Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information
Abstract
:1. Introduction
1.1. Identifying the Structure of Network Diffusion Processes
1.2. Technical Approach and Paper Outline
1.3. Contributions in Context of Prior Related Work
1.4. Notational Conventions
2. Materials and Methods
2.1. Identifying Graph Topologies from Observations of Stationary Graph Signals
2.1.1. Revisiting Stationarity for Graph Learning
2.1.2. Size of the Feasible Set
2.1.3. Proximal Gradient Algorithm for Batch Topology Identification
Algorithm 1 Proximal gradient (PG) for batch topology identification. |
Require:, . 1: Initialize as a sparse, random symmetric matrix, , . 2: while not converged do 3: Compute . 4: Take gradient descent step . 5: Update via the proximal operator in (12). 6: . 7: end while 8: return. |
2.2. Online Network Topology Inference
2.2.1. Algorithm Construction
Algorithm 2 PG for online topology identification. |
Require:, , . 1: Initialize as a sparse, random symmetric matrix, , . 2: fordo 3: Update and . 4: Compute . 5: Take gradient descent step . 6: Update via the proximal operator in (12). 7: end for 8: return. |
2.2.2. Convergence and Regret Analysis
3. Results
3.1. Facebook Friendship Graph: Batch
Number of observations | ||||
F-measure |
3.2. Zachary’s Karate Club: Online
4. Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A. Proof of Proposition 2
Appendix B. Proof of Theorem 1
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Shafipour, R.; Mateos, G. Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information. Algorithms 2020, 13, 228. https://doi.org/10.3390/a13090228
Shafipour R, Mateos G. Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information. Algorithms. 2020; 13(9):228. https://doi.org/10.3390/a13090228
Chicago/Turabian StyleShafipour, Rasoul, and Gonzalo Mateos. 2020. "Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information" Algorithms 13, no. 9: 228. https://doi.org/10.3390/a13090228
APA StyleShafipour, R., & Mateos, G. (2020). Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information. Algorithms, 13(9), 228. https://doi.org/10.3390/a13090228