Title Page
Abstract
Contents
Chapter 1. Introduction 8
Chapter 2. Preliminaries 11
2.1. Graph Neural Networks 11
2.1.1. Mathematical Terminologies 11
2.1.2. Graph Message Passing 12
2.1.3. Spatial-based Graph Neural Networks 13
2.1.4. Spectral-based Graph Neural Networks 15
2.2. Collaborative Filtering 15
2.3. Directed Acyclic Graphs Learning 17
Chapter 3. Related Works 19
3.1. Spectral-based Graph Neural Networks 19
3.1.1. Spectral Network 19
3.1.2. ChebNet 19
3.1.3. Graph Convolutional Networks 20
3.2. Collaborative Filtering 20
3.3. Salient Object Detection 22
3.4. Rain Removal Tasks 24
Chapter 4. Spectral Analysis of Graph Neural Networks 27
4.1. Schwartz space S(Rd) and Ring graph Rₙ[이미지참조] 27
4.2. Convolution on General Graphs 32
Chapter 5. Proposed Method 37
5.1. Proposal Background 37
5.2. Spectral GNNs to Computational Fluid Dynamics 38
5.3. Collaborative Filtering 40
5.4. Salient Object Detection 41
5.5. Rain Removal Task 43
Chapter 6. Experiments 46
6.1. Spectral GNNs to Computational Fluid Dynamics 46
6.1.1. Datasets 46
6.1.2. Experimental Results 47
6.2. Collaborative Filtering 52
6.2.1. Datasets 52
6.2.2. Evaluation Metric 53
6.2.3. Bayesian Personalized Ranking 54
6.2.4. Experimental Results 56
6.3. Salient Object Detection 57
6.3.1. Datasets 57
6.3.2. Evaluation metrics 58
6.3.3. Experimental Results 59
6.4. Rain Removal Task 64
6.4.1. Datasets 64
6.4.2. Experimental Results 64
Chapter 7. Conclusion 70
Bibliography 72
국문초록 80