Spectral Graph Convolutional Networks (GCNs) are a generalization of convolutional networks to learning on graph-structured data. Applications of spectral GCNs have been successful, but limited to a few problems where the graph is fixed, such as shape correspondence and node classification. In this work, we address this limitation by revisiting a particular family of spectral graph networks, Chebyshev GCNs, showing its efficacy in solving graph classification tasks with a variable graph structure and size. Chebyshev GCNs restrict graphs to have at most one edge between any pair of nodes. To this end, we propose a novel multigraph network that learns from multi-relational graphs. We model learned edges with abstract meaning and experiment with different ways to fuse the representations extracted from annotated and learned edges, achieving competitive results on a variety of chemical classification benchmarks.
Graph embedding is an important approach for graph analysis tasks such as node classification and link prediction. The goal of graph embedding is to find a low dimensional representation of graph nodes that preserves the graph information. Recent methods like Graph Convolutional Network (GCN) try to consider node attributes (if available) besides node relations and learn node embeddings for unsupervised and semi-supervised tasks on graphs. On the other hand, multi-layer graph analysis has been received attention recently. However, the existing methods for multi-layer graph embedding cannot incorporate all available information (like node attributes). Moreover, most of them consider either type of nodes or type of edges, and they do not treat within and between layer edges differently. In this paper, we propose a method called MGCN that utilizes the GCN for multi-layer graphs. MGCN embeds nodes of multi-layer graphs using both within and between layers relations and nodes attributes. We evaluate our method on the semi-supervised node classification task. Experimental results demonstrate the superiority of the proposed method to other multi-layer and single-layer competitors and also show the positive effect of using cross-layer edges.
We consider the question of embedding nodes with similar local neighborhoods together in embedding space, commonly referred to as "role embeddings." We propose RAE, an unsupervised framework that learns role embeddings. It combines a within-node loss function and a graph neural network (GNN) architecture to place nodes with similar local neighborhoods close in embedding space. We also propose a faster way of generating negative examples called neighbor shuffling, which quickly creates negative examples directly within batches. These techniques can be easily combined with existing GNN methods to create unsupervised role embeddings at scale. We then explore role action embeddings, which summarize the non-structural features in a node's neighborhood, leading to better performance on node classification tasks. We find that the model architecture proposed here provides strong performance on both graph and node classification tasks, in some cases competitive with semi-supervised methods.
Semi-supervised node classification in graphs is a fundamental problem in graph mining, and the recently proposed graph neural networks (GNNs) have achieved unparalleled results on this task. Due to their massive success, GNNs have attracted a lot of attention, and many novel architectures have been put forward. In this paper we show that existing evaluation strategies for GNN models have serious shortcomings. We show that using the same train/validation/test splits of the same datasets, as well as making significant changes to the training procedure (e.g. early stopping criteria) precludes a fair comparison of different architectures. We perform a thorough empirical evaluation of four prominent GNN models and show that considering different splits of the data leads to dramatically different rankings of models. Even more importantly, our findings suggest that simpler GNN architectures are able to outperform the more sophisticated ones if the hyperparameters and the training procedure are tuned fairly for all models.
We examine two fundamental tasks associated with graph representation learning: link prediction and node classification. We present a new autoencoder architecture capable of learning a joint representation of local graph structure and available node features for the simultaneous multi-task learning of unsupervised link prediction and semi-supervised node classification. Our simple, yet effective and versatile model is efficiently trained end-to-end in a single stage, whereas previous related deep graph embedding methods require multiple training steps that are difficult to optimize. We provide an empirical evaluation of our model on five benchmark relational, graph-structured datasets and demonstrate significant improvement over three strong baselines for graph representation learning. Reference code and data are available at https://github.com/vuptran/graph-representation-learning
Recent advances in representation learning on graphs, mainly leveraging graph convolutional networks, have brought a substantial improvement on many graph-based benchmark tasks. While novel approaches to learning node embeddings are highly suitable for node classification and link prediction, their application to graph classification (predicting a single label for the entire graph) remains mostly rudimentary, typically using a single global pooling step to aggregate node features or a hand-designed, fixed heuristic for hierarchical coarsening of the graph structure. An important step towards ameliorating this is differentiable graph coarsening---the ability to reduce the size of the graph in an adaptive, data-dependent manner within a graph neural network pipeline, analogous to image downsampling within CNNs. However, the previous prominent approach to pooling has quadratic memory requirements during training and is therefore not scalable to large graphs. Here we combine several recent advances in graph neural network design to demonstrate that competitive hierarchical graph classification results are possible without sacrificing sparsity. Our results are verified on several established graph classification benchmarks, and highlight an important direction for future research in graph-based neural networks.
