Infinite-Horizon Graph Filters: Leveraging Power Series to Enhance Sparse Information Aggregation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913321910796288 |
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| author | Zhang, Ruizhe Jiang, Xinke Fang, Yuchen Luo, Jiayuan Xu, Yongxin Zhu, Yichen Chu, Xu Zhao, Junfeng Wang, Yasha |
| author_facet | Zhang, Ruizhe Jiang, Xinke Fang, Yuchen Luo, Jiayuan Xu, Yongxin Zhu, Yichen Chu, Xu Zhao, Junfeng Wang, Yasha |
| contents | Graph Neural Networks (GNNs) have shown considerable effectiveness in a variety of graph learning tasks, particularly those based on the message-passing approach in recent years. However, their performance is often constrained by a limited receptive field, a challenge that becomes more acute in the presence of sparse graphs. In light of the power series, which possesses infinite expansion capabilities, we propose a novel Graph Power Filter Neural Network (GPFN) that enhances node classification by employing a power series graph filter to augment the receptive field. Concretely, our GPFN designs a new way to build a graph filter with an infinite receptive field based on the convergence power series, which can be analyzed in the spectral and spatial domains. Besides, we theoretically prove that our GPFN is a general framework that can integrate any power series and capture long-range dependencies. Finally, experimental results on three datasets demonstrate the superiority of our GPFN over state-of-the-art baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09943 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinite-Horizon Graph Filters: Leveraging Power Series to Enhance Sparse Information Aggregation Zhang, Ruizhe Jiang, Xinke Fang, Yuchen Luo, Jiayuan Xu, Yongxin Zhu, Yichen Chu, Xu Zhao, Junfeng Wang, Yasha Machine Learning Social and Information Networks Graph Neural Networks (GNNs) have shown considerable effectiveness in a variety of graph learning tasks, particularly those based on the message-passing approach in recent years. However, their performance is often constrained by a limited receptive field, a challenge that becomes more acute in the presence of sparse graphs. In light of the power series, which possesses infinite expansion capabilities, we propose a novel Graph Power Filter Neural Network (GPFN) that enhances node classification by employing a power series graph filter to augment the receptive field. Concretely, our GPFN designs a new way to build a graph filter with an infinite receptive field based on the convergence power series, which can be analyzed in the spectral and spatial domains. Besides, we theoretically prove that our GPFN is a general framework that can integrate any power series and capture long-range dependencies. Finally, experimental results on three datasets demonstrate the superiority of our GPFN over state-of-the-art baselines. |
| title | Infinite-Horizon Graph Filters: Leveraging Power Series to Enhance Sparse Information Aggregation |
| topic | Machine Learning Social and Information Networks |
| url | https://arxiv.org/abs/2401.09943 |