Graph Neural Networks (GNNs) have received a lot of interest in the recent times. From the early spectral architectures that could only operate on undirected graphs per a transductive learning paradigm to the current state of the art spatial ones that can apply inductively to arbitrary graphs, GNNs have seen significant contributions from the research community. In this paper, we utilize some theoretical tools to better visualize the operations performed by state of the art spatial GNNs. We analyze the inner workings of these architectures and introduce a simple concept, Node Masking, that allows them to generalize and scale better. To empirically validate the concept, we perform several experiments on some widely-used datasets for node classification in both the transductive and inductive settings, hence laying down strong benchmarks for future research.
In this work, we address semi-supervised classification of graph data, where the categories of those unlabeled nodes are inferred from labeled nodes as well as graph structures. Recent works often solve this problem via advanced graph convolution in a conventionally supervised manner, but the performance could degrade significantly when labeled data is scarce. To this end, we propose a Graph Inference Learning (GIL) framework to boost the performance of semi-supervised node classification by learning the inference of node labels on graph topology. To bridge the connection between two nodes, we formally define a structure relation by encapsulating node attributes, between-node paths, and local topological structures together, which can make the inference conveniently deduced from one node to another node. For learning the inference process, we further introduce meta-optimization on structure relations from training nodes to validation nodes, such that the learnt graph inference capability can be better self-adapted to testing nodes. Comprehensive evaluations on four benchmark datasets (including Cora, Citeseer, Pubmed, and NELL) demonstrate the superiority of our proposed GIL when compared against state-of-the-art methods on the semi-supervised node classification task.
We present Regularized Linear Embedding (RLE), a novel method that projects a collection of linked documents (e.g. citation network) into a pretrained word embedding space. In addition to the textual content, we leverage a matrix of pairwise similarities providing complementary information (e.g., the network proximity of two documents in a citation graph). We first build a simple word vector average for each document, and we use the similarities to alter this average representation. The document representations can help to solve many information retrieval tasks, such as recommendation, classification and clustering. We demonstrate that our approach outperforms or matches existing document network embedding methods on node classification and link prediction tasks. Furthermore, we show that it helps identifying relevant keywords to describe document classes.
The dominant graph neural networks (GNNs) over-rely on the graph links, several serious performance problems with which have been witnessed already, e.g., suspended animation problem and over-smoothing problem. What's more, the inherently inter-connected nature precludes parallelization within the graph, which becomes critical for large-sized graph, as memory constraints limit batching across the nodes. In this paper, we will introduce a new graph neural network, namely GRAPH-BERT (Graph based BERT), solely based on the attention mechanism without any graph convolution or aggregation operators. Instead of feeding GRAPH-BERT with the complete large input graph, we propose to train GRAPH-BERT with sampled linkless subgraphs within their local contexts. GRAPH-BERT can be learned effectively in a standalone mode. Meanwhile, a pre-trained GRAPH-BERT can also be transferred to other application tasks directly or with necessary fine-tuning if any supervised label information or certain application oriented objective is available. We have tested the effectiveness of GRAPH-BERT on several graph benchmark datasets. Based the pre-trained GRAPH-BERT with the node attribute reconstruction and structure recovery tasks, we further fine-tune GRAPH-BERT on node classification and graph clustering tasks specifically. The experimental results have demonstrated that GRAPH-BERT can out-perform the existing GNNs in both the learning effectiveness and efficiency.
Semantic segmentation with deep learning has achieved great progress in classifying the pixels in the image. However, the local location information is usually ignored in the high-level feature extraction by the deep learning, which is important for image semantic segmentation. To avoid this problem, we propose a graph model initialized by a fully convolutional network (FCN) named Graph-FCN for image semantic segmentation. Firstly, the image grid data is extended to graph structure data by a convolutional network, which transforms the semantic segmentation problem into a graph node classification problem. Then we apply graph convolutional network to solve this graph node classification problem. As far as we know, it is the first time that we apply the graph convolutional network in image semantic segmentation. Our method achieves competitive performance in mean intersection over union (mIOU) on the VOC dataset(about 1.34% improvement), compared to the original FCN model.
In this paper, we study a new graph learning problem: learning to count subgraph isomorphisms. Different from other traditional graph learning problems such as node classification and link prediction, subgraph isomorphism counting is NP-complete and requires more global inference to oversee the whole graph. To make it scalable for large-scale graphs and patterns, we propose a learning framework which augments different representation learning architectures and iteratively attends pattern and target data graphs to memorize subgraph isomorphisms for the global counting. We develop both small graphs (<= 1,024 subgraph isomorphisms in each) and large graphs (<= 4,096 subgraph isomorphisms in each) sets to evaluate different models. A mutagenic compound dataset, MUTAG, is also used to evaluate neural models and demonstrate the success of transfer learning. While the learning based approach is inexact, we are able to generalize to count large patterns and data graphs in linear time compared to the exponential time of the original NP-complete problem. Experimental results show that learning based subgraph isomorphism counting can speed up the traditional algorithm, VF2, 10-1,000 times with acceptable errors. Domain adaptation based on fine-tuning also shows the usefulness of our approach in real-world applications.
