MGNN: Graph Neural Networks Inspired by Distance Geometry Problem

• URL: http://arxiv.org/abs/2201.12994v4
• Date: Thu, 31 Aug 2023 01:38:14 GMT
• Title: MGNN: Graph Neural Networks Inspired by Distance Geometry Problem
• Authors: Guanyu Cui, Zhewei Wei
• Abstract summary: Graph Neural Networks (GNNs) have emerged as a prominent research topic in the field of machine learning. In this paper, we propose a GNN model inspired by the congruent-inphilic property of the classifiers in the classification phase of GNNs. We extensively evaluate the effectiveness of our model through experiments conducted on both synthetic and real-world datasets.
• Score: 28.789684784093048
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph Neural Networks (GNNs) have emerged as a prominent research topic in the field of machine learning. Existing GNN models are commonly categorized into two types: spectral GNNs, which are designed based on polynomial graph filters, and spatial GNNs, which utilize a message-passing scheme as the foundation of the model. For the expressive power and universality of spectral GNNs, a natural approach is to improve the design of basis functions for better approximation ability. As for spatial GNNs, models like Graph Isomorphism Networks (GIN) analyze their expressive power based on Graph Isomorphism Tests. Recently, there have been attempts to establish connections between spatial GNNs and geometric concepts like curvature and cellular sheaves, as well as physical phenomena like oscillators. However, despite the recent progress, there is still a lack of comprehensive analysis regarding the universality of spatial GNNs from the perspectives of geometry and physics. In this paper, we propose MetricGNN (MGNN), a spatial GNN model inspired by the congruent-insensitivity property of classifiers in the classification phase of GNNs. We demonstrate that a GNN model is universal in the spatial domain if it can generate embedding matrices that are congruent to any given embedding matrix. This property is closely related to the Distance Geometry Problem (DGP). Since DGP is an NP-Hard combinatorial optimization problem, we propose optimizing an energy function derived from spring networks and the Multi-Dimensional Scaling (MDS) problem. This approach also allows our model to handle both homophilic and heterophilic graphs. Finally, we propose employing the iteration method to optimize our energy function. We extensively evaluate the effectiveness of our model through experiments conducted on both synthetic and real-world datasets. Our code is available at: https://github.com/GuanyuCui/MGNN.

Related papers

• Spatio-Spectral Graph Neural Networks [50.277959544420455]
  We propose Spatio-Spectral Graph Networks (S$2$GNNs) S$2$GNNs combine spatially and spectrally parametrized graph filters. We show that S$2$GNNs vanquish over-squashing and yield strictly tighter approximation-theoretic error bounds than MPGNNs.
  arXiv  Detail & Related papers  (2024-05-29T14:28:08Z)
• GNN-Ensemble: Towards Random Decision Graph Neural Networks [3.7620848582312405]
  Graph Neural Networks (GNNs) have enjoyed wide spread applications in graph-structured data. GNNs are required to learn latent patterns from a limited amount of training data to perform inferences on a vast amount of test data. In this paper, we push one step forward on the ensemble learning of GNNs with improved accuracy, robustness, and adversarial attacks.
  arXiv  Detail & Related papers  (2023-03-20T18:24:01Z)
• EvenNet: Ignoring Odd-Hop Neighbors Improves Robustness of Graph Neural Networks [51.42338058718487]
  Graph Neural Networks (GNNs) have received extensive research attention for their promising performance in graph machine learning. Existing approaches, such as GCN and GPRGNN, are not robust in the face of homophily changes on test graphs. We propose EvenNet, a spectral GNN corresponding to an even-polynomial graph filter.
  arXiv  Detail & Related papers  (2022-05-27T10:48:14Z)
• Graph Neural Networks with Local Graph Parameters [1.8600631687568656]
  Local graph parameters can be added to any Graph Neural Networks (GNNs) architecture. Our results connect GNNs with deep results in finite model theory and finite variable logics.
  arXiv  Detail & Related papers  (2021-06-12T07:43:51Z)
• A Unified View on Graph Neural Networks as Graph Signal Denoising [49.980783124401555]
  Graph Neural Networks (GNNs) have risen to prominence in learning representations for graph structured data. In this work, we establish mathematically that the aggregation processes in a group of representative GNN models can be regarded as solving a graph denoising problem. We instantiate a novel GNN model, ADA-UGNN, derived from UGNN, to handle graphs with adaptive smoothness across nodes.
  arXiv  Detail & Related papers  (2020-10-05T04:57:18Z)
• The Surprising Power of Graph Neural Networks with Random Node Initialization [54.4101931234922]
  Graph neural networks (GNNs) are effective models for representation learning on relational data. Standard GNNs are limited in their expressive power, as they cannot distinguish beyond the capability of the Weisfeiler-Leman graph isomorphism. In this work, we analyze the expressive power of GNNs with random node (RNI) We prove that these models are universal, a first such result for GNNs not relying on computationally demanding higher-order properties.
  arXiv  Detail & Related papers  (2020-10-02T19:53:05Z)
• Permutation-equivariant and Proximity-aware Graph Neural Networks with Stochastic Message Passing [88.30867628592112]
  Graph neural networks (GNNs) are emerging machine learning models on graphs. Permutation-equivariance and proximity-awareness are two important properties highly desirable for GNNs. We show that existing GNNs, mostly based on the message-passing mechanism, cannot simultaneously preserve the two properties. In order to preserve node proximities, we augment the existing GNNs with node representations.
  arXiv  Detail & Related papers  (2020-09-05T16:46:56Z)
• Expressive Power of Invariant and Equivariant Graph Neural Networks [10.419350129060598]
  We show that Folklore Graph Neural Networks (FGNN) are the most expressive architectures proposed so far for a given tensor order. FGNNs are able to learn how to solve the problem, leading to much better average performances than existing algorithms.
  arXiv  Detail & Related papers  (2020-06-28T16:35:45Z)
• Eigen-GNN: A Graph Structure Preserving Plug-in for GNNs [95.63153473559865]
  Graph Neural Networks (GNNs) are emerging machine learning models on graphs. Most existing GNN models in practice are shallow and essentially feature-centric. We show empirically and analytically that the existing shallow GNNs cannot preserve graph structures well. We propose Eigen-GNN, a plug-in module to boost GNNs ability in preserving graph structures.
  arXiv  Detail & Related papers  (2020-06-08T02:47:38Z)
• Random Features Strengthen Graph Neural Networks [40.60905158071766]
  Graph neural networks (GNNs) are powerful machine learning models for various graph learning tasks. In this paper, we demonstrate that GNNs become powerful just by adding a random feature to each node. We show that the addition of random features enables GNNs to solve various problems that normal GNNs, including the graph convolutional networks (GCNs) and graph isomorphism networks (GINs) cannot solve.
  arXiv  Detail & Related papers  (2020-02-08T12:47:29Z)

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.