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Ricci Curvature-Based Semi-Supervised Learning on an Attributed Network

In recent years, on the basis of drawing lessons from traditional neural network models, people have been paying more and more attention to the design of neural network architectures for processing graph structure data, which are called graph neural networks (GNN). GCN, namely, graph convolution net...

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Detalles Bibliográficos
Autores principales: Wu, Wei, Hu, Guangmin, Yu, Fucai
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7997130/
https://www.ncbi.nlm.nih.gov/pubmed/33673440
http://dx.doi.org/10.3390/e23030292
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author Wu, Wei
Hu, Guangmin
Yu, Fucai
author_facet Wu, Wei
Hu, Guangmin
Yu, Fucai
author_sort Wu, Wei
collection PubMed
description In recent years, on the basis of drawing lessons from traditional neural network models, people have been paying more and more attention to the design of neural network architectures for processing graph structure data, which are called graph neural networks (GNN). GCN, namely, graph convolution networks, are neural network models in GNN. GCN extends the convolution operation from traditional data (such as images) to graph data, and it is essentially a feature extractor, which aggregates the features of neighborhood nodes into those of target nodes. In the process of aggregating features, GCN uses the Laplacian matrix to assign different importance to the nodes in the neighborhood of the target nodes. Since graph-structured data are inherently non-Euclidean, we seek to use a non-Euclidean mathematical tool, namely, Riemannian geometry, to analyze graphs (networks). In this paper, we present a novel model for semi-supervised learning called the Ricci curvature-based graph convolutional neural network, i.e., RCGCN. The aggregation pattern of RCGCN is inspired by that of GCN. We regard the network as a discrete manifold, and then use Ricci curvature to assign different importance to the nodes within the neighborhood of the target nodes. Ricci curvature is related to the optimal transport distance, which can well reflect the geometric structure of the underlying space of the network. The node importance given by Ricci curvature can better reflect the relationships between the target node and the nodes in the neighborhood. The proposed model scales linearly with the number of edges in the network. Experiments demonstrated that RCGCN achieves a significant performance gain over baseline methods on benchmark datasets.
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spelling pubmed-79971302021-03-27 Ricci Curvature-Based Semi-Supervised Learning on an Attributed Network Wu, Wei Hu, Guangmin Yu, Fucai Entropy (Basel) Article In recent years, on the basis of drawing lessons from traditional neural network models, people have been paying more and more attention to the design of neural network architectures for processing graph structure data, which are called graph neural networks (GNN). GCN, namely, graph convolution networks, are neural network models in GNN. GCN extends the convolution operation from traditional data (such as images) to graph data, and it is essentially a feature extractor, which aggregates the features of neighborhood nodes into those of target nodes. In the process of aggregating features, GCN uses the Laplacian matrix to assign different importance to the nodes in the neighborhood of the target nodes. Since graph-structured data are inherently non-Euclidean, we seek to use a non-Euclidean mathematical tool, namely, Riemannian geometry, to analyze graphs (networks). In this paper, we present a novel model for semi-supervised learning called the Ricci curvature-based graph convolutional neural network, i.e., RCGCN. The aggregation pattern of RCGCN is inspired by that of GCN. We regard the network as a discrete manifold, and then use Ricci curvature to assign different importance to the nodes within the neighborhood of the target nodes. Ricci curvature is related to the optimal transport distance, which can well reflect the geometric structure of the underlying space of the network. The node importance given by Ricci curvature can better reflect the relationships between the target node and the nodes in the neighborhood. The proposed model scales linearly with the number of edges in the network. Experiments demonstrated that RCGCN achieves a significant performance gain over baseline methods on benchmark datasets. MDPI 2021-02-27 /pmc/articles/PMC7997130/ /pubmed/33673440 http://dx.doi.org/10.3390/e23030292 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) ).
spellingShingle Article
Wu, Wei
Hu, Guangmin
Yu, Fucai
Ricci Curvature-Based Semi-Supervised Learning on an Attributed Network
title Ricci Curvature-Based Semi-Supervised Learning on an Attributed Network
title_full Ricci Curvature-Based Semi-Supervised Learning on an Attributed Network
title_fullStr Ricci Curvature-Based Semi-Supervised Learning on an Attributed Network
title_full_unstemmed Ricci Curvature-Based Semi-Supervised Learning on an Attributed Network
title_short Ricci Curvature-Based Semi-Supervised Learning on an Attributed Network
title_sort ricci curvature-based semi-supervised learning on an attributed network
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7997130/
https://www.ncbi.nlm.nih.gov/pubmed/33673440
http://dx.doi.org/10.3390/e23030292
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