Knowledge representation of graph-based systems is fundamental across many disciplines. To date, most existing methods for representation learning primarily focus on networks with simplex labels, yet real-world objects (nodes) are inherently complex in nature and often contain rich semantics or labels, e.g., a user may belong to diverse interest groups of a social network, resulting in multi-label networks for many applications. The multi-label network nodes not only have multiple labels for each node, such labels are often highly correlated making existing methods ineffective or fail to handle such correlation for node representation learning. In this paper, we propose a novel multi-label graph convolutional network (ML-GCN) for learning node representation for multi-label networks. To fully explore label-label correlation and network topology structures, we propose to model a multi-label network as two Siamese GCNs: a node-node-label graph and a label-label-node graph. The two GCNs each handle one aspect of representation learning for nodes and labels, respectively, and they are seamlessly integrated under one objective function. The learned label representations can effectively preserve the inner-label interaction and node label properties, and are then aggregated to enhance the node representation learning under a unified training framework. Experiments and comparisons on multi-label node classification validate the effectiveness of our proposed approach.
In this paper, we focus on graph representation learning of heterogeneous information network (HIN), in which various types of vertices are connected by various types of relations. Most of the existing methods conducted on HIN revise homogeneous graph embedding models via meta-paths to learn low-dimensional vector space of HIN. In this paper, we propose a novel Heterogeneous Graph Structural Attention Neural Network (HetSANN) to directly encode structural information of HIN without meta-path and achieve more informative representations. With this method, domain experts will not be needed to design meta-path schemes and the heterogeneous information can be processed automatically by our proposed model. Specifically, we implicitly represent heterogeneous information using the following two methods: 1) we model the transformation between heterogeneous vertices through a projection in low-dimensional entity spaces; 2) afterwards, we apply the graph neural network to aggregate multi-relational information of projected neighborhood by means of attention mechanism. We also present three extensions of HetSANN, i.e., voices-sharing product attention for the pairwise relationships in HIN, cycle-consistency loss to retain the transformation between heterogeneous entity spaces, and multi-task learning with full use of information. The experiments conducted on three public datasets demonstrate that our proposed models achieve significant and consistent improvements compared to state-of-the-art solutions.
In recent years, Graph Convolutional Networks (GCNs) and their variants have been widely utilized in learning tasks that involve graphs. These tasks include recommendation systems, node classification, among many others. In node classification problem, the input is a graph in which the edges represent the association between pairs of nodes, multi-dimensional feature vectors are associated with the nodes, and some of the nodes in the graph have known labels. The objective is to predict the labels of the nodes that are not labeled, using the nodes features, in conjunction with graph topology. While GCNs have been successfully applied to this problem, the caveats that they inherit from traditional deep learning models pose significant challenges to broad utilization of GCNs in node classification. One such caveat is that training a GCN requires a large number of labeled training instances, which is often not the case in realistic settings. To remedy this requirement, state-of-the-art methods leverage network diffusion-based approaches to propagate labels across the network before training GCNs. However, these approaches ignore the tendency of the network diffusion methods in biasing proximity with centrality, resulting in the propagation of labels to the nodes that are well-connected in the graph. To address this problem, here we present an alternate approach to extrapolating node labels in GCNs in the following three steps: (i) clustering of the network to identify communities, (ii) use of network diffusion algorithms to quantify the proximity of each node to the communities, thereby obtaining a low-dimensional topological profile for each node, (iii) comparing these topological profiles to identify nodes that are most similar to the labeled nodes.
The goal of network embedding is to transform nodes in a network to a low-dimensional embedding vectors. Recently, heterogeneous network has shown to be effective in representing diverse information in data. However, heterogeneous network embedding suffers from the imbalance issue, i.e. the size of relation types (or the number of edges in the network regarding the type) is imbalanced. In this paper, we devise a new heterogeneous network embedding method, called BHIN2vec, which considers the balance among all relation types in a network. We view the heterogeneous network embedding as simultaneously solving multiple tasks in which each task corresponds to each relation type in a network. After splitting the skip-gram loss into multiple losses corresponding to different tasks, we propose a novel random-walk strategy to focus on the tasks with high loss values by considering the relative training ratio. Unlike previous random walk strategies, our proposed random-walk strategy generates training samples according to the relative training ratio among different tasks, which results in a balanced training for the node embedding. Our extensive experiments on node classification and recommendation demonstrate the superiority of BHIN2vec compared to the state-of-the-art methods. Also, based on the relative training ratio, we analyze how much each relation type is represented in the embedding space.
