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Inhomogeneous graph trend filtering via A ℓ2,0-norm cardinality penalty

Inhomogeneous graph trend filtering via A ℓ2,0-norm cardinality penalty
Inhomogeneous graph trend filtering via A ℓ2,0-norm cardinality penalty
We study estimation of piecewise smooth signals over a graph. We propose a ℓ2,0-norm penalized Graph Trend Filtering (GTF) model to estimate piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness across the nodes. We prove that the proposed GTF model is simultaneously a k-means clustering on the signal over the nodes and a minimum graph cut on the edges of the graph, where the clustering and the cut share the same assignment matrix. We propose two methods to solve the proposed GTF model: a spectral decomposition method and a method based on simulated annealing. In the experiment on synthetic and real-world datasets, we show that the proposed GTF model has a better performances compared with existing approaches on the tasks of denoising, support recovery and semi-supervised classification. We also show that the proposed GTF model can be solved more efficiently than existing models for the dataset with a large edge set.
graph signal processing, graph trend filtering, ℓ2,0- norm, spectral method, simulated annealing
2373-776X
Huang, Xiaoqing
9e7d79f2-1ccb-40db-ae87-b6a1f95acc0a
Ang, Andersen
ed509ecd-39a3-4887-a709-339fdaded867
Huang, Kun
b0602d21-21b8-4e73-a942-2d7a8f96caf6
Zhang, Jie
9a34f4bd-0ae3-4538-bcb1-63e8e7c2a94f
Wang, Yijie
1b315708-7a8b-49c4-bd95-b4f534b492f1
Huang, Xiaoqing
9e7d79f2-1ccb-40db-ae87-b6a1f95acc0a
Ang, Andersen
ed509ecd-39a3-4887-a709-339fdaded867
Huang, Kun
b0602d21-21b8-4e73-a942-2d7a8f96caf6
Zhang, Jie
9a34f4bd-0ae3-4538-bcb1-63e8e7c2a94f
Wang, Yijie
1b315708-7a8b-49c4-bd95-b4f534b492f1

Huang, Xiaoqing, Ang, Andersen, Huang, Kun, Zhang, Jie and Wang, Yijie (2025) Inhomogeneous graph trend filtering via A ℓ2,0-norm cardinality penalty. IEEE Transactions on Signal and Information Processing over Networks, 11. (doi:10.1109/TSIPN.2025.355302).

Record type: Article

Abstract

We study estimation of piecewise smooth signals over a graph. We propose a ℓ2,0-norm penalized Graph Trend Filtering (GTF) model to estimate piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness across the nodes. We prove that the proposed GTF model is simultaneously a k-means clustering on the signal over the nodes and a minimum graph cut on the edges of the graph, where the clustering and the cut share the same assignment matrix. We propose two methods to solve the proposed GTF model: a spectral decomposition method and a method based on simulated annealing. In the experiment on synthetic and real-world datasets, we show that the proposed GTF model has a better performances compared with existing approaches on the tasks of denoising, support recovery and semi-supervised classification. We also show that the proposed GTF model can be solved more efficiently than existing models for the dataset with a large edge set.

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2304.05223v4 - Accepted Manuscript
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Accepted/In Press date: 5 March 2025
e-pub ahead of print date: 21 March 2025
Keywords: graph signal processing, graph trend filtering, ℓ2,0- norm, spectral method, simulated annealing

Identifiers

Local EPrints ID: 500375
URI: http://eprints.soton.ac.uk/id/eprint/500375
ISSN: 2373-776X
PURE UUID: b8923a67-d002-4218-8dea-73d93f4f4e26
ORCID for Andersen Ang: ORCID iD orcid.org/0000-0002-8330-758X

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Date deposited: 28 Apr 2025 16:46
Last modified: 22 Aug 2025 02:38

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Contributors

Author: Xiaoqing Huang
Author: Andersen Ang ORCID iD
Author: Kun Huang
Author: Jie Zhang
Author: Yijie Wang

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