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Register a new userNode Feature Kernels Increase Graph Convolutional Network Robustness
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Changmin Wu
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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The robustness of the much-used Graph Convolutional Networks (GCNs) to perturbations of their input is becoming a topic of increasing importance. In this paper, the random GCN is introduced for which a random matrix theory analysis is possible. This analysis suggests that if the graph is sufficiently perturbed, or in the extreme case random, then the GCN fails to benefit from the node features. It is furthermore observed that enhancing the message passing step in GCNs by adding the node feature kernel to the adjacency matrix of the graph structure solves this problem. An empirical study of a GCN utilised for node classification on six real datasets further confirms the theoretical findings and demonstrates that perturbations of the graph structure can result in GCNs performing significantly worse than Multi-Layer Perceptrons run on the node features alone. In practice, adding a node feature kernel to the message passing of perturbed graphs results in a significant improvement of the GCNs performance, thereby rendering it more robust to graph perturbations. Our code is publicly available at:https://github.com/ChangminWu/RobustGCN.
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Modeling generative process of growing graphs has wide applications in social networks and recommendation systems, where cold start problem leads to new nodes isolated from existing graph. Despite the emerging literature in learning graph representation and graph generation, most of them can not handle isolated new nodes without nontrivial modifications. The challenge arises due to the fact that learning to generate representations for nodes in observed graph relies heavily on topological features, whereas for new nodes only node attributes are available. Here we propose a unified generative graph convolutional network that learns node representations for all nodes adaptively in a generative model framework, by sampling graph generation sequences constructed from observed graph data. We optimize over a variational lower bound that consists of a graph reconstruction term and an adaptive Kullback-Leibler divergence regularization term. We demonstrate the superior performance of our approach on several benchmark citation network datasets.
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Graph embedding methods represent nodes in a continuous vector space, preserving information from the graph (e.g. by sampling random walks). There are many hyper-parameters to these methods (such as random walk length) which have to be manually tuned for every graph. In this paper, we replace random walk hyper-parameters with trainable parameters that we automatically learn via backpropagation. In particular, we learn a novel attention model on the power series of the transition matrix, which guides the random walk to optimize an upstream objective. Unlike previous approaches to attention models, the method that we propose utilizes attention parameters exclusively on the data (e.g. on the random walk), and not used by the model for inference. We experiment on link prediction tasks, as we aim to produce embeddings that best-preserve the graph structure, generalizing to unseen information. We improve state-of-the-art on a comprehensive suite of real world datasets including social, collaboration, and biological networks. Adding attention to random walks can reduce the error by 20% to 45% on datasets we attempted. Further, our learned attention parameters are different for every graph, and our automatically-found values agree with the optimal choice of hyper-parameter if we manually tune existing methods.
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