Graph embedding has become a key component of many data mining and analysis systems. Current graph embedding approaches either sample a large number of node pairs from a graph to learn node embeddings via stochastic optimization or factorize a high-order proximity/adjacency matrix of the graph via computationally expensive matrix factorization techniques. These approaches typically require significant resources for the learning process and rely on multiple parameters, which limits their applicability in practice. Moreover, most of the existing graph embedding techniques operate effectively in one specific metric space only (e.g., the one produced with cosine similarity), do not preserve higher-order structural features of the input graph and cannot automatically determine a meaningful number of embedding dimensions. Typically, the produced embeddings are not easily interpretable, which complicates further analyses and limits their applicability. To address these issues, we propose DAOR, a highly efficient and parameter-free graph embedding technique producing metric space-robust, compact and interpretable embeddings without any manual tuning. Compared to a dozen state-of-the-art graph embedding algorithms, DAOR yields competitive results on both node classification (which benefits form high-order proximity) and link prediction (which relies on low-order proximity mostly). Unlike existing techniques, however, DAOR does not require any parameter tuning and improves the embeddings generation speed by several orders of magnitude. Our approach has hence the ambition to greatly simplify and speed up data analysis tasks involving graph representation learning.
In clinical practice, human radiologists actually review medical images with high resolution monitors and zoom into region of interests (ROIs) for a close-up examination. Inspired by this observation, we propose a hierarchical graph neural network to detect abnormal lesions from medical images by automatically zooming into ROIs. We focus on mammogram analysis for breast cancer diagnosis for this study. Our proposed network consist of two graph attention networks performing two tasks: (1) node classification to predict whether to zoom into next level; (2) graph classification to classify whether a mammogram is normal/benign or malignant. The model is trained and evaluated on INbreast dataset and we obtain comparable AUC with state-of-the-art methods.
This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can be viewed as a specific discretisation scheme. The key idea is how to characterise the continuous dynamics of node representations, i.e. the derivatives of node representations, w.r.t. time. Inspired by existing diffusion-based methods on graphs (e.g. PageRank and epidemic models on social networks), we define the derivatives as a combination of the current node representations, the representations of neighbors, and the initial values of the nodes. We propose and analyse two possible dynamics on graphs---including each dimension of node representations (a.k.a. the feature channel) change independently or interact with each other---both with theoretical justification. The proposed continuous graph neural networks are robust to over-smoothing and hence allow us to build deeper networks, which in turn are able to capture the long-range dependencies between nodes. Experimental results on the task of node classification demonstrate the effectiveness of our proposed approach over competitive baselines.
Graph Neural Networks (GNNs) have proved to be an effective representation learning framework for graph-structured data, and have achieved state-of-the-art performance on many practical predictive tasks, such as node classification, link prediction and graph classification. Among the variants of GNNs, Graph Attention Networks (GATs) learn to assign dense attention coefficients over all neighbors of a node for feature aggregation, and improve the performance of many graph learning tasks. However, real-world graphs are often very large and noisy, and GATs are prone to overfitting if not regularized properly. Even worse, the local aggregation mechanism of GATs may fail on disassortative graphs, where nodes within local neighborhood provide more noise than useful information for feature aggregation. In this paper, we propose Sparse Graph Attention Networks (SGATs) that learn sparse attention coefficients under an $L_0$-norm regularization, and the learned sparse attentions are then used for all GNN layers, resulting in an edge-sparsified graph. By doing so, we can identify noisy/task-irrelevant edges, and thus perform feature aggregation on most informative neighbors. Extensive experiments on synthetic and real-world graph learning benchmarks demonstrate the superior performance of SGATs. In particular, SGATs can remove about 50\%-80\% edges from large assortative graphs, while retaining similar classification accuracies. On disassortative graphs, SGATs prune majority of noisy edges and outperform GATs in classification accuracies by significant margins. Furthermore, the removed edges can be interpreted intuitively and quantitatively. To the best of our knowledge, this is the first graph learning algorithm that shows significant redundancies in graphs and edge-sparsified graphs can achieve similar or sometimes higher predictive performances than original graphs.
