Towards Subgraph Isomorphism Counting with Graph Kernels
Xin Liu, Weiqi Wang, Jiaxin Bai, Yangqiu Song
TL;DR
This paper explores the use of enhanced graph kernels, including polynomial and Gaussian variants, to approximate subgraph isomorphism counting, a #P-complete problem, by capturing neighborhood information for improved accuracy.
Contribution
It introduces novel enhancements to graph kernels for subgraph isomorphism counting, integrating neighborhood information to improve approximation capabilities.
Findings
Enhanced kernels outperform baseline methods in experiments
Neighborhood information improves counting accuracy
Potential for scalable approximate counting methods
Abstract
Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the solution. Graph kernels that implicitly capture the correlations among substructures in diverse graphs have exhibited great discriminative power in graph classification, so we pioneeringly investigate their potential in counting subgraph isomorphisms and further explore the augmentation of kernel capability through various variants, including polynomial and Gaussian kernels. Through comprehensive analysis, we enhance the graph kernels by incorporating neighborhood information. Finally, we present the results of extensive experiments to demonstrate the effectiveness of the enhanced graph kernels and discuss promising directions for future research.
Peer Reviews
Decision·Submitted to ICLR 2024
The experiments are conducted on real datasets (including heterogeneous ones where there exists different vertex labels). Also, various kinds of graph kernels as well as various methodologies (e.g., w/ or w.o./ normalization, combination with kernel tricks) are tested, that make the experimental results more rigorous.
I think this paper fails to present any advantages of graph kernel methods for solving subgraph isomorphism counting problems over the other existing methods. * For homogeneous data, this paper demonstrates that the 3-WL kernel combined with the proposed neighborhood information extraction outperforms the existing learning approach where neural network is used directly. However, for homogeneous data, as described in Section 2, there are various non-learning approximation algorithms like sampling
1. The paper introduces a novel approach by utilizing graph kernels for subgraph isomorphism counting, offering a fresh perspective on this important problem. 2. The presentation of the paper is clear and concise, making it accessible and enhancing the reader's comprehension of the proposed methods. 3. The authors provide a compelling set of experiments that empirically demonstrate the advantages and effectiveness of the enhanced graph kernels.
1. The paper could benefit from the inclusion of a clearly defined real-world application or use case to highlight the practical significance of the problem and its solution. While the paper discusses various applications of subgraph isomorphism counting, a concrete application or case study would better illustrate the real-world relevance of the research. 2. The complexity and computational efficiency of the proposed method are not adequately discussed. It is essential to conduct a thorough an
- This is the first work to investigate whether graph kernels can count substructures. The work is purely empirical, but some of the conclusions are likely to be useful to practitioners. - The kernels outperform the baselines on most of the datasets. The proposed neighborhood-aware color assignment algorithm seems to improve over the standard color assignment algorithms. - The presentation is clear and the paper is easy to read.
- I would suggest the authors give some context or motivate why it is important to count subgraphs/substructures. Are there any individuals or communities interested in this task? For the experiments, the authors construct some synthetic datasets and they also employ datasets whose inherent task is different from the one considered in this paper (graph classification datasets from the TUDataset repository). Thus, it is not clear to me whether there is interest into this task. - The originality
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Taxonomy
TopicsAdvanced Graph Neural Networks · Bayesian Modeling and Causal Inference · Graph Theory and Algorithms