In recent years, substantial progress has been made on Graph Convolutional Networks (GCNs). However, the computing of GCN usually requires a large memory space for keeping the entire graph. In consequence, GCN is not flexible enough, especially for large scale graphs in complex real-world applications. Fortunately, methods based on Matrix Factorization (MF) naturally support constructing mini-batches, and thus are more friendly to distributed computing compared with GCN. Accordingly, in this paper, we analyze the connections between GCN and MF, and simplify GCN as matrix factorization with unitization and co-training. Furthermore, under the guidance of our analysis, we propose an alternative model to GCN named Unitized and Co-training Matrix Factorization (UCMF). Extensive experiments have been conducted on several real-world datasets. On the task of semi-supervised node classification, the experimental results illustrate that UCMF achieves similar or superior performances compared with GCN. Meanwhile, distributed UCMF significantly outperforms distributed GCN methods, which shows that UCMF can greatly benefit large scale and complex real-world applications. Moreover, we have also conducted experiments on a typical task of graph embedding, i.e., community detection, and the proposed UCMF model outperforms several representative graph embedding models.
Graph neural networks have shown superior performance in a wide range of applications providing a powerful representation of graph-structured data. Recent works show that the representation can be further improved by auxiliary tasks. However, the auxiliary tasks for heterogeneous graphs, which contain rich semantic information with various types of nodes and edges, have less explored in the literature. In this paper, to learn graph neural networks on heterogeneous graphs we propose a novel self-supervised auxiliary learning method using meta-paths, which are composite relations of multiple edge types. Our proposed method is learning to learn a primary task by predicting meta-paths as auxiliary tasks. This can be viewed as a type of meta-learning. The proposed method can identify an effective combination of auxiliary tasks and automatically balance them to improve the primary task. Our methods can be applied to any graph neural networks in a plug-in manner without manual labeling or additional data. The experiments demonstrate that the proposed method consistently improves the performance of link prediction and node classification on heterogeneous graphs.
We propose Graph Contrastive Learning (GraphCL), a general framework for learning node representations in a self supervised manner. GraphCL learns node embeddings by maximizing the similarity between the representations of two randomly perturbed versions of the intrinsic features and link structure of the same node's local subgraph. We use graph neural networks to produce two representations of the same node and leverage a contrastive learning loss to maximize agreement between them. In both transductive and inductive learning setups, we demonstrate that our approach significantly outperforms the state-of-the-art in unsupervised learning on a number of node classification benchmarks.
Recently there was an increasing interest in applications of graph neural networks in non-Euclidean geometry; however, are non-Euclidean representations always useful for graph learning tasks? For different problems such as node classification and link prediction we compute hyperbolic embeddings and conclude that for tasks that require global prediction consistency it might be useful to use non-Euclidean embeddings, while for other tasks Euclidean models are superior. To do so we first fix an issue of the existing models associated with the optimization process at zero curvature. Current hyperbolic models deal with gradients at the origin in ad-hoc manner, which is inefficient and can lead to numerical instabilities. We solve the instabilities of kappa-Stereographic model at zero curvature cases and evaluate the approach of embedding graphs into the manifold in several graph representation learning tasks.
In this paper, we present a learning-based approach to determining acceptance of arguments under several abstract argumentation semantics. More specifically, we propose an argumentation graph neural network (AGNN) that learns a message-passing algorithm to predict the likelihood of an argument being accepted. The experimental results demonstrate that the AGNN can almost perfectly predict the acceptability under different semantics and scales well for larger argumentation frameworks. Furthermore, analysing the behaviour of the message-passing algorithm shows that the AGNN learns to adhere to basic principles of argument semantics as identified in the literature, and can thus be trained to predict extensions under the different semantics - we show how the latter can be done for multi-extension semantics by using AGNNs to guide a basic search. We publish our code at https://github.com/DennisCraandijk/DL-Abstract-Argumentation
Node classification in attributed graphs is an important task in multiple practical settings, but it can often be difficult or expensive to obtain labels. Active learning can improve the achieved classification performance for a given budget on the number of queried labels. The best existing methods are based on graph neural networks, but they often perform poorly unless a sizeable validation set of labelled nodes is available in order to choose good hyperparameters. We propose a novel graph-based active learning algorithm for the task of node classification in attributed graphs; our algorithm uses graph cognizant logistic regression, equivalent to a linearized graph convolutional neural network (GCN), for the prediction phase and maximizes the expected error reduction in the query phase. To reduce the delay experienced by a labeller interacting with the system, we derive a preemptive querying system that calculates a new query during the labelling process, and to address the setting where learning starts with almost no labelled data, we also develop a hybrid algorithm that performs adaptive model averaging of label propagation and linearized GCN inference. We conduct experiments on five public benchmark datasets, demonstrating a significant improvement over state-of-the-art approaches and illustrate the practical value of the method by applying it to a private microwave link network dataset.
