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.
Highlights
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]
PTC, and NCI1 involve chemical compounds represented by their molecular graph, where the atom type is represented by node labels, and bonds correspond to edges
We proposed a node aggregation scheme for graph convolutional neural networks inspired by DeepSets [32] that exploits self-organizing maps followed by graph convolutions to transform the node embeddings, and aggregates them according to the DeepSets formulation in a fixed-size graph-level representation
Summary
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]. When considering graph-level prediction tasks, 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. An approach that is commonly adopted in many graph neural network architectures proposed in the literature is to consider simple aggregation schemes such as the mean, the element-wise maximum, or the sum. We define A 2 RnÂn as the adjacency matrix of the graph, with elements aij 1⁄4 1 () ðvi; vjÞ 2 E. Let alPso D 2 RnÂn be the diagonal degree matrix where dii 1⁄4 j aij, and L the normalized graph laplacian defined by L 1⁄4 I À DÀ12ADÀ12, where I is the identity matrix
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