HGK-GNN

While Graph Neural Networks (GNNs) have achieved remarkable results in a variety of applications, recent studies exposed important shortcomings in their ability to capture heterogeneous structures and attributes of an underlying graph. Furthermore, though many Heterogeneous GNN (HGNN) variants have been proposed and have achieved state-of-the-art results, there are limited theoretical understandings of their properties. To this end, we introduce graph kernel to HGNNs and develop a Heterogeneous Graph Kernel-based Graph Neural Networks (HGK-GNN). Specifically, we incorporate the Mahalanobis distance (MD) to build a Heterogeneous Graph Kernel (HGK), and incorporating it into deep neural architectures, thus leveraging a heterogeneous GNN with a heterogeneous aggregation scheme. Also, we mathematically bridge HGK-GNN to metapath-based HGNNs, which are the most popular and effective variants of HGNNs. We theoretically analyze HGK-GNN with the indispensable Encoder and Aggregator component in metapath-based HGNNs, through which we provide a theoretical perspective to understand the most popular HGNNs. To the best of our knowledge, we are the first to introduce HGK into the field of HGNNs, and mark a first step in the direction of theoretically understanding and analyzing HGNNs. Correspondingly, both graph and node classification experiments are leveraged to evaluate HGK-GNN, where HGK-GNN outperforms a wide range of baselines on six real-world datasets, endorsing the analysis.