The Graph Convolutional Network (GCN) model and its variants are powerful graph embedding tools for facilitating classification and clustering on graphs. However, a major challenge is to reduce the complexity of layered GCNs and make them parallelizable and scalable on very large graphs -- state-of the art techniques are unable to achieve scalability without losing accuracy and efficiency. In this paper, we propose novel parallelization techniques for graph sampling-based GCNs that achieve superior scalable performance on very large graphs without compromising accuracy. Specifically, our GCN guarantees work-efficient training and produces order of magnitude savings in computation and communication. To scale GCN training on tightly-coupled shared memory systems, we develop parallelization strategies for the key steps in training: For the graph sampling step, we exploit parallelism within and across multiple sampling instances, and devise an efficient data structure for concurrent accesses that provides theoretical guarantee of near-linear speedup with number of processing units. For the feature propagation step within the sampled graph, we improve cache utilization and reduce DRAM communication by data partitioning. We prove that our partitioning strategy is a 2-approximation for minimizing the communication time compared to the optimal strategy. We demonstrate that our parallel graph embedding outperforms state-of-the-art methods in scalability (with respect to number of processors, graph size and GCN model size), efficiency and accuracy on several large datasets. On a 40-core Xeon platform, our parallel training achieves $64\times$ speedup (with AVX) in the sampling step and $25\times$ speedup in the feature propagation step, compared to the serial implementation, resulting in a net speedup of $21\times$.
Graphs are essential representations of many real-world data such as social networks. Recent years have witnessed the increasing efforts made to extend the neural network models to graph-structured data. These methods, which are usually known as the graph neural networks, have been applied to advance many graphs related tasks such as reasoning dynamics of the physical system, graph classification, and node classification. Most of the existing graph neural network models have been designed for static graphs, while many real-world graphs are inherently dynamic. For example, social networks are naturally evolving as new users joining and new relations being created. Current graph neural network models cannot utilize the dynamic information in dynamic graphs. However, the dynamic information has been proven to enhance the performance of many graph analytic tasks such as community detection and link prediction. Hence, it is necessary to design dedicated graph neural networks for dynamic graphs. In this paper, we propose DGNN, a new {\bf D}ynamic {\bf G}raph {\bf N}eural {\bf N}etwork model, which can model the dynamic information as the graph evolving. In particular, the proposed framework can keep updating node information by capturing the sequential information of edges (interactions), the time intervals between edges and information propagation coherently. Experimental results on various dynamic graphs demonstrate the effectiveness of the proposed framework.
We propose a novel approach for learning node representations in directed graphs, which maintains separate views or embedding spaces for the two distinct node roles induced by the directionality of the edges. We argue that the previous approaches either fail to encode the edge directionality or their encodings cannot be generalized across tasks. With our simple \emph{alternating random walk} strategy, we generate role specific vertex neighborhoods and train node embeddings in their corresponding source/target roles while fully exploiting the semantics of directed graphs. We also unearth the limitations of evaluations on directed graphs in previous works and propose a clear strategy for evaluating link prediction and graph reconstruction in directed graphs. We conduct extensive experiments to showcase our effectiveness on several real-world datasets on link prediction, node classification and graph reconstruction tasks. We show that the embeddings from our approach are indeed robust, generalizable and well performing across multiple kinds of tasks and graphs. We show that we consistently outperform all baselines for node classification task. In addition to providing a theoretical interpretation of our method we also show that we are considerably more robust than the other directed graph approaches.
