Foundations and Trends® in Signal Processing > Vol 17 > Issue 3

Generalizing Graph Signal Processing: High Dimensional Spaces, Models and Structures

By Xingchao Jian, Nanyang Technological University, Singapore, XINGCHAO001@e.ntu.edu.sg | Feng Ji, Nanyang Technological University, Singapore, jifeng@ntu.edu.sg | Wee Peng Tay, Nanyang Technological University, Singapore, wptay@ntu.edu.sg

 
Suggested Citation
Xingchao Jian, Feng Ji and Wee Peng Tay (2023), "Generalizing Graph Signal Processing: High Dimensional Spaces, Models and Structures", Foundations and TrendsĀ® in Signal Processing: Vol. 17: No. 3, pp 209-290. http://dx.doi.org/10.1561/2000000119

Publication Date: 06 Mar 2023
© 2023 X. Jian et al.
 
Subjects
Statistical signal processing,  Statistical signal processing: Estimation and regression,  Signal reconstruction,  Sampling,  Subband and transform methods,  Signal decompositions,  Linear and nonlinear filtering,  Distributed and network signal processing
 

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In this article:
1. Introduction
2. GSP Basics
3. High Dimensional Signal Spaces
4. Statistical Models Dealing with Uncertainty
5. High Dimensionality in Graph Structures and Topological Models
6. Conclusion and Future Work
Acknowledgements
References

Abstract

Graph signal processing (GSP) has seen rapid developments in recent years. Since its introduction around ten years ago, we have seen numerous new ideas and practical applications related to the field. In this tutorial, we give an overview of some recent advances in generalizing GSP, with a focus on the extension to high-dimensional spaces, models, and structures. Alongside new frameworks proposed to tackle such problems, many new mathematical tools are being introduced. In the first part of the monograph, we will review traditional GSP, highlight the challenges it faces, and motivate efforts in overcoming such challenges, which will be the theme of the rest of the monograph.

DOI:10.1561/2000000119
ISBN: 978-1-63828-150-4
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ISBN: 978-1-63828-151-1
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Table of contents:
1. Introduction
2. GSP Basics
3. High Dimensional Signal Spaces
4. Statistical Models Dealing with Uncertainty
5. High Dimensionality in Graph Structures and Topological Models
6. Conclusion and Future Work
Acknowledgements
References

Generalizing Graph Signal Processing: High Dimensional Spaces, Models and Structures

In modern data analysis, massive measurements from a network require novel signal processing techniques, which are expected to be adapted to the network topology, have distributed implementation, and are flexible enough for various applications. Graph signal processing (GSP) theories and techniques are geared towards these goals.

GSP has seen rapid developments in recent years. Since its introduction around ten years ago, we have seen numerous new ideas and practical applications related to the field. In this tutorial, an overview of recent advances in generalizing GSP is presented, with a focus on the extension to high-dimensional spaces, models, and structures. Alongside new frameworks proposed to tackle such problems, many new mathematical tools are introduced.

In the first part of the monograph, traditional GSP is reviewed, challenges that it faces are highlighted, and efforts in overcoming such challenges are motivated. These efforts then become the theme for the rest of the publication. Included are the generalization of GSP to high dimensional vertex signal spaces, the theory of random shift operators and the wide-sense stationary (WSS) statistical signal models, and the treatment of high dimensionality in graph structures and generalized graph-like structures. The monograph concludes with an outline of possible future directions.

 
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