
Simplification of Graph Convolutional Networks: A Matrix Factorizationbased Perspective
In recent years, substantial progress has been made on Graph Convolution...
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Multilayered Graph Embedding with Graph Convolutional Networks
Recently, graph embedding emerges as an effective approach for graph ana...
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FisherBures Adversary Graph Convolutional Networks
In a graph convolutional network, we assume that the graph G is generate...
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Graphs, Convolutions, and Neural Networks
Network data can be conveniently modeled as a graph signal, where data v...
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Signed Graph Attention Networks
Graph or network data is ubiquitous in the real world, including social ...
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Embedding Graphs under Centrality Constraints for Network Visualization
Visual rendering of graphs is a key task in the mapping of complex netwo...
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Data ultrametricity and clusterability
The increasing needs of clustering massive datasets and the high cost of...
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Explainable, Stable, and Scalable Graph Convolutional Networks for Learning Graph Representation
The network embedding problem that maps nodes in a graph to vectors in Euclidean space can be very useful for addressing several important tasks on a graph. Recently, graph neural networks (GNNs) have been proposed for solving such a problem. However, most embedding algorithms and GNNs are difficult to interpret and do not scale well to handle millions of nodes. In this paper, we tackle the problem from a new perspective based on the equivalence of three constrained optimization problems: the network embedding problem, the trace maximization problem of the modularity matrix in a sampled graph, and the matrix factorization problem of the modularity matrix in a sampled graph. The optimal solutions to these three problems are the dominant eigenvectors of the modularity matrix. We proposed two algorithms that belong to a special class of graph convolutional networks (GCNs) for solving these problems: (i) Clustering As Feature Embedding GCN (CAFEGCN) and (ii) sphereGCN. Both algorithms are stable trace maximization algorithms, and they yield good approximations of dominant eigenvectors. Moreover, there are lineartime implementations for sparse graphs. In addition to solving the network embedding problem, both proposed GCNs are capable of performing dimensionality reduction. Various experiments are conducted to evaluate our proposed GCNs and show that our proposed GCNs outperform almost all the baseline methods. Moreover, CAFEGCN could be benefited from the labeled data and have tremendous improvements in various performance metrics.
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