Graph Pooling with Maximum-Weight $k$-Independent Sets

• URL: http://arxiv.org/abs/2208.03523v1
• Date: Sat, 6 Aug 2022 14:12:47 GMT
• Title: Graph Pooling with Maximum-Weight $k$-Independent Sets
• Authors: Davide Bacciu, Alessio Conte, Francesco Landolfi
• Abstract summary: We introduce a graph coarsening mechanism based on the graph-theoretic concept of maximum-weight $k$-independent sets. We prove theoretical guarantees for distortion bounds on path lengths, as well as the ability to preserve key topological properties in the coarsened graphs.
• Score: 12.251091325930837
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph reductions are fundamental when dealing with large scale networks and relational data. They allow to downsize tasks of high computational impact by solving them in coarsened structures. At the same time, graph reductions play the role of pooling layers in graph neural networks, to extract multi-resolution representations from structures. In these contexts, the ability of the reduction mechanism to preserve distance relationships and topological properties appears fundamental, along with a scalability enabling its application to real-world sized problems. In this paper, we introduce a graph coarsening mechanism based on the graph-theoretic concept of maximum-weight $k$-independent sets, providing a greedy algorithm that allows efficient parallel implementation on GPUs. Our method is the first graph-structured counterpart of controllable equispaced coarsening mechanisms in regular data (images, sequences). We prove theoretical guarantees for distortion bounds on path lengths, as well as the ability to preserve key topological properties in the coarsened graphs. We leverage these concepts to define a graph pooling mechanism that we empirically assess in graph classification tasks, showing that it compares favorably against pooling methods in literature.

Related papers

• GraphCroc: Cross-Correlation Autoencoder for Graph Structural Reconstruction [6.817416560637197]
  Graph autoencoders (GAEs) reconstruct graph structures from node embeddings. We introduce a cross-correlation mechanism that significantly enhances the GAE representational capabilities. We also propose GraphCroc, a new GAE that supports flexible encoder architectures tailored for various downstream tasks.
  arXiv  Detail & Related papers  (2024-10-04T12:59:45Z)
• Deep Manifold Graph Auto-Encoder for Attributed Graph Embedding [51.75091298017941]
  This paper proposes a novel Deep Manifold (Variational) Graph Auto-Encoder (DMVGAE/DMGAE) for attributed graph data. The proposed method surpasses state-of-the-art baseline algorithms by a significant margin on different downstream tasks across popular datasets.
  arXiv  Detail & Related papers  (2024-01-12T17:57:07Z)
• SynGraphy: Succinct Summarisation of Large Networks via Small Synthetic Representative Graphs [4.550112751061436]
  We describe SynGraphy, a method for visually summarising the structure of large network datasets. It works by drawing smaller graphs generated to have similar structural properties to the input graphs.
  arXiv  Detail & Related papers  (2023-02-15T16:00:15Z)
• Graph Kernel Neural Networks [53.91024360329517]
  We propose to use graph kernels, i.e. kernel functions that compute an inner product on graphs, to extend the standard convolution operator to the graph domain. This allows us to define an entirely structural model that does not require computing the embedding of the input graph. Our architecture allows to plug-in any type of graph kernels and has the added benefit of providing some interpretability.
  arXiv  Detail & Related papers  (2021-12-14T14:48:08Z)
• Edge but not Least: Cross-View Graph Pooling [76.71497833616024]
  This paper presents a cross-view graph pooling (Co-Pooling) method to better exploit crucial graph structure information. Through cross-view interaction, edge-view pooling and node-view pooling seamlessly reinforce each other to learn more informative graph-level representations.
  arXiv  Detail & Related papers  (2021-09-24T08:01:23Z)
• Accurate Learning of Graph Representations with Graph Multiset Pooling [45.72542969364438]
  We propose a Graph Multiset Transformer (GMT) that captures the interaction between nodes according to their structural dependencies. Our experimental results show that GMT significantly outperforms state-of-the-art graph pooling methods on graph classification benchmarks.
  arXiv  Detail & Related papers  (2021-02-23T07:45:58Z)
• Graph Coarsening with Neural Networks [8.407217618651536]
  We propose a framework for measuring the quality of coarsening algorithm and show that depending on the goal, we need to carefully choose the Laplace operator on the coarse graph. Motivated by the observation that the current choice of edge weight for the coarse graph may be sub-optimal, we parametrize the weight assignment map with graph neural networks and train it to improve the coarsening quality in an unsupervised way.
  arXiv  Detail & Related papers  (2021-02-02T06:50:07Z)
• Multilayer Clustered Graph Learning [66.94201299553336]
  We use contrastive loss as a data fidelity term, in order to properly aggregate the observed layers into a representative graph. Experiments show that our method leads to a clustered clusters w.r.t. We learn a clustering algorithm for solving clustering problems.
  arXiv  Detail & Related papers  (2020-10-29T09:58:02Z)
• 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)
• 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.