2021 IEEE International Conference on Acoustics, Speech and Signal Processing

6-11 June 2021 • Toronto, Ontario, Canada

Extracting Knowledge from Information

2021 IEEE International Conference on Acoustics, Speech and Signal Processing

6-11 June 2021 • Toronto, Ontario, Canada

Extracting Knowledge from Information
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Paper Detail

Paper IDSPTM-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
SessionSPTM-16: Graph Topology Inference
LocationGather.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.