Graph kernels used to be the dominant approach to feature engineering for structured data, which are superseded by modern GNNs as the former lacks learnability. Recently, a suite of Kernel Convolution Networks (KCNs) successfully revitalized graph kernels by introducing learnability, which convolves input with learnable hidden graphs using a certain graph kernel. The random walk kernel (RWK) has been used as the default kernel in many KCNs, gaining increasing attention. In this paper, we first revisit the RWK and its current usage in KCNs, revealing several shortcomings of the existing designs, and propose an improved graph kernel RWK+, by introducing color-matching random walks and deriving its efficient computation. We then propose RWK+CN, a KCN that uses RWK+ as the core kernel to learn descriptive graph features with an unsupervised objective, which can not be achieved by GNNs. Further, by unrolling RWK+, we discover its connection with a regular GCN layer, and propose a novel GNN layer RWK+Conv. In the first part of experiments, we demonstrate the descriptive learning ability of RWK+CN with the improved random walk kernel RWK+ on unsupervised pattern mining tasks; in the second part, we show the effectiveness of RWK+ for a variety of KCN architectures and supervised graph learning tasks, and demonstrate the expressiveness of RWK+Conv layer, especially on the graph-level tasks. RWK+ and RWK+Conv adapt to various real-world applications, including web applications such as bot detection in a web-scale Twitter social network, and community classification in Reddit social interaction networks.

该研究提出了改进的图核函数RWK+，引入了颜色匹配的随机游走并导出了高效的计算方法，进而提出了使用RWK+为核心的KCN模型RWK+CN，通过无监督目标学习描述性图特征。此外，该研究还在实验中展示了RWK+的表达能力以及RWK+Conv层在图级任务上的有效性，并说明了RWK+和RWK+Conv在各种真实世界应用中的适应性。

带有改进随机游走核的描述性卷积网络