  Graph representation learning has now become the de facto standard when
handling graph-structured data, with the framework of message-passing graph
neural networks (MPNN) being the most prevailing algorithmic tool. Despite its
popularity, the family of MPNNs suffers from several drawbacks such as
transparency and expressivity. Recently, the idea of designing neural models on
graphs using the theory of graph kernels has emerged as a more transparent as
well as sometimes more expressive alternative to MPNNs known as kernel graph
neural networks (KGNNs). Developments on KGNNs are currently a nascent field of
research, leaving several challenges from algorithmic design and adaptation to
other learning paradigms such as self-supervised learning. In this paper, we
improve the design and learning of KGNNs. Firstly, we extend the algorithmic
formulation of KGNNs by allowing a more flexible graph-level similarity
definition that encompasses former proposals like random walk graph kernel, as
well as providing a smoother optimization objective that alleviates the need of
introducing combinatorial learning procedures. Secondly, we enhance KGNNs
through the lens of self-supervision via developing a novel
structure-preserving graph data augmentation method called latent graph
augmentation (LGA). Finally, we perform extensive empirical evaluations to
demonstrate the efficacy of our proposed mechanisms. Experimental results over
benchmark datasets suggest that our proposed model achieves competitive
performance that is comparable to or sometimes outperforming state-of-the-art
graph representation learning frameworks with or without self-supervision on
graph classification tasks. Comparisons against other previously established
graph data augmentation methods verify that the proposed LGA augmentation
scheme captures better semantics of graph-level invariance.
