Descriptive Kernel Convolution Network with Improved Random Walk Kernel
Keywords: kernel convolution network, graph kernel
TL;DR: We improve the random walk kernel by introducing color-matching based random walks, and show that the unrolling of the proposed version for efficient computation shares connection to GNNs.
Abstract: Graph kernels used to be the dominant approach to feature engineering for structured data, which are superseded by modern GNNs as the former lacks learnability.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. To this reason, we propose an improved graph kernel RWK$^{+}$ by introducing color-matching random walks, and derive 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 our proposed 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 our proposed RWK$^{+}$Conv layer, especially on the graph-level tasks. Our proposed 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.
Track: Graph Algorithms and Learning for the Web
Submission Guidelines Scope: Yes
Submission Guidelines Blind: Yes
Submission Guidelines Format: Yes
Submission Guidelines Limit: Yes
Submission Guidelines Authorship: Yes
Student Author: Yes
Submission Number: 521
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