CayleyNets: Graph Convolutional Neural Networks With Complex Rational Spectral Filters

Levie, Ron; Monti, Federico; Bresson, Xavier; Bronstein, Michael M.

doi:10.1109/tsp.2018.2879624

Cited by 518 publications

(358 citation statements)

References 29 publications

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“…Decomposing a graph signal to its pure harmonic coefficients is by definition the graph Fourier transform, and filters are defined by multiplying the different frequency components by different values. For some examples of spectral methods see, e.g., [9,10,11,12]. Additional references for both methods can be found in [4].…”

Section: Introductionmentioning

confidence: 99%

On the Transferability of Spectral Graph Filters

Levie

Isufi

Kutyniok

2019

2019 13th International Conference on Sampling Theory and Applications (SampTA)

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This paper focuses on spectral filters on graphs, namely filters defined as elementwise multiplication in the frequency domain of a graph. In many graph signal processing settings, it is important to transfer a filter from one graph to another. One example is in graph convolutional neural networks (ConvNets), where the dataset consists of signals defined on many different graphs, and the learned filters should generalize to signals on new graphs, not present in the training set. A necessary condition for transferability (the ability to transfer filters) is stability. Namely, given a graph filter, if we add a small perturbation to the graph, then the filter on the perturbed graph is a small perturbation of the original filter. It is a common misconception that spectral filters are not stable, and this paper aims at debunking this mistake. We introduce a space of filters, called the Cayley smoothness space, that contains the filters of state-of-the-art spectral filtering methods, and whose filters can approximate any generic spectral filter. For filters in this space, the perturbation in the filter is bounded by a constant times the perturbation in the graph, and filters in the Cayley smoothness space are thus termed linearly stable. By combining stability with the known property of equivariance, we prove that graph spectral filters are transferable.

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Section: Introductionmentioning

confidence: 99%

On the Transferability of Spectral Graph Filters

Levie

Isufi

Kutyniok

2019

2019 13th International Conference on Sampling Theory and Applications (SampTA)

Self Cite

View full text Add to dashboard Cite

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“…Most of the aforementioned methods can fit in the framework of "message passing" neural networks [17], which mainly involves transforming, propagating and aggregating node features across the graph through edges. Another stream of graph neural networks was developed based on the graph Fourier transform [4,8,19,24]. The features are first transferred to the spectral domain, next filtered with learnable filters and then transferred back to the spatial domain.…”

Section: Related Workmentioning

confidence: 99%

Graph Convolutional Networks with EigenPooling

Wang

Aggarwal

et al. 2019

Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

269

139

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Graph neural networks, which generalize deep neural network models to graph structured data, have attracted increasing attention in recent years. They usually learn node representations by transforming, propagating and aggregating node features and have been proven to improve the performance of many graph related tasks such as node classification and link prediction. To apply graph neural networks for the graph classification task, approaches to generate the graph representation from node representations are demanded. A common way is to globally combine the node representations. However, rich structural information is overlooked. Thus a hierarchical pooling procedure is desired to preserve the graph structure during the graph representation learning. There are some recent works on hierarchically learning graph representation analogous to the pooling step in conventional convolutional neural (CNN) networks. However, the local structural information is still largely neglected during the pooling process. In this paper, we introduce a pooling operator EigenPooling based on graph Fourier transform, which can utilize the node features and local structures during the pooling process. We then design pooling layers based on the pooling operator, which are further combined with traditional GCN convolutional layers to form a graph neural network framework EigenGCN for graph classification. Theoretical analysis is provided to understand EigenPooling from both local and global perspectives. Experimental results of the graph classification task on 6 commonly used benchmarks demonstrate the effectiveness of the proposed framework.

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“…Since the computation of eigenvectors is involved, computational complexity has become a serious issue. Many researchers have worked on optimizing the convolution filters to reduce the computational complexity [13], [19], [23], [24]. However, the learning process in all the aforementioned spectral approaches usually depends on the Laplacian eigenbasis, which handles the entire graph at one time.…”

Section: Related Workmentioning

confidence: 99%

DAGCN: Dual Attention Graph Convolutional Networks

Chen

Pan

Jiang

et al. 2019

2019 International Joint Conference on Neural Networks (IJCNN)

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Graph convolutional networks (GCNs) have recently become one of the most powerful tools for graph analytics tasks in numerous applications, ranging from social networks and natural language processing to bioinformatics and chemoinformatics, thanks to their ability to capture the complex relationships between concepts. At present, the vast majority of GCNs use a neighborhood aggregation framework to learn a continuous and compact vector, then performing a pooling operation to generalize graph embedding for the classification task. These approaches have two disadvantages in the graph classification task: (1)when only the largest sub-graph structure (k-hop neighbor) is used for neighborhood aggregation, a large amount of early-stage information is lost during the graph convolution step; (2) simple average/sum pooling or max pooling utilized, which loses the characteristics of each node and the topology between nodes. In this paper, we propose a novel framework called, dual attention graph convolutional networks (DAGCN) to address these problems. DAGCN automatically learns the importance of neighbors at different hops using a novel attention graph convolution layer, and then employs a second attention component, a selfattention pooling layer, to generalize the graph representation from the various aspects of a matrix graph embedding. The dual attention network is trained in an end-to-end manner for the graph classification task. We compare our model with state-of-the-art graph kernels and other deep learning methods. The experimental results show that our framework not only outperforms other baselines but also achieves a better rate of convergence.

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CayleyNets: Graph Convolutional Neural Networks With Complex Rational Spectral Filters

Cited by 518 publications

References 29 publications

On the Transferability of Spectral Graph Filters

On the Transferability of Spectral Graph Filters

Graph Convolutional Networks with EigenPooling

DAGCN: Dual Attention Graph Convolutional Networks

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