Embedding nodes of a large network into a metric (e.g., Euclidean) space has become an area of active research in statistical machine learning, which has found applications in natural and social sciences. Generally, a representation of a network object is learned in a Euclidean geometry and is then used for subsequent tasks regarding the nodes and/or edges of the network, such as community detection, node classification and link prediction. Network embedding algorithms have been proposed in multiple disciplines, often with domain-specific notations and details. In addition, different measures and tools have been adopted to evaluate and compare the methods proposed under different settings, often dependent of the downstream tasks. As a result, it is challenging to study these algorithms in the literature systematically. Motivated by the recently proposed Veridical Data Science (VDS) framework, we propose a framework for network embedding algorithms and discuss how the principles of predictability, computability and stability apply in this context. The utilization of this framework in network embedding holds the potential to motivate and point to new directions for future research.
Graph Neural Networks (GNN) have been extensively used to extract meaningful representations from graph structured data and to perform predictive tasks such as node classification and link prediction. In recent years, there has been a lot of work incorporating edge features along with node features for prediction tasks. One of the main difficulties in using edge features is that they are often handcrafted, hard to get, specific to a particular domain, and may contain redundant information. In this work, we present a framework for creating new edge features, applicable to any domain, via a combination of self-supervised and unsupervised learning. In addition to this, we use Forman-Ricci curvature as an additional edge feature to encapsulate the local geometry of the graph. We then encode our edge features via a Set Transformer and combine them with node features extracted from popular GNN architectures for node classification in an end-to-end training scheme. We validate our work on three biological datasets comprising of single-cell RNA sequencing data of neurological disease, \textit{in vitro} SARS-CoV-2 infection, and human COVID-19 patients. We demonstrate that our method achieves better performance on node classification tasks over baseline Graph Attention Network (GAT) and Graph Convolutional Network (GCN) models. Furthermore, given the attention mechanism on edge and node features, we are able to interpret the cell types and genes that determine the course and severity of COVID-19, contributing to a growing list of potential disease biomarkers and therapeutic targets.
Graph Convolutional Network (GCN) has experienced great success in graph analysis tasks. It works by smoothing the node features across the graph. The current GCN models overwhelmingly assume that the node feature information is complete. However, real-world graph data are often incomplete and containing missing features. Traditionally, people have to estimate and fill in the unknown features based on imputation techniques and then apply GCN. However, the process of feature filling and graph learning are separated, resulting in degraded and unstable performance. This problem becomes more serious when a large number of features are missing. We propose an approach that adapts GCN to graphs containing missing features. In contrast to traditional strategy, our approach integrates the processing of missing features and graph learning within the same neural network architecture. Our idea is to represent the missing data by Gaussian Mixture Model (GMM) and calculate the expected activation of neurons in the first hidden layer of GCN, while keeping the other layers of the network unchanged. This enables us to learn the GMM parameters and network weight parameters in an end-to-end manner. Notably, our approach does not increase the computational complexity of GCN and it is consistent with GCN when the features are complete. We demonstrate through extensive experiments that our approach significantly outperforms the imputation-based methods in node classification and link prediction tasks. We show that the performance of our approach for the case with a low level of missing features is even superior to GCN for the case with complete features.
We propose a novel neural network architecture, called autoencoder-constrained graph convolutional network, to solve node classification task on graph domains. As suggested by its name, the core of this model is a convolutional network operating directly on graphs, whose hidden layers are constrained by an autoencoder. Comparing with vanilla graph convolutional networks, the autoencoder step is added to reduce the information loss brought by Laplacian smoothing. We consider applying our model on both homogeneous graphs and heterogeneous graphs. For homogeneous graphs, the autoencoder approximates to the adjacency matrix of the input graph by taking hidden layer representations as encoder and another one-layer graph convolutional network as decoder. For heterogeneous graphs, since there are multiple adjacency matrices corresponding to different types of edges, the autoencoder approximates to the feature matrix of the input graph instead, and changes the encoder to a particularly designed multi-channel pre-processing network with two layers. In both cases, the error occurred in the autoencoder approximation goes to the penalty term in the loss function. In extensive experiments on citation networks and other heterogeneous graphs, we demonstrate that adding autoencoder constraints significantly improves the performance of graph convolutional networks. Further, we notice that our technique can be applied on graph attention network to improve the performance as well. This reveals the wide applicability of the proposed autoencoder technique.
