An Attention-based Collaboration Framework for Multi-View Network Representation Learning

Learning distributed node representations in networks has been attracting increasing attention recently due to its effectiveness in a variety of applications. Existing approaches usually study networks with a single type of proximity between nodes, which defines a single view of a network. However, in reality there usually exists multiple types of proximities between nodes, yielding networks with multiple views. This paper studies learning node representations for networks with multiple views, which aims to infer robust node representations across different views. We propose a multi-view representation learning approach, which promotes the collaboration of different views and lets them vote for the robust representations. During the voting process, an attention mechanism is introduced, which enables each node to focus on the most informative views. Experimental results on real-world networks show that the proposed approach outperforms existing state-of-the-art approaches for network representation learning with a single view and other competitive approaches with multiple views.Comment: CIKM 201

동종, 이종, 그리고 나무 형태의 그래프를 위한 비지도 표현 학습

학위논문(박사) -- 서울대학교대학원 : 공과대학 전기·정보공학부, 2022. 8. 최진영.그래프 데이터에 대한 비지도 표현 학습의 목적은 그래프의 구조와 노드의 속성을 잘 반영하는 유용한 노드 단위 혹은 그래프 단위의 벡터 형태 표현을 학습하는 것이다. 최근, 그래프 데이터에 대해 강력한 표현 학습 능력을 갖춘 그래프 신경망을 활용한 비지도 그래프 표현 학습 모델의 설계가 주목을 받고 있다. 많은 방법들은 한 종류의 엣지와 한 종류의 노드가 존재하는 동종 그래프에 대한 학습에 집중을 한다. 하지만 이 세상에 수많은 종류의 관계가 존재하기 때문에, 그래프 또한 구조적, 의미론적 속성을 통해 다양한 종류로 분류할 수 있다. 그래서, 그래프로부터 유용한 표현을 학습하기 위해서는 비지도 학습 프레임워크는 입력 그래프의 특징을 제대로 고려해야만 한다. 본 학위논문에서 우리는 널리 접할 수 있는 세가지 그래프 구조인 동종 그래프, 트리 형태의 그래프, 그리고 이종 그래프에 대한 그래프 신경망을 활용하는 비지도 학습 모델들을 제안한다. 처음으로, 우리는 동종 그래프의 노드에 대하여 저차원 표현을 학습하는 그래프 컨볼루션 오토인코더 모델을 제안한다. 기존의 그래프 오토인코더는 구조의 전체가 학습이 불가능해서 제한적인 표현 학습 능력을 가질 수 있는 반면에, 제안하는 오토인코더는 노드의 피쳐를 복원하며,구조의 전체가 학습이 가능하다. 노드의 피쳐를 복원하기 위해서, 우리는 인코더 부분의 역할이 이웃한 노드끼리 유사한 표현을 가지게 하는 라플라시안 스무딩이라는 것에 주목하여 디코더 부분에서는 이웃 노드의 표현과 멀어지게 하는 라플라시안 샤프닝을 하도록 설계하였다. 또한 라플라시안 샤프닝을 그대로 적용하면 불안정성을 유발할 수 있기 때문에, 엣지의 가중치 값에 음의 값을 줄 수 있는 부호형 그래프를 활용하여 안정적인 라플라시안 샤프닝의 형태를 제안하였다. 동종 그래프에 대한 노드 클러스터링과 링크 예측 실험을 통하여 제안하는 방법이 안정적으로 우수한 성능을 보임을 확인하였다. 둘째로, 우리는 트리의 형태를 가지는 계층적인 관계를 가지고 있는 그래프의 노드 표현을 정확하게 학습하기 위하여 쌍곡선 공간에서 동작하는 오토인코더 모델을 제안한다. 유클리디언 공간은 트리를 사상하기에 부적절하다는 최근의 분석을 통하여, 쌍곡선 공간에서 그래프 신경망의 레이어를 활용하여 노드의 저차원 표현을 학습하게 된다. 이 때, 그래프 신경망이 쌍곡선 기하학에서 계층 정보를 담고 있는 거리의 값을 활용하여 노드의 이웃사이의 중요도를 활용하도록 설계하였다. 우리는 논문 인용 관계 네트워크, 계통도, 이미지 사이의 네트워크등에 대해 제안한 모델을 적용하여 노드 클러스터링과 링크 예측 실험을 하였으며, 트리의 형태를 가지는 그래프에 대해서 제안한 모델이 유클리디언 공간에서 수행하는 모델에 비해 향상된 성능을 보였다는 것을 확인하였다. 마지막으로, 우리는 여러 종류의 노드와 엣지를 가지는 이종그래프에 대한 대조 학습 모델을 제안한다. 우리는 기존의 방법들이 학습하기 이전에 충분한 도메인 지식을 사용하여 설계한 메타패스나 메타그래프에 의존한다는 단점과 많은 이종그래프의 엣지가 다른 노드 종류사이의 관계에 집중하고 있다는 점을 주목하였다. 이를 통해 우리는 사전과정이 필요없으며 다른 종류 사이의 관계에 더하여 같은 종류 사이의 관계도 동시에 효율적으로 학습하게 하는 메타노드라는 개념을 제안하였다. 또한 메타노드를 기반으로하는 그래프 신경망과 대조 학습 모델을 제안하였다. 우리는 제안한 모델을 메타패스를 사용하는 이종그래프 학습 모델과 노드 클러스터링 등의 실험 성능으로 비교해보았을 때, 비등하거나 높은 성능을 보였음을 확인하였다.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 101박