Following the success of deep convolutional networks in various vision and speech related tasks, researchers have started investigating generalizations of the well-known technique for graph-structured data. A recently-proposed method called Graph Convolutional Networks has been able to achieve state-of-the-art results in the task of node classification. However, since the proposed method relies on localized first-order approximations of spectral graph convolutions, it is unable to capture higher-order interactions between nodes in the graph. In this work, we propose a motif-based graph attention model, called Motif Convolutional Networks (MCNs), which generalizes past approaches by using weighted multi-hop motif adjacency matrices to capture higher-order neighborhoods. A novel attention mechanism is used to allow each individual node to select the most relevant neighborhood to apply its filter. Experiments show that our proposed method is able to achieve state-of-the-art results on the semi-supervised node classification task.
Network representation learning (NRL) methods aim to map each vertex into a low dimensional space by preserving the local and global structure of a given network, and in recent years they have received a significant attention thanks to their success in several challenging problems. Although various approaches have been proposed to compute node embeddings, many successful methods benefit from random walks in order to transform a given network into a collection of sequences of nodes and then they target to learn the representation of nodes by predicting the context of each vertex within the sequence. In this paper, we introduce a general framework to enhance the embeddings of nodes acquired by means of the random walk-based approaches. Similar to the notion of topical word embeddings in NLP, the proposed method assigns each vertex to a topic with the favor of various statistical models and community detection methods, and then generates the enhanced community representations. We evaluate our method on two downstream tasks: node classification and link prediction. The experimental results demonstrate that the incorporation of vertex and topic embeddings outperform widely-known baseline NRL methods.
Neural message passing algorithms for semi-supervised classification on graphs have recently achieved great success. However, for classifying a node these methods only consider nodes that are a few propagation steps away and the size of this utilized neighborhood is hard to extend. In this paper, we use the relationship between graph convolutional networks (GCN) and PageRank to derive an improved propagation scheme based on personalized PageRank. We utilize this propagation procedure to construct a simple model, personalized propagation of neural predictions (PPNP), and its fast approximation, APPNP. Our model's training time is on par or faster and its number of parameters on par or lower than previous models. It leverages a large, adjustable neighborhood for classification and can be easily combined with any neural network. We show that this model outperforms several recently proposed methods for semi-supervised classification in the most thorough study done so far for GCN-like models. Our implementation is available online.
Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs to capture different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance.
Modern data analysis pipelines are becoming increasingly complex due to the presence of multi-view information sources. While graphs are effective in modeling complex relationships, in many scenarios a single graph is rarely sufficient to succinctly represent all interactions, and hence multi-layered graphs have become popular. Though this leads to richer representations, extending solutions from the single-graph case is not straightforward. Consequently, there is a strong need for novel solutions to solve classical problems, such as node classification, in the multi-layered case. In this paper, we consider the problem of semi-supervised learning with multi-layered graphs. Though deep network embeddings, e.g. DeepWalk, are widely adopted for community discovery, we argue that feature learning with random node attributes, using graph neural networks, can be more effective. To this end, we propose to use attention models for effective feature learning, and develop two novel architectures, GrAMME-SG and GrAMME-Fusion, that exploit the inter-layer dependencies for building multi-layered graph embeddings. Using empirical studies on several benchmark datasets, we evaluate the proposed approaches and demonstrate significant performance improvements in comparison to state-of-the-art network embedding strategies. The results also show that using simple random features is an effective choice, even in cases where explicit node attributes are not available.
We present Deep Graph Infomax (DGI), a general approach for learning node representations within graph-structured data in an unsupervised manner. DGI relies on maximizing mutual information between patch representations and corresponding high-level summaries of graphs---both derived using established graph convolutional network architectures. The learnt patch representations summarize subgraphs centered around nodes of interest, and can thus be reused for downstream node-wise learning tasks. In contrast to most prior approaches to unsupervised learning with GCNs, DGI does not rely on random walk objectives, and is readily applicable to both transductive and inductive learning setups. We demonstrate competitive performance on a variety of node classification benchmarks, which at times even exceeds the performance of supervised learning.
