Generalized Permutants and Graph GENEOs

• URL: http://arxiv.org/abs/2206.14798v1
• Date: Wed, 29 Jun 2022 17:56:37 GMT
• Title: Generalized Permutants and Graph GENEOs
• Authors: Faraz Ahmad, Massimo Ferri, Patrizio Frosini
• Abstract summary: We adapt the theory of group equivariant non-expansive operators (GENEOs) to act on the space of all graphs weighted on vertices or edges. This is done by showing how the general concept of GENEO can be used to transform graphs and to give information about their structure. An experimental section concludes the paper, illustrating the possible use of our operators to extract information from graphs.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper we establish a bridge between Topological Data Analysis and Geometric Deep Learning, adapting the topological theory of group equivariant non-expansive operators (GENEOs) to act on the space of all graphs weighted on vertices or edges. This is done by showing how the general concept of GENEO can be used to transform graphs and to give information about their structure. This requires the introduction of the new concepts of generalized permutant and generalized permutant measure and the mathematical proof that these concepts allow us to build GENEOs between graphs. An experimental section concludes the paper, illustrating the possible use of our operators to extract information from graphs. This paper is part of a line of research devoted to developing a compositional and geometric theory of GENEOs for Geometric Deep Learning.

Related papers

• Generalization of Geometric Graph Neural Networks [84.01980526069075]
  We study the generalization capabilities of geometric graph neural networks (GNNs) We prove a generalization gap between the optimal empirical risk and the optimal statistical risk of this GNN. The most important observation is that the generalization capability can be realized with one large graph instead of being limited to the size of the graph as in previous results.
  arXiv  Detail & Related papers  (2024-09-08T18:55:57Z)
• A novel approach to graph distinction through GENEOs and permutants [0.0]
  This paper explores the use of GENEOs for distinguishing $r$-regular graphs up to isomorphisms. Our experiments show that GENEOs offer a good compromise between efficiency and computational cost in comparing $r$-regular graphs. GENEOs could be a general-purpose approach to discriminative problems in Machine Learning.
  arXiv  Detail & Related papers  (2024-06-12T09:53:14Z)
• A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications [67.33002207179923]
  This paper presents a survey of data structures, models, and applications related to geometric GNNs. We provide a unified view of existing models from the geometric message passing perspective. We also summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation.
  arXiv  Detail & Related papers  (2024-03-01T12:13:04Z)
• A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems [87.30652640973317]
  Recent advances in computational modelling of atomic systems represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. This paper provides a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems.
  arXiv  Detail & Related papers  (2023-12-12T18:44:19Z)
• Geometry Contrastive Learning on Heterogeneous Graphs [50.58523799455101]
  This paper proposes a novel self-supervised learning method, termed as Geometry Contrastive Learning (GCL) GCL views a heterogeneous graph from Euclidean and hyperbolic perspective simultaneously, aiming to make a strong merger of the ability of modeling rich semantics and complex structures. Extensive experiments on four benchmarks data sets show that the proposed approach outperforms the strong baselines.
  arXiv  Detail & Related papers  (2022-06-25T03:54:53Z)
• Geometry Interaction Knowledge Graph Embeddings [153.69745042757066]
  We propose Geometry Interaction knowledge graph Embeddings (GIE), which learns spatial structures interactively between the Euclidean, hyperbolic and hyperspherical spaces. Our proposed GIE can capture a richer set of relational information, model key inference patterns, and enable expressive semantic matching across entities.
  arXiv  Detail & Related papers  (2022-06-24T08:33:43Z)
• Plane Geometry Diagram Parsing [29.921409628478152]
  We propose a powerful diagram based on deep learning and graph reasoning. A modified instance segmentation method is proposed to extract geometric primitives. The graph neural network (GNN) is leveraged to realize relation parsing and primitive classification.
  arXiv  Detail & Related papers  (2022-05-19T07:47:01Z)
• Self-Supervised Graph Representation Learning via Topology Transformations [61.870882736758624]
  We present the Topology Transformation Equivariant Representation learning, a general paradigm of self-supervised learning for node representations of graph data. In experiments, we apply the proposed model to the downstream node and graph classification tasks, and results show that the proposed method outperforms the state-of-the-art unsupervised approaches.
  arXiv  Detail & Related papers  (2021-05-25T06:11:03Z)
• Graph Geometry Interaction Learning [41.10468385822182]
  We develop a novel Geometry Interaction Learning (GIL) method for graphs, a well-suited and efficient alternative for learning abundant geometric properties in graph. Our method endows each node the freedom to determine the importance of each geometry space via a flexible dual feature interaction learning and probability assembling mechanism. Promising experimental results are presented for five benchmark datasets on node classification and link prediction tasks.
  arXiv  Detail & Related papers  (2020-10-23T02:40:28Z)

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.