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Spectral Graph Representation Learning
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 신현정 | - |
| dc.contributor.author | 지종호 | - |
| dc.date.accessioned | 2022-11-29T02:33:07Z | - |
| dc.date.available | 2022-11-29T02:33:07Z | - |
| dc.date.issued | 2022-02 | - |
| dc.identifier.other | 31638 | - |
| dc.identifier.uri | https://dspace.ajou.ac.kr/handle/2018.oak/20599 | - |
| dc.description | 학위논문(박사)--아주대학교 일반대학원 :인공지능학과,2022. 2 | - |
| dc.description.tableofcontents | 1 Introduction 1 2 Fundamentals 12 2.1 Heat Kernel on Graphs 12 2.2 Gromov-Wasserstein Distance 17 3 Graph Representation and Metric 20 3.1 Spectral Heat Kernel Gromov-Wasserstein Discrepancy 21 3.1.1 Spectral Distributions and Heat Kernels 21 3.1.2 Spectral Heat Kernel Gromov-Wasserstein Discrepancy 23 3.1.3 SHGW Optimization 24 3.2 Approximated SHGW 27 3.3 Experiments 31 3.3.1 Benchmark Datasets 31 3.3.2 Samples from Spectral Distributions 35 3.3.3 Samples from Heat Kernels 35 3.3.4 Graph Classification Results 37 3.3.5 Influence of Hyperparameters 38 3.3.6 Computational Complexity Analysis 39 4 Graph Classification with Neural Networks 44 4.1 Heat Kernel Graph Networks 44 4.1.1 Related Works 45 4.1.2 Graph Neural Networks 48 4.1.3 Heat Kernel Graph Networks 49 4.1.4 Optimal Diffusion Rate 50 4.2 Extension to Multi-Head Heat Kernels 51 4.3 Experiments 55 4.3.1 Benchmark Datasets 55 4.3.2 Graph Classification Results 56 4.3.3 Effect of Multi-Head Heat Kernels 59 5 Conclusion and Future Work 62 5.1 Contribution 62 5.1.1 GW Framework with Heat Kernel 63 5.1.2 GNN Framework with Heat Kernel Convolution 64 5.2 Future Work 65 | - |
| dc.language.iso | eng | - |
| dc.publisher | The Graduate School, Ajou University | - |
| dc.rights | 아주대학교 논문은 저작권에 의해 보호받습니다. | - |
| dc.title | Spectral Graph Representation Learning | - |
| dc.type | Thesis | - |
| dc.contributor.affiliation | 아주대학교 일반대학원 | - |
| dc.contributor.department | 일반대학원 인공지능학과 | - |
| dc.date.awarded | 2022. 2 | - |
| dc.description.degree | Doctoral | - |
| dc.identifier.localId | 1244987 | - |
| dc.identifier.uci | I804:41038-000000031638 | - |
| dc.identifier.url | https://dcoll.ajou.ac.kr/dcollection/common/orgView/000000031638 | - |
| dc.subject.keyword | Gromov-Wasserstein distance | - |
| dc.subject.keyword | graph distance | - |
| dc.subject.keyword | graph neural networks | - |
| dc.subject.keyword | graph representation | - |
| dc.subject.keyword | heat kernel | - |
| dc.description.alternativeAbstract | A graph is a form which can efficiently represent the structured data. It is already conventional tool used in wide range of domains, from bioinformatics and pharmacology to social network and network system. In this thesis we aim to develop unsupervised and supervised frameworks for graph representation learning by combining the methods from spectral graph theory. Eigenvalues and the heat kernel are an important component from spectral graph theory that describes graph structure and the flow of information through the edges in the graph. First, the proposed unsupervised framework is developed using spectral distributions from the eigenvalues and heat kernels on graphs. These two components are carried out for graph comparison with the optimal transport like method, Gromov-Wasserstein discrepancy. The framwork is suitable for graph representation in that it satisfies three graph properties, permutation-invariance, structural-adaptivity and scale-adaptivity. Additionally, we introduce approximation for Gromov-Wasserstein discrepancy to boil down the computational complexity for large-scale graph comparison. The experiments on the benchmark datasets, including molecules, proteins and scientific collaboration, are conducted to validate the performance in graph classification task. We further investigate the samples in real-world graphs and check whether similar graphs selected from the proposed method is actually similar and the dissimilar graphs are dissimilar. Second, we propose a supervised graph representation learning method with graph neural networks. The model incorporates the heat kernel in graph convolution and satisfies the graph properties. Usually diffusion rate in the heat kernel is selected with trial-error. However, we substitute the diffusion rate to learnable parameter so that the model can decide the diffusion rate and the heat kernel is decided subsequently. Moreover, heat kernel trace normalization is suggested to enhance the discernability of the model on regular graphs. It complements the problem of representing non-isomorphic regular graphs the same in conventional graph convolution method. Multi-head heat kernels are applied to the model to further learn the comprehensive local and global structure of the graph. We experiment on benchmark datasets and show competitive performance on graph classification against baseline methods and verify whether the multi-head heat kernel improves the performance. Additionally, we analyze the heat kernels in the model to identify that learned heat kernels in real-world graphs utilizes local and global structure from the heat kernels. | - |
- Appears in Collections:
- Graduate School of Ajou University > Department of Artificial Intelligence > 4. Theses(Ph.D)
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