Graph embedding methods transform high-dimensional and complex graph contents into low-dimensional representations. They are useful for a wide range of graph analysis tasks including link prediction, node classification, recommendation and visualization. Most existing approaches represent graph nodes as point vectors in a low-dimensional embedding space, ignoring the uncertainty present in the real-world graphs. Furthermore, many real-world graphs are large-scale and rich in content (e.g. node attributes). In this work, we propose GLACE, a novel, scalable graph embedding method that preserves both graph structure and node attributes effectively and efficiently in an end-to-end manner. GLACE effectively models uncertainty through Gaussian embeddings, and supports inductive inference of new nodes based on their attributes. In our comprehensive experiments, we evaluate GLACE on real-world graphs, and the results demonstrate that GLACE significantly outperforms state-of-the-art embedding methods on multiple graph analysis tasks.
Architecture design has become a crucial component of successful deep learning. Recent progress in automatic neural architecture search (NAS) shows a lot of promise. However, discovered architectures often fail to generalize in the final evaluation. Architectures with a higher validation accuracy during the search phase may perform worse in the evaluation. Aiming to alleviate this common issue, we introduce sequential greedy architecture search (SGAS), an efficient method for neural architecture search. By dividing the search procedure into sub-problems, SGAS chooses and prunes candidate operations in a greedy fashion. We apply SGAS to search architectures for Convolutional Neural Networks (CNN) and Graph Convolutional Networks (GCN). Extensive experiments show that SGAS is able to find state-of-the-art architectures for tasks such as image classification, point cloud classification and node classification in protein-protein interaction graphs with minimal computational cost. Please visit https://www.deepgcns.org/auto/sgas for more information about SGAS.
Graph is a natural representation of data for a variety of real-word applications, such as knowledge graph mining, social network analysis and biological network comparison. For these applications, graph embedding is crucial as it provides vector representations of the graph. One limitation of existing graph embedding methods is that their embedding optimization procedures are disconnected from the target application. In this paper, we propose a novel approach, namely Customized Graph Embedding (CGE) to tackle this problem. The CGE algorithm learns customized vector representations of graph nodes by differentiating the importance of distinct graph paths automatically for a specific application. Extensive experiments were carried out on a diverse set of node classification datasets, which demonstrate strong performances of CGE and provide deep insights into the model.
Representing networks in a low dimensional latent space is a crucial task with many interesting applications in graph learning problems, such as link prediction and node classification. A widely applied network representation learning paradigm is based on the combination of random walks for sampling context nodes and the traditional \textit{Skip-Gram} model to capture center-context node relationships. In this paper, we emphasize on exponential family distributions to capture rich interaction patterns between nodes in random walk sequences. We introduce the generic \textit{exponential family graph embedding} model, that generalizes random walk-based network representation learning techniques to exponential family conditional distributions. We study three particular instances of this model, analyzing their properties and showing their relationship to existing unsupervised learning models. Our experimental evaluation on real-world datasets demonstrates that the proposed techniques outperform well-known baseline methods in two downstream machine learning tasks.
Graph representation learning is to learn universal node representations that preserve both node attributes and structural information. The derived node representations can be used to serve various downstream tasks, such as node classification and node clustering. When a graph is heterogeneous, the problem becomes more challenging than the homogeneous graph node learning problem. Inspired by the emerging information theoretic-based learning algorithm, in this paper we propose an unsupervised graph neural network Heterogeneous Deep Graph Infomax (HDGI) for heterogeneous graph representation learning. We use the meta-path structure to analyze the connections involving semantics in heterogeneous graphs and utilize graph convolution module and semantic-level attention mechanism to capture local representations. By maximizing local-global mutual information, HDGI effectively learns high-level node representations that can be utilized in downstream graph-related tasks. Experiment results show that HDGI remarkably outperforms state-of-the-art unsupervised graph representation learning methods on both classification and clustering tasks. By feeding the learned representations into a parametric model, such as logistic regression, we even achieve comparable performance in node classification tasks when comparing with state-of-the-art supervised end-to-end GNN models.
Graph Neural Networks (GNN) have been shown to work effectively for modeling graph structured data to solve tasks such as node classification, link prediction and graph classification. There has been some recent progress in defining the notion of pooling in graphs whereby the model tries to generate a graph level representation by downsampling and summarizing the information present in the nodes. Existing pooling methods either fail to effectively capture the graph substructure or do not easily scale to large graphs. In this work, we propose ASAP (Adaptive Structure Aware Pooling), a sparse and differentiable pooling method that addresses the limitations of previous graph pooling architectures. ASAP utilizes a novel self-attention network along with a modified GNN formulation to capture the importance of each node in a given graph. It also learns a sparse soft cluster assignment for nodes at each layer to effectively pool the subgraphs to form the pooled graph. Through extensive experiments on multiple datasets and theoretical analysis, we motivate our choice of the components used in ASAP. Our experimental results show that combining existing GNN architectures with ASAP leads to state-of-the-art results on multiple graph classification benchmarks. ASAP has an average improvement of 4%, compared to current sparse hierarchical state-of-the-art method.