Pseudoinverse Graph Convolutional Networks: Fast Filters Tailored for Large Eigengaps of Dense Graphs and Hypergraphs

• URL: http://arxiv.org/abs/2008.00720v2
• Date: Thu, 28 Jan 2021 10:36:37 GMT
• Title: Pseudoinverse Graph Convolutional Networks: Fast Filters Tailored for Large Eigengaps of Dense Graphs and Hypergraphs
• Authors: Dominik Alfke, Martin Stoll
• Abstract summary: Graph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised classification on graph-based datasets. We propose a new GCN variant whose three-part filter space is targeted at dense graphs.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised classification on graph-based datasets. We propose a new GCN variant whose three-part filter space is targeted at dense graphs. Examples include Gaussian graphs for 3D point clouds with an increased focus on non-local information, as well as hypergraphs based on categorical data. These graphs differ from the common sparse benchmark graphs in terms of the spectral properties of their graph Laplacian. Most notably we observe large eigengaps, which are unfavorable for popular existing GCN architectures. Our method overcomes these issues by utilizing the pseudoinverse of the Laplacian. Another key ingredient is a low-rank approximation of the convolutional matrix, ensuring computational efficiency and increasing accuracy at the same time. We outline how the necessary eigeninformation can be computed efficiently in each applications and discuss the appropriate choice of the only metaparameter, the approximation rank. We finally showcase our method's performance regarding runtime and accuracy in various experiments with real-world datasets.

Related papers

• GSpect: Spectral Filtering for Cross-Scale Graph Classification [9.800723513820046]
  We propose GSpect, an advanced spectral graph filtering model for cross-scale graph classification tasks. On open data sets, GSpect improves the performance of classification accuracy by 1.62% on average, and for a maximum of 3.33% on PROTEINS. GSpect fills the gap in cross-scale graph classification studies and has potential to provide assistance in application research like diagnosis of brain disease.
  arXiv  Detail & Related papers  (2024-08-31T03:26:32Z)
• Spectral Greedy Coresets for Graph Neural Networks [61.24300262316091]
  The ubiquity of large-scale graphs in node-classification tasks hinders the real-world applications of Graph Neural Networks (GNNs) This paper studies graph coresets for GNNs and avoids the interdependence issue by selecting ego-graphs based on their spectral embeddings. Our spectral greedy graph coreset (SGGC) scales to graphs with millions of nodes, obviates the need for model pre-training, and applies to low-homophily graphs.
  arXiv  Detail & Related papers  (2024-05-27T17:52:12Z)
• GRAN is superior to GraphRNN: node orderings, kernel- and graph embeddings-based metrics for graph generators [0.6816499294108261]
  We study kernel-based metrics on distributions of graph invariants and manifold-based and kernel-based metrics in graph embedding space. We compare GraphRNN and GRAN, two well-known generative models for graphs, and unveil the influence of node orderings.
  arXiv  Detail & Related papers  (2023-07-13T12:07:39Z)
• 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)
• 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)
• Scalable Graph Neural Networks for Heterogeneous Graphs [12.44278942365518]
  Graph neural networks (GNNs) are a popular class of parametric model for learning over graph-structured data. Recent work has argued that GNNs primarily use the graph for feature smoothing, and have shown competitive results on benchmark tasks. In this work, we ask whether these results can be extended to heterogeneous graphs, which encode multiple types of relationship between different entities.
  arXiv  Detail & Related papers  (2020-11-19T06:03:35Z)
• Graph Pooling with Node Proximity for Hierarchical Representation Learning [80.62181998314547]
  We propose a novel graph pooling strategy that leverages node proximity to improve the hierarchical representation learning of graph data with their multi-hop topology. Results show that the proposed graph pooling strategy is able to achieve state-of-the-art performance on a collection of public graph classification benchmark datasets.
  arXiv  Detail & Related papers  (2020-06-19T13:09:44Z)
• Heuristic Semi-Supervised Learning for Graph Generation Inspired by Electoral College [80.67842220664231]
  We propose a novel pre-processing technique, namely ELectoral COllege (ELCO), which automatically expands new nodes and edges to refine the label similarity within a dense subgraph. In all setups tested, our method boosts the average score of base models by a large margin of 4.7 points, as well as consistently outperforms the state-of-the-art.
  arXiv  Detail & Related papers  (2020-06-10T14:48:48Z)
• CoSimGNN: Towards Large-scale Graph Similarity Computation [5.17905821006887]
  Graph Neural Networks (GNNs) provide a data-driven solution for this task. Existing GNN-based methods, which either respectively embeds two graphs or deploy cross-graph interactions for whole graph pairs, are still not able to achieve competitive results. We propose the "embedding-coarsening-matching" framework CoSimGNN, which first embeds and coarsens large graphs with adaptive pooling operation and then deploys fine-grained interactions on the coarsened graphs for final similarity scores.
  arXiv  Detail & Related papers  (2020-05-14T16:33:13Z)
• Graph Highway Networks [77.38665506495553]
  Graph Convolution Networks (GCN) are widely used in learning graph representations due to their effectiveness and efficiency. They suffer from the notorious over-smoothing problem, in which the learned representations converge to alike vectors when many layers are stacked. We propose Graph Highway Networks (GHNet) which utilize gating units to balance the trade-off between homogeneity and heterogeneity in the GCN learning process.
  arXiv  Detail & Related papers  (2020-04-09T16:26:43Z)
• Block-Approximated Exponential Random Graphs [77.4792558024487]
  An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. We propose an approximative framework to such non-trivial ERGs that result in dyadic independence (i.e., edge independent) distributions. Our methods are scalable to sparse graphs consisting of millions of nodes.
  arXiv  Detail & Related papers  (2020-02-14T11:42:16Z)

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.