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 | ||
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. |