Enhancing Graph Representation Learning with Localized Topological Features

• URL: http://arxiv.org/abs/2501.09178v1
• Date: Wed, 15 Jan 2025 22:12:27 GMT
• Title: Enhancing Graph Representation Learning with Localized Topological Features
• Authors: Zuoyu Yan, Qi Zhao, Ze Ye, Tengfei Ma, Liangcai Gao, Zhi Tang, Yusu Wang, Chao Chen,
• Abstract summary: We propose a principled approach to extract the rich connectivity information of graphs based on the theory of persistent homology. Our method utilizes the topological features to enhance the representation learning of graph neural networks.
• Score: 29.562627708301694
• License:
• Abstract: Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be beneficial to explicitly extract and incorporate high-order topological and geometric information into these models. In this paper, we propose a principled approach to extract the rich connectivity information of graphs based on the theory of persistent homology. Our method utilizes the topological features to enhance the representation learning of graph neural networks and achieve state-of-the-art performance on various node classification and link prediction benchmarks. We also explore the option of end-to-end learning of the topological features, i.e., treating topological computation as a differentiable operator during learning. Our theoretical analysis and empirical study provide insights and potential guidelines for employing topological features in graph learning tasks.

Related papers

• TopER: Topological Embeddings in Graph Representation Learning [8.052380377159398]
  Topological Evolution Rate (TopER) is a low-dimensional embedding approach grounded in topological data analysis. TopER simplifies a key topological approach, Persistent Homology, by calculating the evolution rate of graph substructures. Our models achieve or surpass state-of-the-art results across molecular, biological, and social network datasets in tasks such as classification, clustering, and visualization.
  arXiv  Detail & Related papers  (2024-10-02T17:31:33Z)
• Characterizing the Influence of Topology on Graph Learning Tasks [47.48010635921621]
  Graph neural networks (GNNs) have achieved remarkable success in a wide range of tasks by encoding features combined with topology to create effective representations. We propose a metric, TopoInf, which characterizes the influence of graph topology by measuring the level of compatibility between the topological information of graph data and downstream task objectives.
  arXiv  Detail & Related papers  (2024-04-11T06:04:06Z)
• Joint Feature and Differentiable $ k $-NN Graph Learning using Dirichlet Energy [103.74640329539389]
  We propose a deep FS method that simultaneously conducts feature selection and differentiable $ k $-NN graph learning. We employ Optimal Transport theory to address the non-differentiability issue of learning $ k $-NN graphs in neural networks. We validate the effectiveness of our model with extensive experiments on both synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2023-05-21T08:15:55Z)
• A Theory of Link Prediction via Relational Weisfeiler-Leman on Knowledge Graphs [6.379544211152605]
  Graph neural networks are prominent models for representation learning over graph-structured data. Our goal is to provide a systematic understanding of the landscape of graph neural networks for knowledge graphs.
  arXiv  Detail & Related papers  (2023-02-04T17:40:03Z)
• State of the Art and Potentialities of Graph-level Learning [54.68482109186052]
  Graph-level learning has been applied to many tasks including comparison, regression, classification, and more. Traditional approaches to learning a set of graphs rely on hand-crafted features, such as substructures. Deep learning has helped graph-level learning adapt to the growing scale of graphs by extracting features automatically and encoding graphs into low-dimensional representations.
  arXiv  Detail & Related papers  (2023-01-14T09:15:49Z)
• Heterogeneous Graph Neural Networks using Self-supervised Reciprocally Contrastive Learning [102.9138736545956]
  Heterogeneous graph neural network (HGNN) is a very popular technique for the modeling and analysis of heterogeneous graphs. We develop for the first time a novel and robust heterogeneous graph contrastive learning approach, namely HGCL, which introduces two views on respective guidance of node attributes and graph topologies. In this new approach, we adopt distinct but most suitable attribute and topology fusion mechanisms in the two views, which are conducive to mining relevant information in attributes and topologies separately.
  arXiv  Detail & Related papers  (2022-04-30T12:57:02Z)
• Hyperbolic Graph Neural Networks: A Review of Methods and Applications [55.5502008501764]
  Graph neural networks generalize conventional neural networks to graph-structured data. The performance of Euclidean models in graph-related learning is still bounded and limited by the representation ability of Euclidean geometry. Recently, hyperbolic space has gained increasing popularity in processing graph data with tree-like structure and power-law distribution.
  arXiv  Detail & Related papers  (2022-02-28T15:08:48Z)
• Learning Connectivity with Graph Convolutional Networks for Skeleton-based Action Recognition [14.924672048447338]
  We introduce a novel framework for graph convolutional networks that learns the topological properties of graphs. The design principle of our method is based on the optimization of a constrained objective function. Experiments conducted on the challenging task of skeleton-based action recognition shows the superiority of the proposed method.
  arXiv  Detail & Related papers  (2021-12-06T19:43:26Z)
• Towards Deeper Graph Neural Networks [63.46470695525957]
  Graph convolutions perform neighborhood aggregation and represent one of the most important graph operations. Several recent studies attribute this performance deterioration to the over-smoothing issue. We propose Deep Adaptive Graph Neural Network (DAGNN) to adaptively incorporate information from large receptive fields.
  arXiv  Detail & Related papers  (2020-07-18T01:11:14Z)
• GCC: Graph Contrastive Coding for Graph Neural Network Pre-Training [62.73470368851127]
  Graph representation learning has emerged as a powerful technique for addressing real-world problems. We design Graph Contrastive Coding -- a self-supervised graph neural network pre-training framework. We conduct experiments on three graph learning tasks and ten graph datasets.
  arXiv  Detail & Related papers  (2020-06-17T16:18:35Z)

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.