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MST-HGCN: a minimum spanning tree hyperbolic graph convolutional network

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Abstract

Graph neural networks (GNNs) have achieved outstanding results in research tasks on graph data. Most existing GNN models are defined in Euclidean space. However, when embedding hierarchical and scale-free graphs, models lying in hyperbolic space attain significant improvements over Euclidean graph convolutional networks (GCNs). To further enhance the performance of hyperbolic graph convolution and expand the applicability of related models to different data, we propose a hyperbolic graph convolution model based on the minimum spanning tree (MST-HGCN). Our method utilizes the minimum spanning tree (MST) algorithm to extract and process the topological structure of the input graph, which yields a more hierarchical topological structure and largely eliminates noisy edges. Then, several different topological structures based on the same spanning tree are produced by randomly re-adding the edges deleted by the MST algorithm; subsequently, a consistency loss is introduced to jointly optimize different outputs obtained from these topological structures. Experiments on node classification tasks and link prediction tasks for datasets with different hierarchy extents show that, our method comprehensively outperforms the vanilla hyperbolic GCN model on all the datasets, approaching or even outperforming the representative Euclidean comparison methods, which indicates that our method has better performance and data applicability.

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Data Availability

The datasets analysed during the current study are available in the HGCN repository, https://github.com/HazyResearch/hypgcn.

Notes

  1. https://github.com/dmlc/dgl

  2. https://github.com/optuna/optuna

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  1. Beihang University, XueYuan Road No.37, Beijing, 100191, Beijing, China

    Yanxi Liu, Bo Lang & Fengnan Quan

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Liu, Y., Lang, B. & Quan, F. MST-HGCN: a minimum spanning tree hyperbolic graph convolutional network. Appl Intell 53, 14515–14526 (2023). https://doi.org/10.1007/s10489-022-04256-y

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