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Attributed Graph Classification via Deep Graph Convolutional Neural Networks
From social networks to biological networks, graphs are a natural way to represent a diverse set of real-world data. This research presents attributed graph convolutional neural network with a pooling layer (AGCP for short), a novel end-to-end deep neural network model which captures the higher-order latent attributes of weighted, labeled, undirected, attributed graphs of arbitrary size. The architecture of AGCP is an efficient variant of convolutional neural network (CNN) and has a linear filter function that convolves over the fixed topological structure of a graph to learn local and global attributes of the graph. Convolution is followed by a pooling layer that coarsens the graph while preserving the global structure of the original input graph using information gain. On the other hand, advances in high throughput technologies for next-generation sequencing have enabled machine learning research to acquire and extract knowledge from biological networks. We apply AGCP on three bioinformatics networks, ENZYMES, D&D, and GINA a graph dataset of gene interaction networks with genomic mutation attributes as the attributes of the vertices. In several experiments on these datasets, we demonstrate that AGCP yields better results in terms of classification accuracy relative to the previously proposed models by a considerable margin
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Έλ ν΄λ¬μ€ν°λ§ λ±μ μ€ν μ±λ₯μΌλ‘ λΉκ΅ν΄λ³΄μμ λ, λΉλ±νκ±°λ λμ μ±λ₯μ 보μμμ νμΈνμλ€.The goal of unsupervised graph representation learning is extracting useful node-wise or graph-wise vector representation that is aware of the intrinsic structures of the graph and its attributes. These days, designing methodology of unsupervised graph representation learning based on graph neural networks has growing attention due to their powerful representation ability. Many methods are focused on a homogeneous graph that is a network with a single type of node and a single type of edge. However, as many types of relationships exist in this world, graphs can also be classified into various types by structural and semantic properties. For this reason, to learn useful representations from graphs, the unsupervised learning framework must consider the characteristics of the input graph. In this dissertation, we focus on designing unsupervised learning models using graph neural networks for three graph structures that are widely available: homogeneous graphs, tree-like graphs, and heterogeneous graphs.
First, we propose a symmetric graph convolutional autoencoder which produces a low-dimensional latent representation from a homogeneous graph. In contrast to the existing graph autoencoders with asymmetric decoder parts, the proposed autoencoder has a newly designed decoder which builds a completely symmetric autoencoder form. For the reconstruction of node features, the decoder is designed based on Laplacian sharpening as the counterpart of Laplacian smoothing of the encoder, which allows utilizing the graph structure in the whole processes of the proposed autoencoder architecture. In order to prevent the numerical instability of the network caused by the Laplacian sharpening introduction, we further propose a new numerically stable form of the Laplacian sharpening by incorporating the signed graphs. The experimental results of clustering, link prediction and visualization tasks on homogeneous graphs strongly support that the proposed model is stable and outperforms various state-of-the-art algorithms.
Second, we analyze how unsupervised tasks can benefit from learned representations in hyperbolic space. To explore how well the hierarchical structure of unlabeled data can be represented in hyperbolic spaces, we design a novel hyperbolic message passing autoencoder whose overall auto-encoding is performed in hyperbolic space. The proposed model conducts auto-encoding the networks via fully utilizing hyperbolic geometry in message passing. Through extensive quantitative and qualitative analyses, we validate the properties and benefits of the unsupervised hyperbolic representations of tree-like graphs.
Third, we propose the novel concept of metanode for message passing to learn both heterogeneous and homogeneous relationships between any two nodes without meta-paths and meta-graphs. Unlike conventional methods, metanodes do not require a predetermined step to manipulate the given relations between different types to enrich relational information. Going one step further, we propose a metanode-based message passing layer and a contrastive learning model using the proposed layer. In our experiments, we show the competitive performance of the proposed metanode-based message passing method on node clustering and node classification tasks, when compared to state-of-the-art methods for message passing networks for heterogeneous graphs.1 Introduction 1
2 Representation Learning on Graph-Structured Data 4
2.1 Basic Introduction 4
2.1.1 Notations 5
2.2 Traditional Approaches 5
2.2.1 Graph Statistic 5
2.2.2 Neighborhood Overlap 7
2.2.3 Graph Kernel 9
2.2.4 Spectral Approaches 10
2.3 Node Embeddings I: Factorization and Random Walks 15
2.3.1 Factorization-based Methods 15
2.3.2 Random Walk-based Methods 16
2.4 Node Embeddings II: Graph Neural Networks 17
2.4.1 Overview of Framework 17
2.4.2 Representative Models 18
2.5 Learning in Unsupervised Environments 21
2.5.1 Predictive Coding 21
2.5.2 Contrastive Coding 22
2.6 Applications 24
2.6.1 Classifications 24
2.6.2 Link Prediction 26
3 Autoencoder Architecture for Homogeneous Graphs 27
3.1 Overview 27
3.2 Preliminaries 30
3.2.1 Spectral Convolution on Graphs 30
3.2.2 Laplacian Smoothing 32
3.3 Methodology 33
3.3.1 Laplacian Sharpening 33
3.3.2 Numerically Stable Laplacian Sharpening 34
3.3.3 Subspace Clustering Cost for Image Clustering 37
3.3.4 Training 39
3.4 Experiments 40
3.4.1 Datasets 40
3.4.2 Experimental Settings 42
3.4.3 Comparing Methods 42
3.4.4 Node Clustering 43
3.4.5 Image Clustering 45
3.4.6 Ablation Studies 46
3.4.7 Link Prediction 47
3.4.8 Visualization 47
3.5 Summary 49
4 Autoencoder Architecture for Tree-like Graphs 50
4.1 Overview 50
4.2 Preliminaries 52
4.2.1 Hyperbolic Embeddings 52
4.2.2 Hyperbolic Geometry 53
4.3 Methodology 55
4.3.1 Geometry-Aware Message Passing 56
4.3.2 Nonlinear Activation 57
4.3.3 Loss Function 58
4.4 Experiments 58
4.4.1 Datasets 59
4.4.2 Compared Methods 61
4.4.3 Experimental Details 62
4.4.4 Node Clustering and Link Prediction 64
4.4.5 Image Clustering 66
4.4.6 Structure-Aware Unsupervised Embeddings 68
4.4.7 Hyperbolic Distance to Filter Training Samples 71
4.4.8 Ablation Studies 74
4.5 Further Discussions 75
4.5.1 Connection to Contrastive Learning 75
4.5.2 Failure Cases of Hyperbolic Embedding Spaces 75
4.6 Summary 77
5 Contrastive Learning for Heterogeneous Graphs 78
5.1 Overview 78
5.2 Preliminaries 82
5.2.1 Meta-path 82
5.2.2 Representation Learning on Heterogeneous Graphs 82
5.2.3 Contrastive methods for Heterogeneous Graphs 83
5.3 Methodology 84
5.3.1 Definitions 84
5.3.2 Metanode-based Message Passing Layer 86
5.3.3 Contrastive Learning Framework 88
5.4 Experiments 89
5.4.1 Experimental Details 90
5.4.2 Node Classification 94
5.4.3 Node Clustering 96
5.4.4 Visualization 96
5.4.5 Effectiveness of Metanodes 97
5.5 Summary 99
6 Conclusions 101λ°
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