
On the Transferability of Spectral Graph Filters
This paper focuses on spectral filters on graphs, namely filters defined...
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Stationary signal processing on graphs
Graphs are a central tool in machine learning and information processing...
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Framework for Designing Filters of Spectral Graph Convolutional Neural Networks in the Context of Regularization Theory
Graph convolutional neural networks (GCNNs) have been widely used in gra...
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Bridging the Gap Between Spectral and Spatial Domains in Graph Neural Networks
This paper aims at revisiting Graph Convolutional Neural Networks by bri...
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Graph Neural Networks with distributed ARMA filters
Recent graph neural networks implement convolutional layers based on pol...
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Interpretable Stability Bounds for Spectral Graph Filters
Graphstructured data arise in a variety of realworld context ranging f...
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GraphFlow: A New Graph Convolutional Network Based on Parallel Flows
In view of the huge success of convolution neural networks (CNN) for ima...
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Transferability of Spectral Graph Convolutional Neural Networks
This paper focuses on spectral graph convolutional neural networks (ConvNets), where filters are defined as elementwise multiplication in the frequency domain of a graph. In machine learning settings where the dataset consists of signals defined on many different graphs, the trained ConvNet should generalize to signal on graphs unseen in the training set. It is thus important to transfer filters from one graph to the other. Transferability, which is a certain type of generalization capability, can be loosely defined as follows: if two graphs describe the same phenomenon, then a single filter/ConvNet should have similar repercussions on both graphs. This paper aims at debunking the common misconception that spectral filters are not transferable. We show that if two graphs discretize the same continuous metric space, then a spectral filter/ConvNet has approximately the same repercussion on both graphs. Our analysis is more permissive than the standard analysis. Transferability is typically described as the robustness of the filter to small graph perturbations and reindexing of the vertices. Our analysis accounts also for large graph perturbations. We prove transferability between graphs that can have completely different dimensions and topologies, only requiring that both graphs discretize the same underlying continuous space.
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