In network representation learning we learn how to represent heterogeneous information networks in a low-dimensional space so as to facilitate effective search, classification, and prediction solutions. Previous network representation learning methods typically require sufficient task-specific labeled data to address domain-specific problems. The trained model usually cannot be transferred to out-of-domain datasets. We propose a self-supervised pre-training and fine-tuning framework, PF-HIN, to capture the features of a heterogeneous information network. Unlike traditional network representation learning models that have to train the entire model all over again for every downstream task and dataset, PF-HIN only needs to fine-tune the model and a small number of extra task-specific parameters, thus improving model efficiency and effectiveness. During pre-training, we first transform the neighborhood of a given node into a sequence. PF-HIN is pre-trained based on two self-supervised tasks, masked node modeling and adjacent node prediction. We adopt deep bi-directional transformer encoders to train the model, and leverage factorized embedding parameterization and cross-layer parameter sharing to reduce the parameters. In the fine-tuning stage, we choose four benchmark downstream tasks, i.e., link prediction, similarity search, node classification, and node clustering. PF-HIN consistently and significantly outperforms state-of-the-art alternatives on each of these tasks, on four datasets.
We present Wiki-CS, a novel dataset derived from Wikipedia for benchmarking Graph Neural Networks. The dataset consists of nodes corresponding to Computer Science articles, with edges based on hyperlinks and 10 classes representing different branches of the field. We use the dataset to evaluate semi-supervised node classification and single-relation link prediction models. Our experiments show that these methods perform well on a new domain, with structural properties different from earlier benchmarks. The dataset is publicly available, along with the implementation of the data pipeline and the benchmark experiments, at https://github.com/pmernyei/wiki-cs-dataset .
Graph embeddings are a ubiquitous tool for machine learning tasks, such as node classification and link prediction, on graph-structured data. However, computing the embeddings for large-scale graphs is prohibitively inefficient even if we are interested only in a small subset of relevant vertices. To address this, we present an efficient graph coarsening approach, based on Schur complements, for computing the embedding of the relevant vertices. We prove that these embeddings are preserved exactly by the Schur complement graph that is obtained via Gaussian elimination on the non-relevant vertices. As computing Schur complements is expensive, we give a nearly-linear time algorithm that generates a coarsened graph on the relevant vertices that provably matches the Schur complement in expectation in each iteration. Our experiments involving prediction tasks on graphs demonstrate that computing embeddings on the coarsened graph, rather than the entire graph, leads to significant time savings without sacrificing accuracy.
We study the problem of node classification on graphs with few-shot novel labels, which has two distinctive properties: (1) There are novel labels to emerge in the graph; (2) The novel labels have only a few representative nodes for training a classifier. The study of this problem is instructive and corresponds to many applications such as recommendations for newly formed groups with only a few users in online social networks. To cope with this problem, we propose a novel Meta Transformed Network Embedding framework (MetaTNE), which consists of three modules: (1) A \emph{structural module} provides each node a latent representation according to the graph structure. (2) A \emph{meta-learning module} captures the relationships between the graph structure and the node labels as prior knowledge in a meta-learning manner. Additionally, we introduce an \emph{embedding transformation function} that remedies the deficiency of the straightforward use of meta-learning. Inherently, the meta-learned prior knowledge can be used to facilitate the learning of few-shot novel labels. (3) An \emph{optimization module} employs a simple yet effective scheduling strategy to train the above two modules with a balance between graph structure learning and meta-learning. Experiments on four real-world datasets show that MetaTNE brings a huge improvement over the state-of-the-art methods.
Graph convolutional networks (GCNs) are a powerful deep learning approach for graph-structured data. Recently, GCNs and subsequent variants have shown superior performance in various application areas on real-world datasets. Despite their success, most of the current GCN models are shallow, due to the {\em over-smoothing} problem. In this paper, we study the problem of designing and analyzing deep graph convolutional networks. We propose the GCNII, an extension of the vanilla GCN model with two simple yet effective techniques: {\em Initial residual} and {\em Identity mapping}. We provide theoretical and empirical evidence that the two techniques effectively relieves the problem of over-smoothing. Our experiments show that the deep GCNII model outperforms the state-of-the-art methods on various semi- and full-supervised tasks. Code is available at https://github.com/chennnM/GCNII .