Graph convolutional network (GCN) provides a powerful means for graph-based semi-supervised tasks. However, as a localized first-order approximation of spectral graph convolution, the classic GCN can not take full advantage of unlabeled data, especially when the unlabeled node is far from labeled ones. To capitalize on the information from unlabeled nodes to boost the training for GCN, we propose a novel framework named Self-Ensembling GCN (SEGCN), which marries GCN with Mean Teacher - another powerful model in semi-supervised learning. SEGCN contains a student model and a teacher model. As a student, it not only learns to correctly classify the labeled nodes, but also tries to be consistent with the teacher on unlabeled nodes in more challenging situations, such as a high dropout rate and graph collapse. As a teacher, it averages the student model weights and generates more accurate predictions to lead the student. In such a mutual-promoting process, both labeled and unlabeled samples can be fully utilized for backpropagating effective gradients to train GCN. In three article classification tasks, i.e. Citeseer, Cora and Pubmed, we validate that the proposed method matches the state of the arts in the classification accuracy.
Graph Convolutional Networks (GCNs) have become a crucial tool on learning representations of graph vertices. The main challenge of adapting GCNs on large-scale graphs is the scalability issue that it incurs heavy cost both in computation and memory due to the uncontrollable neighborhood expansion across layers. In this paper, we accelerate the training of GCNs through developing an adaptive layer-wise sampling method. By constructing the network layer by layer in a top-down passway, we sample the lower layer conditioned on the top one, where the sampled neighborhoods are shared by different parent nodes and the over expansion is avoided owing to the fixed-size sampling. More importantly, the proposed sampler is adaptive and applicable for explicit variance reduction, which in turn enhances the training of our method. Furthermore, we propose a novel and economical approach to promote the message passing over distant nodes by applying skip connections. Intensive experiments on several benchmarks verify the effectiveness of our method regarding the classification accuracy while enjoying faster convergence speed.
Edge features contain important information about graphs. However, current state-of-the-art neural network models designed for graph learning, e.g. graph convolutional networks (GCN) and graph attention networks (GAT), adequately utilize edge features, especially multi-dimensional edge features. In this paper, we build a new framework for a family of new graph neural network models that can more sufficiently exploit edge features, including those of undirected or multi-dimensional edges. The proposed framework can consolidate current graph neural network models; e.g. graph convolutional networks (GCN) and graph attention networks (GAT). The proposed framework and new models have the following novelties: First, we propose to use doubly stochastic normalization of graph edge features instead of the commonly used row or symmetric normalization approches used in current graph neural networks. Second, we construct new formulas for the operations in each individual layer so that they can handle multi-dimensional edge features. Third, for the proposed new framework, edge features are adaptive across network layers. As a result, our proposed new framework and new models can exploit a rich source of graph information. We apply our new models to graph node classification on several citation networks, whole graph classification, and regression on several molecular datasets. Compared with the current state-of-the-art methods, i.e. GCNs and GAT, our models obtain better performance, which testify to the importance of exploiting edge features in graph neural networks.
Network embedding algorithms are able to learn latent feature representations of nodes, transforming networks into lower dimensional vector representations. Typical key applications, which have effectively been addressed using network embeddings, include link prediction, multilabel classification and community detection. In this paper, we propose BiasedWalk, a scalable, unsupervised feature learning algorithm that is based on biased random walks to sample context information about each node in the network. Our random-walk based sampling can behave as Breath-First-Search (BFS) and Depth-First-Search (DFS) samplings with the goal to capture homophily and role equivalence between the nodes in the network. We have performed a detailed experimental evaluation comparing the performance of the proposed algorithm against various baseline methods, on several datasets and learning tasks. The experiment results show that the proposed method outperforms the baseline ones in most of the tasks and datasets.
Networks are ubiquitous structure that describes complex relationships between different entities in the real world. As a critical component of prediction task over nodes in networks, learning the feature representation of nodes has become one of the most active areas recently. Network Embedding, aiming to learn non-linear and low-dimensional feature representation based on network topology, has been proved to be helpful on tasks of network analysis, especially node classification. For many real-world systems, multiple types of relations are naturally represented by multiple networks. However, existing network embedding methods mainly focus on single network embedding and neglect the information shared among different networks. In this paper, we propose a novel multiple network embedding method based on semisupervised autoencoder, named DeepMNE, which captures complex topological structures of multi-networks and takes the correlation among multi-networks into account. We evaluate DeepMNE on the task of node classification with two real-world datasets. The experimental results demonstrate the superior performance of our method over four state-of-the-art algorithms.