Advancing Graph Neural Networks with HL-HGAT: A Hodge-Laplacian and Attention Mechanism Approach for Heterogeneous Graph-Structured Data

• URL: http://arxiv.org/abs/2403.06687v2
• Date: Mon, 22 Apr 2024 16:18:53 GMT
• Title: Advancing Graph Neural Networks with HL-HGAT: A Hodge-Laplacian and Attention Mechanism Approach for Heterogeneous Graph-Structured Data
• Authors: Jinghan Huang, Qiufeng Chen, Yijun Bian, Pengli Zhu, Nanguang Chen, Moo K. Chung, Anqi Qiu,
• Abstract summary: This study introduces a novel perspective by considering a graph as a simplicial complex, encompassing nodes, edges, triangles, and $k$-simplices. Our contribution is the Hodge-Laplacian heterogeneous graph attention network (HL-HGAT), designed to learn heterogeneous signal representations across $k$-simplices.
• Score: 4.757249417213973
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• Generalized Simplicial Attention Neural Networks [22.171364354867723]
  We introduce Generalized Simplicial Attention Neural Networks (GSANs) GSANs process data living on simplicial complexes using masked self-attentional layers. These schemes learn how to combine data associated with neighbor simplices of consecutive order in a task-oriented fashion.
  arXiv  Detail & Related papers  (2023-09-05T11:29:25Z)
• Seq-HGNN: Learning Sequential Node Representation on Heterogeneous Graph [57.2953563124339]
  We propose a novel heterogeneous graph neural network with sequential node representation, namely Seq-HGNN. We conduct extensive experiments on four widely used datasets from Heterogeneous Graph Benchmark (HGB) and Open Graph Benchmark (OGB)
  arXiv  Detail & Related papers  (2023-05-18T07:27:18Z)
• Heterogeneous Graph Convolutional Neural Network via Hodge-Laplacian for Brain Functional Data [4.80657982213439]
  This study proposes a novel heterogeneous graph convolutional neural network (HGCNN) to handle complex brain fMRI data. We introduce a generic formulation of spectral filters on heterogeneous graphs by introducing the $k-th$lacian (HL) operator. We design HL-node, HL-edge, and HL-HGCNN neural networks to learn signal representation at a graph node, edge levels, and both, respectively.
  arXiv  Detail & Related papers  (2023-02-18T12:58:50Z)
• Relation Embedding based Graph Neural Networks for Handling Heterogeneous Graph [58.99478502486377]
  We propose a simple yet efficient framework to make the homogeneous GNNs have adequate ability to handle heterogeneous graphs. Specifically, we propose Relation Embedding based Graph Neural Networks (RE-GNNs), which employ only one parameter per relation to embed the importance of edge type relations and self-loop connections.
  arXiv  Detail & Related papers  (2022-09-23T05:24:18Z)
• Simple and Efficient Heterogeneous Graph Neural Network [55.56564522532328]
  Heterogeneous graph neural networks (HGNNs) have powerful capability to embed rich structural and semantic information of a heterogeneous graph into node representations. Existing HGNNs inherit many mechanisms from graph neural networks (GNNs) over homogeneous graphs, especially the attention mechanism and the multi-layer structure. This paper conducts an in-depth and detailed study of these mechanisms and proposes Simple and Efficient Heterogeneous Graph Neural Network (SeHGNN)
  arXiv  Detail & Related papers  (2022-07-06T10:01:46Z)
• Dist2Cycle: A Simplicial Neural Network for Homology Localization [66.15805004725809]
  Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations. We propose a graph convolutional model for learning functions parametrized by the $k$-homological features of simplicial complexes.
  arXiv  Detail & Related papers  (2021-10-28T14:59:41Z)
• Explicit Pairwise Factorized Graph Neural Network for Semi-Supervised Node Classification [59.06717774425588]
  We propose the Explicit Pairwise Factorized Graph Neural Network (EPFGNN), which models the whole graph as a partially observed Markov Random Field. It contains explicit pairwise factors to model output-output relations and uses a GNN backbone to model input-output relations. We conduct experiments on various datasets, which shows that our model can effectively improve the performance for semi-supervised node classification on graphs.
  arXiv  Detail & Related papers  (2021-07-27T19:47:53Z)
• Spatial-Spectral Clustering with Anchor Graph for Hyperspectral Image [88.60285937702304]
  This paper proposes a novel unsupervised approach called spatial-spectral clustering with anchor graph (SSCAG) for HSI data clustering. The proposed SSCAG is competitive against the state-of-the-art approaches.
  arXiv  Detail & Related papers  (2021-04-24T08:09:27Z)
• Graph Networks with Spectral Message Passing [1.0742675209112622]
  We introduce the Spectral Graph Network, which applies message passing to both the spatial and spectral domains. Our results show that the Spectral GN promotes efficient training, reaching high performance with fewer training iterations despite having more parameters.
  arXiv  Detail & Related papers  (2020-12-31T21:33:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.