Graph kernels are conventional methods for computing graph similarities. However, most of the R-convolution graph kernels face two challenges: 1) They cannot compare graphs at multiple different scales, and 2) they do not consider the distributions of substructures when computing the kernel matrix. These two challenges limit their performances. To mitigate the two challenges, we propose a novel graph kernel called the Multi-scale Path-pattern Graph kernel (MPG), at the heart of which is the multi-scale path-pattern node feature map. Each element of the path-pattern node feature map is the number of occurrences of a path-pattern around a node. A path-pattern is constructed by the concatenation of all the node labels in a path of a truncated BFS tree rooted at each node. Since the path-pattern node feature map can only compare graphs at local scales, we incorporate into it the multiple different scales of the graph structure, which are captured by the truncated BFS trees of different depth. We use the Wasserstein distance to compute the similarity between the multi-scale path-pattern node feature maps of two graphs, considering the distributions of path-patterns. We empirically validate MPG on various benchmark graph datasets and demonstrate that it achieves state-of-the-art performance.

翻译：图核是计算图相似度的传统方法。然而，大多数R-卷积图核面临两个挑战：1）它们无法在多个不同尺度上比较图，2）在计算核矩阵时未考虑子结构的分布。这两个挑战限制了它们的性能。为缓解这两个挑战，我们提出一种新型图核——多尺度路径模式图核（MPG），其核心是多尺度路径模式节点特征映射。路径模式节点特征映射的每个元素是节点周围路径模式的出现次数。路径模式通过以每个节点为根的截断广度优先搜索树中路径上所有节点标签的串联构建。由于路径模式节点特征映射仅能比较图在局部尺度上的相似性，我们通过整合不同深度的截断广度优先搜索树捕获的图结构多尺度信息来增强其能力。我们采用Wasserstein距离计算两个图的多尺度路径模式节点特征映射之间的相似度，同时考虑路径模式的分布。我们在多个基准图数据集上对MPG进行实证验证，证明其达到了最先进的性能。