Advancing Graph Neural Networks with HL-HGAT: A Hodge-Laplacian and Attention Mechanism Approach for Heterogeneous Graph-Structured Data
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929323108204544 |
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| author | Huang, Jinghan Chen, Qiufeng Bian, Yijun Zhu, Pengli Chen, Nanguang Chung, Moo K. Qiu, Anqi |
| author_facet | Huang, Jinghan Chen, Qiufeng Bian, Yijun Zhu, Pengli Chen, Nanguang Chung, Moo K. Qiu, Anqi |
| contents | Graph neural networks (GNNs) have proven effective in capturing relationships among nodes in a graph. This study introduces a novel perspective by considering a graph as a simplicial complex, encompassing nodes, edges, triangles, and $k$-simplices, enabling the definition of graph-structured data on any $k$-simplices. Our contribution is the Hodge-Laplacian heterogeneous graph attention network (HL-HGAT), designed to learn heterogeneous signal representations across $k$-simplices. The HL-HGAT incorporates three key components: HL convolutional filters (HL-filters), simplicial projection (SP), and simplicial attention pooling (SAP) operators, applied to $k$-simplices. HL-filters leverage the unique topology of $k$-simplices encoded by the Hodge-Laplacian (HL) operator, operating within the spectral domain of the $k$-th HL operator. To address computation challenges, we introduce a polynomial approximation for HL-filters, exhibiting spatial localization properties. Additionally, we propose a pooling operator to coarsen $k$-simplices, combining features through simplicial attention mechanisms of self-attention and cross-attention via transformers and SP operators, capturing topological interconnections across multiple dimensions of simplices. The HL-HGAT is comprehensively evaluated across diverse graph applications, including NP-hard problems, graph multi-label and classification challenges, and graph regression tasks in logistics, computer vision, biology, chemistry, and neuroscience. The results demonstrate the model's efficacy and versatility in handling a wide range of graph-based scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06687 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Advancing Graph Neural Networks with HL-HGAT: A Hodge-Laplacian and Attention Mechanism Approach for Heterogeneous Graph-Structured Data Huang, Jinghan Chen, Qiufeng Bian, Yijun Zhu, Pengli Chen, Nanguang Chung, Moo K. Qiu, Anqi Machine Learning Computer Vision and Pattern Recognition Graph neural networks (GNNs) have proven effective in capturing relationships among nodes in a graph. This study introduces a novel perspective by considering a graph as a simplicial complex, encompassing nodes, edges, triangles, and $k$-simplices, enabling the definition of graph-structured data on any $k$-simplices. Our contribution is the Hodge-Laplacian heterogeneous graph attention network (HL-HGAT), designed to learn heterogeneous signal representations across $k$-simplices. The HL-HGAT incorporates three key components: HL convolutional filters (HL-filters), simplicial projection (SP), and simplicial attention pooling (SAP) operators, applied to $k$-simplices. HL-filters leverage the unique topology of $k$-simplices encoded by the Hodge-Laplacian (HL) operator, operating within the spectral domain of the $k$-th HL operator. To address computation challenges, we introduce a polynomial approximation for HL-filters, exhibiting spatial localization properties. Additionally, we propose a pooling operator to coarsen $k$-simplices, combining features through simplicial attention mechanisms of self-attention and cross-attention via transformers and SP operators, capturing topological interconnections across multiple dimensions of simplices. The HL-HGAT is comprehensively evaluated across diverse graph applications, including NP-hard problems, graph multi-label and classification challenges, and graph regression tasks in logistics, computer vision, biology, chemistry, and neuroscience. The results demonstrate the model's efficacy and versatility in handling a wide range of graph-based scenarios. |
| title | Advancing Graph Neural Networks with HL-HGAT: A Hodge-Laplacian and Attention Mechanism Approach for Heterogeneous Graph-Structured Data |
| topic | Machine Learning Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2403.06687 |