Modeling sparse graph sequences and signals using generalized graphons
Graphons are limit objects of sequences of graphs and are used to analyze the behavior of large graphs. Recently, graphon signal processing has been developed to study signal processing on large graphs. A major limitation of this approach is that any sparse sequence of graphs inevitably converges to...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2025
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| Online Access: | https://hdl.handle.net/10356/182368 |
| _version_ | 1826119649896431616 |
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| author | Ji, Feng Jian, Xingchao Tay, Wee Peng |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Ji, Feng Jian, Xingchao Tay, Wee Peng |
| author_sort | Ji, Feng |
| collection | NTU |
| description | Graphons are limit objects of sequences of graphs and are used to analyze the behavior of large graphs. Recently, graphon signal processing has been developed to study signal processing on large graphs. A major limitation of this approach is that any sparse sequence of graphs inevitably converges to the zero graphon, rendering the resulting signal processing theory trivial and inadequate for sparse graph sequences. To overcome this limitation, we propose a new signal processing framework that leverages the concept of generalized graphons and introduces the stretched cut distance as a measure to compare these graphons. Our framework focuses on the sampling of graph sequences from generalized graphons and explores the convergence properties of associated operators, spectra, and signals. Our signal processing framework provides a comprehensive approach to analyzing and processing signals on graph sequences, even if they are sparse. Finally, we discuss the practical implications of our theory for real-world large networks through numerical experiments. |
| first_indexed | 2025-03-09T12:30:08Z |
| format | Journal Article |
| id | ntu-10356/182368 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-03-09T12:30:08Z |
| publishDate | 2025 |
| record_format | dspace |
| spelling | ntu-10356/1823682025-01-27T02:38:57Z Modeling sparse graph sequences and signals using generalized graphons Ji, Feng Jian, Xingchao Tay, Wee Peng School of Electrical and Electronic Engineering Engineering Sparse graph sequence Signal processing of generalized graphons Graphons are limit objects of sequences of graphs and are used to analyze the behavior of large graphs. Recently, graphon signal processing has been developed to study signal processing on large graphs. A major limitation of this approach is that any sparse sequence of graphs inevitably converges to the zero graphon, rendering the resulting signal processing theory trivial and inadequate for sparse graph sequences. To overcome this limitation, we propose a new signal processing framework that leverages the concept of generalized graphons and introduces the stretched cut distance as a measure to compare these graphons. Our framework focuses on the sampling of graph sequences from generalized graphons and explores the convergence properties of associated operators, spectra, and signals. Our signal processing framework provides a comprehensive approach to analyzing and processing signals on graph sequences, even if they are sparse. Finally, we discuss the practical implications of our theory for real-world large networks through numerical experiments. Info-communications Media Development Authority (IMDA) Ministry of Education (MOE) National Research Foundation (NRF) This research was supported in part by Singapore Ministry of Education Academic Research Fund Tier 2 under Grant MOE-T2EP20220-0002, and in part by the National Research Foundation, Singapore and Infocomm Media Development Authority under its Future Communications Research and Development Programme. 2025-01-27T02:38:57Z 2025-01-27T02:38:57Z 2024 Journal Article Ji, F., Jian, X. & Tay, W. P. (2024). Modeling sparse graph sequences and signals using generalized graphons. IEEE Transactions On Signal Processing, 72, 5048-5064. https://dx.doi.org/10.1109/TSP.2024.3482350 1053-587X https://hdl.handle.net/10356/182368 10.1109/TSP.2024.3482350 2-s2.0-85207398980 72 5048 5064 en MOE-T2EP20220-0002 IEEE Transactions on Signal Processing © 2024 IEEE. All rights reserved. |
| spellingShingle | Engineering Sparse graph sequence Signal processing of generalized graphons Ji, Feng Jian, Xingchao Tay, Wee Peng Modeling sparse graph sequences and signals using generalized graphons |
| title | Modeling sparse graph sequences and signals using generalized graphons |
| title_full | Modeling sparse graph sequences and signals using generalized graphons |
| title_fullStr | Modeling sparse graph sequences and signals using generalized graphons |
| title_full_unstemmed | Modeling sparse graph sequences and signals using generalized graphons |
| title_short | Modeling sparse graph sequences and signals using generalized graphons |
| title_sort | modeling sparse graph sequences and signals using generalized graphons |
| topic | Engineering Sparse graph sequence Signal processing of generalized graphons |
| url | https://hdl.handle.net/10356/182368 |
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