Paper Info
Title
Reconstruction-Cognizant Graph Sampling Using Gershgorin Disc Alignment
Abstract
Graph sampling with noise is a fundamental problem in graph signal processing (GSP). Previous works assume an unbiased least square (LS) signal reconstruction scheme and select samples greedily via expensive extreme eigenvector computation. A popular biased scheme using graph Laplacian regularization (GLR) solves a system of linear equations for its reconstruction. Assuming this GLR-based scheme, we propose a reconstruction-cognizant sampling strategy to maximize the numerical stability of the linear system i.e., minimize the condition number of the coefficient matrix. Specifically, we maximize the eigenvalue lower bounds of the matrix, represented by left-ends of Gershgorin discs of the coefficient matrix. To accomplish this efficiently, we propose an iterative algorithm to traverse the graph nodes via Breadth First Search (BFS) and align the left-ends of all corresponding Gershgorin discs at lower-bound threshold T using two basic operations: disc shifting and scaling. We then perform binary search to maximize T given a sample budget K. Experiments on real graph data show that the proposed algorithm can effectively promote large eigenvalue lower bounds, and the reconstruction MSE is the same or smaller than existing sampling methods for different budget K at much lower complexity.
Year
Venue
Keywords
2019
2019 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP)
Graph sampling, graph Laplacian regularization, Gershgorin circle theorem
Field
DocType
ISSN
Laplacian matrix,Mathematical optimization,Coefficient matrix,Matrix (mathematics),Computer science,Breadth-first search,Gershgorin circle theorem,Sampling (statistics),Signal reconstruction,Eigenvalues and eigenvectors
Conference
1520-6149
Citations 
PageRank 
References 
0
0.34
14
Authors
5
Name
Order
Citations
PageRank
Yuanchao Bai1344.36
Gene Cheung Connie Chan21387121.82
Fen Wang3107.29
Xianming Liu446147.55
Wen Gao511374741.77