A Hierarchical Transitive-Aligned Graph Kernel for Un-attributed Graphs

TL;DR

This paper introduces a Hierarchical Transitive-Aligned graph kernel that improves graph comparison by incorporating structural correspondences and transitivity, leading to better classification accuracy on standard datasets.

Contribution

It proposes a novel hierarchical transitive-aligned kernel that captures structural correspondences and transitivity, enhancing graph similarity measures over existing kernels.

Findings

Outperforms state-of-the-art graph kernels in classification accuracy

Incorporates locational correspondence information into kernel computation

Guarantees transitivity in graph vertex alignments

Abstract

In this paper, we develop a new graph kernel, namely the Hierarchical Transitive-Aligned kernel, by transitively aligning the vertices between graphs through a family of hierarchical prototype graphs. Comparing to most existing state-of-the-art graph kernels, the proposed kernel has three theoretical advantages. First, it incorporates the locational correspondence information between graphs into the kernel computation, and thus overcomes the shortcoming of ignoring structural correspondences arising in most R-convolution kernels. Second, it guarantees the transitivity between the correspondence information that is not available for most existing matching kernels. Third, it incorporates the information of all graphs under comparisons into the kernel computation process, and thus encapsulates richer characteristics. By transductively training the C-SVM classifier, experimental evaluations demonstrate the effectiveness of the new transitive-aligned kernel. The proposed kernel can outperform state-of-the-art graph kernels on standard graph-based datasets in terms of the classification accuracy.