On the complexity of graph reconstruction

Dieter Kratsch; Lane A. Hemaspaandra

doi:10.1007/bf01578845

Graph reconstruction from the observation of diffused signals

2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton) ◽

10.1109/allerton.2015.7447170 ◽

2015 ◽

Cited By ~ 3

Author(s):

Bastien Pasdeloup ◽

Michael Rabbat ◽

Vincent Gripon ◽

Dominique Pastor ◽

Gregoire Mercier

Keyword(s):

Graph Reconstruction

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Multi-View Attribute Graph Convolution Networks for Clustering

Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2020/411 ◽

2020 ◽

Cited By ~ 1

Author(s):

Jiafeng Cheng ◽

Qianqian Wang ◽

Zhiqiang Tao ◽

Deyan Xie ◽

Quanxue Gao

Keyword(s):

Neural Networks ◽

State Of The Art ◽

Graph Embedding ◽

Structured Data ◽

Attention Networks ◽

Graph Data ◽

Graph Reconstruction ◽

Node Attributes ◽

Graph Neural Networks ◽

Geometric Relationship

Graph neural networks (GNNs) have made considerable achievements in processing graph-structured data. However, existing methods can not allocate learnable weights to different nodes in the neighborhood and lack of robustness on account of neglecting both node attributes and graph reconstruction. Moreover, most of multi-view GNNs mainly focus on the case of multiple graphs, while designing GNNs for solving graph-structured data of multi-view attributes is still under-explored. In this paper, we propose a novel Multi-View Attribute Graph Convolution Networks (MAGCN) model for the clustering task. MAGCN is designed with two-pathway encoders that map graph embedding features and learn the view-consistency information. Specifically, the first pathway develops multi-view attribute graph attention networks to reduce the noise/redundancy and learn the graph embedding features for each multi-view graph data. The second pathway develops consistent embedding encoders to capture the geometric relationship and probability distribution consistency among different views, which adaptively finds a consistent clustering embedding space for multi-view attributes. Experiments on three benchmark graph datasets show the superiority of our method compared with several state-of-the-art algorithms.

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Graph Reconstruction via Distance Oracles

Automata, Languages, and Programming - Lecture Notes in Computer Science ◽

10.1007/978-3-642-39206-1_62 ◽

2013 ◽

pp. 733-744 ◽

Cited By ~ 3

Author(s):

Claire Mathieu ◽

Hang Zhou

Keyword(s):

Distance Oracles ◽

Graph Reconstruction

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Graph reconstruction from path correlation data

Inverse Problems ◽

10.1088/1361-6420/aae798 ◽

2018 ◽

Vol 35 (1) ◽

pp. 015001 ◽

Cited By ~ 1

Author(s):

Gregory Berkolaiko ◽

Nick Duffield ◽

Mahmood Ettehad ◽

Kyriakos Manousakis

Keyword(s):

Correlation Data ◽

Graph Reconstruction

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GLEE: Geometric Laplacian Eigenmap Embedding

Journal of Complex Networks ◽

10.1093/comnet/cnaa007 ◽

2020 ◽

Vol 8 (2) ◽

Author(s):

Leo Torres ◽

Kevin S Chan ◽

Tina Eliassi-Rad

Keyword(s):

Link Prediction ◽

Graph Embedding ◽

Laplacian Matrix ◽

Dimensional Representation ◽

Laplacian Eigenmaps ◽

New Approach ◽

Graph Reconstruction ◽

Node Similarity ◽

Distance Minimization ◽

Low Dimensional

Abstract Graph embedding seeks to build a low-dimensional representation of a graph $G$. This low-dimensional representation is then used for various downstream tasks. One popular approach is Laplacian Eigenmaps (LE), which constructs a graph embedding based on the spectral properties of the Laplacian matrix of $G$. The intuition behind it, and many other embedding techniques, is that the embedding of a graph must respect node similarity: similar nodes must have embeddings that are close to one another. Here, we dispose of this distance-minimization assumption. Instead, we use the Laplacian matrix to find an embedding with geometric properties instead of spectral ones, by leveraging the so-called simplex geometry of $G$. We introduce a new approach, Geometric Laplacian Eigenmap Embedding, and demonstrate that it outperforms various other techniques (including LE) in the tasks of graph reconstruction and link prediction.

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