No Pattern, No Recognition: a Survey about Reproducibility and Distortion Issues of Text Clustering and Topic Modeling

Extracting knowledge from unlabeled texts using machine learning algorithms can be complex. Document categorization and information retrieval are two applications that may benefit from unsupervised learning (e.g., text clustering and topic modeling), including exploratory data analysis. However, the unsupervised learning paradigm poses reproducibility issues. The initialization can lead to variability depending on the machine learning algorithm. Furthermore, the distortions can be misleading when regarding cluster geometry. Amongst the causes, the presence of outliers and anomalies can be a determining factor. Despite the relevance of initialization and outlier issues for text clustering and topic modeling, the authors did not find an in-depth analysis of them. This survey provides a systematic literature review (2011-2022) of these subareas and proposes a common terminology since similar procedures have different terms. The authors describe research opportunities, trends, and open issues. The appendices summarize the theoretical background of the text vectorization, the factorization, and the clustering algorithms that are directly or indirectly related to the reviewed works

Diagnosis of Autism Spectrum Disorder Based on Brain Network Clustering

Developments in magnetic resonance imaging (MRI) provide new non-invasive approach—functional MRI (fMRI)—to study functions of brain. With the help of fMRI, I can build functional brain networks (FBN) to model correlations of brain activities between cortical regions. Studies focused on brain diseases, including autism spectrum disorder (ASD), have been conducted based on analyzing alterations in FBNs of patients. New biomarkers are identified, and new theories and assumptions are proposed on pathology of brain diseases. Considering that traditional clinical ASD diagnosis instruments, which greatly rely on interviews and observations, can yield large variance, recent studies start to combine machine learning methods and FBN to perform auto-classification of ASD. Such studies have achieved relatively good accuracy. However, in most of these studies, features they use are extracted from the whole brain networks thus the dimension of the features can be high. High-dimensional features may yield overfitting issues and increase computational complexity. Therefore, I need a feature selection strategy that effectively reduces feature dimensions while keeping a good classification performance. In this study, I present a new feature selection strategy that extracting features from functional modules but not the whole brain networks. I will show that my strategy not only reduces feature dimensions, but also improve performances of auto-classifications of ASD. The whole study can be separated into 4 stages: building FBNs, identification of functional modules, statistical analysis of modular alterations and, finally, training classifiers with modular features for auto-classification of ASD. I firstly demonstrate the whole procedure to build FBNs from fMRI images. To identify functional module, I propose a new network clustering algorithm based on joint non-negative matrix factorization. Different from traditional brain network clustering algorithms that mostly perform on an average network of all subjects, I design my algorithm to factorize multiple brain networks simultaneously because the clustering results should be valid not only on the average network but also on each individual network. I show the modules I find are more valid in both views. Then I statistically analyze the alterations in functional modules between ASD and typically developed (TD) group to determine from which modules I extract features from. Several indices based on graph theory are calculated to measure modular properties. I find significant alterations in two modules. With features from these two modules, I train several widely-used classifiers and validate the classifiers on a real-world dataset. The performances of classifiers trained by modular features are better than those with whole-brain features, which demonstrates the effectiveness of my feature selection strategy

Innovative Algorithms and Evaluation Methods for Biological Motif Finding

Biological motifs are defined as overly recurring sub-patterns in biological systems. Sequence motifs and network motifs are the examples of biological motifs. Due to the wide range of applications, many algorithms and computational tools have been developed for efficient search for biological motifs. Therefore, there are more computationally derived motifs than experimentally validated motifs, and how to validate the biological significance of the ‘candidate motifs’ becomes an important question. Some of sequence motifs are verified by their structural similarities or their functional roles in DNA or protein sequences, and stored in databases. However, biological role of network motifs is still invalidated and currently no databases exist for this purpose. In this thesis, we focus not only on the computational efficiency but also on the biological meanings of the motifs. We provide an efficient way to incorporate biological information with clustering analysis methods: For example, a sparse nonnegative matrix factorization (SNMF) method is used with Chou-Fasman parameters for the protein motif finding. Biological network motifs are searched by various clustering algorithms with Gene ontology (GO) information. Experimental results show that the algorithms perform better than existing algorithms by producing a larger number of high-quality of biological motifs. In addition, we apply biological network motifs for the discovery of essential proteins. Essential proteins are defined as a minimum set of proteins which are vital for development to a fertile adult and in a cellular life in an organism. We design a new centrality algorithm with biological network motifs, named MCGO, and score proteins in a protein-protein interaction (PPI) network to find essential proteins. MCGO is also combined with other centrality measures to predict essential proteins using machine learning techniques. We have three contributions to the study of biological motifs through this thesis; 1) Clustering analysis is efficiently used in this work and biological information is easily integrated with the analysis; 2) We focus more on the biological meanings of motifs by adding biological knowledge in the algorithms and by suggesting biologically related evaluation methods. 3) Biological network motifs are successfully applied to a practical application of prediction of essential proteins

Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure