Joint learning of graph processes and graph topologies for time vertex signal estimation

Date

2024-8-28

Author

Yaldız, Berkay

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

111
views

217
downloads

Cite This

In recent years, the analysis of data that evolves over time and across interconnected entities has gained significant interest. Such data, often represented as time-vertex graph signals, encapsulate the dynamic nature of various real-world systems, including social networks, sensor networks, and traffic systems. Traditional methods that separately handle temporal and network dependencies without considering network correctness often fall short in capturing the full complexity of these datasets. To address this, in this thesis, we use a parametric statistical modelling approach called Auto-Regressive Moving Average (ARMA) jointly wide sense stationarity in order to analyze the joint time-vertex behavior of time-varying graph random processes, while we also aim to improve the partially known network topology via the graph Laplacian. We explore ARMA graph process models, where our primary objective is to develop a comprehensive framework that integrates ARMA modeling with graph learning techniques to enhance the analysis of time-varying signals characterized by both temporal and network dependencies. Our study introduces a novel approach where the joint power spectral density derived from the graph ARMA model is used to estimate the covariance matrix of the process. This matrix provides a basis for our graph learning algorithm, which iteratively refines both the joint process and the graph Laplacian. By integrating the dynamic characteristics of ARMA models with graph learning techniques, the proposed method facilitates the discovery of underlying structures and relationships within time-varying graph signals. Simulations and real-world experiments are conducted to validate the effectiveness of the framework, demonstrating its potential for time-vertex signal analysis. The results indicate improvements in capturing spatiotemporal dependencies for network data with a time-varying structure.

Subject Keywords

Graph signal processing, Time-vertex signal processing, Stationary graph signal processing, Graph laplacian matrix learning, Spatiotemporal signal processing

URI

https://hdl.handle.net/11511/111536

Collections

Graduate School of Natural and Applied Sciences, Thesis