Graphon Pooling for Reducing Dimensionality of Signals and Convolutional Operators on Graphs

Parada-Mayorga, Alejandro; Wang, Zhiyang; Ribeiro, Alejandro

doi:10.1109/tsp.2023.3318471

Cited by 4 publications

(11 citation statements)

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“…Notice that such scenarios appear in common applications where networks increase in size in somewhat structured ways, such as power electricity and sensor networks. Contribution (C5) also has a fundamental connection with the results derived in [25] for the operation of pooling in large graphs, where the equipartitions in [0, 1] can be used to reduce the size of a graph while preserving structural properties of the original graphs. We test the Algorithm's performance in (C5) considering multiple scenarios with several types of graphs, graphons, and with several instances for the number of nodes.…”

Section: Arxiv:240106279v1 [Cslg] 11 Jan 2024mentioning

confidence: 92%

“…. Although originally conceived for the study of large graphs, they quickly became valuable tools to analyze data that is defined on the graphs and on convergent sequences of graphs [24], [25], [33], [34].…”

Section: Graphons and Signal Processing On Graphonsmentioning

confidence: 99%

“…In this context, discretization methods are applied to the graphon to derive the adjacency matrix of a graph. On the other hand, we can build a graphon representation from a graph [24], [25], [34]. Regarding the first scenario, we highlight the following discretization method: (GD1) Building a regular grid on [0, 1] 2 and associating the area of the graphon W (u, v) in each subdomain of the grid to a given entry in an adjacency matrix A (see Fig.…”

Section: Graphons and Signal Processing On Graphonsmentioning

confidence: 99%

“…Although other discretizations such as irregular grids and irregular sampling can be used to generate graphs from graphons, it was formally proved in [24] and [25] that regular grids have unique attributes in terms of convergence and label invariance/equivariance properties. Additionally, as we will show later, regular partitions provide a natural way to build graphon representations of graphs -it is indeed the most commonly used and studied method to represent graphs as graphons [24].…”

Section: Graphons and Signal Processing On Graphonsmentioning

confidence: 99%

“…(possibly different from the previous scenario) will be associated with the same subset of [0, 1]. In [25] it is shown that when considering equipartitions, the signal models and operators defined on the graphon are stable with respect to changes in the labeling.…”

Section: Graphons and Signal Processing On Graphonsmentioning

confidence: 99%

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Graphon Pooling in Graph Neural Networks

Parada-Mayorga

Ruiz

Ribeiro

2021

2020 28th European Signal Processing Conference (EUSIPCO)

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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.

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Section: Arxiv:240106279v1 [Cslg] 11 Jan 2024mentioning

confidence: 92%