Scalable Global Alignment Graph Kernel Using Random Features: From Node Embedding to Graph Embedding
This addresses the need for efficient and accurate graph similarity measures in machine learning, particularly for graph classification tasks, though it is incremental as it builds on existing global alignment kernels.
The paper tackles the problem of graph kernels losing structural information and having high computational complexity by proposing a new global alignment graph kernel that is positive-definite and scalable. The result shows that their method, Random Graph Embeddings (RGE), achieves quasi-linear scalability and outperforms or matches 12 state-of-the-art algorithms on nine benchmark datasets.
Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when representing graphs. Some recent global graph kernels, which utilizes the alignment of geometric node embeddings of graphs, yield state-of-the-art performance. However, these graph kernels are not necessarily positive-definite. More importantly, computing the graph kernel matrix will have at least quadratic {time} complexity in terms of the number and the size of the graphs. In this paper, we propose a new family of global alignment graph kernels, which take into account the global properties of graphs by using geometric node embeddings and an associated node transportation based on earth mover's distance. Compared to existing global kernels, the proposed kernel is positive-definite. Our graph kernel is obtained by defining a distribution over \emph{random graphs}, which can naturally yield random feature approximations. The random feature approximations lead to our graph embeddings, which is named as "random graph embeddings" (RGE). In particular, RGE is shown to achieve \emph{(quasi-)linear scalability} with respect to the number and the size of the graphs. The experimental results on nine benchmark datasets demonstrate that RGE outperforms or matches twelve state-of-the-art graph classification algorithms.