Graphon Pooling in Graph Neural Networks
| Autor: | Luana Ruiz, Alejandro Parada-Mayorga, Alejandro Ribeiro |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Structure (mathematical logic)
FOS: Computer and information sciences Computer Science - Machine Learning Sequence Computer science Dimensionality reduction Pooling Sampling (statistics) 020206 networking & telecommunications Machine Learning (stat.ML) 02 engineering and technology Overfitting Graph Convolution Machine Learning (cs.LG) Statistics - Machine Learning 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Node (circuits) Algorithm |
| Zdroj: | EUSIPCO |
| DOI: | 10.48550/arxiv.2003.01795 |
| Popis: | Graph neural networks (GNNs) have been used effectively in different applications involving the processing of signals on irregular structures modeled by graphs. Relying on the use of shift-invariant graph filters, GNNs extend the operation of convolution to graphs. However, the operations of pooling and sampling are still not clearly defined and the approaches proposed in the literature either modify the graph structure in a way that does not preserve its spectral properties, or require defining a policy for selecting which nodes to keep. In this work, we propose a new strategy for pooling and sampling on GNNs using graphons which preserves the spectral properties of the graph. To do so, we consider the graph layers in a GNN as elements of a sequence of graphs that converge to a graphon. In this way we have no ambiguity in the node labeling when mapping signals from one layer to the other and a spectral representation that is consistent throughout the layers. We evaluate this strategy in a synthetic and a real-world numerical experiment where we show that graphon pooling GNNs are less prone to overfitting and improve upon other pooling techniques, especially when the dimensionality reduction ratios between layers is large. |
| Databáze: | OpenAIRE |
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