Graph neural networks (GNNs) have emerged as a powerful approach for solving many network mining tasks. However, learning on large graphs remains a challenge - many recently proposed scalable GNN approaches rely on an expensive message-passing procedure to propagate information through the graph. We present the PPRGo model which utilizes an efficient approximation of information diffusion in GNNs resulting in significant speed gains while maintaining state-of-the-art prediction performance. In addition to being faster, PPRGo is inherently scalable, and can be trivially parallelized for large datasets like those found in industry settings. We demonstrate that PPRGo outperforms baselines in both distributed and single-machine training environments on a number of commonly used academic graphs. To better analyze the scalability of large-scale graph learning methods, we introduce a novel benchmark graph with 12.4 million nodes, 173 million edges, and 2.8 million node features. We show that training PPRGo from scratch and predicting labels for all nodes in this graph takes under 2 minutes on a single machine, far outpacing other baselines on the same graph. We discuss the practical application of PPRGo to solve large-scale node classification problems at Google.
The objective of unsupervised graph representation learning (GRL) is to learn a low-dimensional space of node embeddings that reflect the structure of a given unlabeled graph. Existing algorithms for this task rely on negative sampling objectives that maximize the similarity in node embeddings at nearby nodes (referred to as "cohesion") by maintaining positive and negative corpus of node pairs. While positive samples are drawn from node pairs that co-occur in short random walks, conventional approaches construct negative corpus by uniformly sampling random pairs, thus ignoring valuable information about structural dissimilarity among distant node pairs (referred to as "separation"). In this paper, we present a novel Distance-aware Negative Sampling (DNS) which maximizes the separation of distant node-pairs while maximizing cohesion at nearby node-pairs by setting the negative sampling probability proportional to the pair-wise shortest distances. Our approach can be used in conjunction with any GRL algorithm and we demonstrate the efficacy of our approach over baseline negative sampling methods over downstream node classification tasks on a number of benchmark datasets and GRL algorithms. All our codes and datasets are available at https://github.com/Distance-awareNS/DNS/.
Graph convolutional networks (GCN) have been recently utilized to extract the underlying structures of datasets with some labeled data and high-dimensional features. Existing GCNs mostly rely on a first-order Chebyshev approximation of graph wavelet-kernels. Such a generic propagation model does not always suit the various datasets and their features. This work revisits the fundamentals of graph wavelet and explores the utility of signal propagation in the vertex domain to approximate the spectral wavelet-kernels. We first derive the conditions for representing the graph wavelet-kernels via vertex propagation. We next propose alternative propagation models for GCN layers based on Taylor expansions. We further analyze the choices of detailed graph representations for TGCNs. Experiments on citation networks, multimedia datasets and synthetic graphs demonstrate the advantage of Taylor-based GCN (TGCN) in the node classification problems over the traditional GCN methods.
Graph Neural Networks (GNNs) have achieved state-of-the-art results on many graph analysis tasks such as node classification and link prediction. However, important unsupervised problems on graphs, such as graph clustering, have proved more resistant to advances in GNNs. Graph clustering has the same overall goal as node pooling in GNNs - does this mean that GNN pooling methods do a good job at clustering graphs? Surprisingly, the answer is no - current GNN pooling methods often fail to recover the cluster structure in cases where simple baselines, such as k-means applied on learned representations, work well. We investigate further by carefully designing a set of experiments to study different signal-to-noise scenarios both in graph structure and attribute data. To address these methods' poor performance in clustering, we introduce Deep Modularity Networks (DMoN), an unsupervised pooling method inspired by the modularity measure of clustering quality, and show how it tackles recovery of the challenging clustering structure of real-world graphs. Similarly, on real-world data, we show that DMoN produces high quality clusters which correlate strongly with ground truth labels, achieving state-of-the-art results with over 40% improvement over other pooling methods across different metrics.
Graph data are pervasive in many real-world applications. Recently, increasing attention has been paid on graph neural networks (GNNs), which aim to model the local graph structures and capture the hierarchical patterns by aggregating the information from neighbors with stackable network modules. Motivated by the observation that different nodes often require different iterations of aggregation to fully capture the structural information, in this paper, we propose to explicitly sample diverse iterations of aggregation for different nodes to boost the performance of GNNs. It is a challenging task to develop an effective aggregation strategy for each node, given complex graphs and sparse features. Moreover, it is not straightforward to derive an efficient algorithm since we need to feed the sampled nodes into different number of network layers. To address the above challenges, we propose Policy-GNN, a meta-policy framework that models the sampling procedure and message passing of GNNs into a combined learning process. Specifically, Policy-GNN uses a meta-policy to adaptively determine the number of aggregations for each node. The meta-policy is trained with deep reinforcement learning (RL) by exploiting the feedback from the model. We further introduce parameter sharing and a buffer mechanism to boost the training efficiency. Experimental results on three real-world benchmark datasets suggest that Policy-GNN significantly outperforms the state-of-the-art alternatives, showing the promise in aggregation optimization for GNNs.