented. Numerical examples show that the proposed method significantly outperforms its $\ell_1$-based counterpart for sparse grid graphs. |
