SOM-based aggregation for graph convolutional neural networks
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S.I. : WSOM 2019
SOM-based aggregation for graph convolutional neural networks Luca Pasa1
•
Nicolo` Navarin1 • Alessandro Sperduti1
Received: 13 May 2020 / Accepted: 27 October 2020 Ó The Author(s) 2020
Abstract Graph property prediction is becoming more and more popular due to the increasing availability of scientific and social data naturally represented in a graph form. Because of that, many researchers are focusing on the development of improved graph neural network models. One of the main components of a graph neural network is the aggregation operator, needed to generate a graph-level representation from a set of node-level embeddings. The aggregation operator is critical since it should, in principle, provide a representation of the graph that is isomorphism invariant, i.e. the graph representation should be a function of graph nodes treated as a set. DeepSets (in: Advances in neural information processing systems, pp 3391–3401, 2017) provides a framework to construct a set-aggregation operator with universal approximation properties. In this paper, we propose a DeepSets aggregation operator, based on Self-Organizing Maps (SOM), to transform a set of node-level representations into a single graph-level one. The adoption of SOMs allows to compute node representations that embed the information about their mutual similarity. Experimental results on several real-world datasets show that our proposed approach achieves improved predictive performance compared to the commonly adopted sum aggregation and many state-of-the-art graph neural network architectures in the literature. Keywords Graph neural networks Self-organizing maps Node aggregation
1 Introduction Neural Networks for Graphs (GNNs), while dating back to more than 20 years ago [27], have recently gained popularity due to the good results in tasks such as semi-supervised node classification [14], link prediction [13], graph classification [22] and graph generation [18]. The main component making possible the application of neural networks to graph data is the Graph Convolution (GC), for which several definitions have been proposed in the literature. The majority of GC proposals share the basic principle of generating a (fixed-size) node representation considering its local neighborhood.
& Luca Pasa [email protected] Nicolo` Navarin [email protected] Alessandro Sperduti [email protected] 1
Department of Mathematics, University of Padua, Padova, Italy
When considering graph-level prediction tasks, however, these topologically enriched representations at nodelevel need to be aggregated in order to obtain a single (fixed-size) representation of the graph. This aggregation component is crucial since it has to transform a variable number of node-level representations into a single graphlevel one. Moreover, an effective and efficient graph-level representation should be, as much as possible, invariant to different isomorphic representations of the input graph, thus letting the learning proce
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