Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved superior performance in tasks such as node classification. However, analyzing heterogeneous graph of different types of nodes and links still brings great challenges for injecting the heterogeneity into a graph neural network. A general remedy is to manually or automatically design meta-paths to transform a heterogeneous graph into a homogeneous graph, but this is suboptimal since the features from the first-order neighbors are not fully leveraged for training and inference. In this paper, we propose simple and effective graph neural networks for heterogeneous graph, excluding the use of meta-paths. Specifically, our models focus on relaxing the heterogeneity stress for model parameters by expanding model capacity of general GNNs in an effective way. Extensive experimental results on six real-world graphs not only show the superior performance of our proposed models over the state-of-the-arts, but also demonstrate the potentially good balance between reducing the heterogeneity stress and increasing the parameter size. Our code is freely available for reproducing our results.
In this paper, we introduce InstantEmbedding, an efficient method for generating single-node representations using local PageRank computations. We theoretically prove that our approach produces globally consistent representations in sublinear time. We demonstrate this empirically by conducting extensive experiments on real-world datasets with over a billion edges. Our experiments confirm that InstantEmbedding requires drastically less computation time (over 9,000 times faster) and less memory (by over 8,000 times) to produce a single node's embedding than traditional methods including DeepWalk, node2vec, VERSE, and FastRP. We also show that our method produces high quality representations, demonstrating results that meet or exceed the state of the art for unsupervised representation learning on tasks like node classification and link prediction.
Graphs have been widely adopted to denote structural connections between entities. The relations are in many cases heterogeneous, but entangled together and denoted merely as a single edge between a pair of nodes. For example, in a social network graph, users in different latent relationships like friends and colleagues, are usually connected via a bare edge that conceals such intrinsic connections. In this paper, we introduce a novel graph convolutional network (GCN), termed as factorizable graph convolutional network(FactorGCN), that explicitly disentangles such intertwined relations encoded in a graph. FactorGCN takes a simple graph as input, and disentangles it into several factorized graphs, each of which represents a latent and disentangled relation among nodes. The features of the nodes are then aggregated separately in each factorized latent space to produce disentangled features, which further leads to better performances for downstream tasks. We evaluate the proposed FactorGCN both qualitatively and quantitatively on the synthetic and real-world datasets, and demonstrate that it yields truly encouraging results in terms of both disentangling and feature aggregation. Code is publicly available at https://github.com/ihollywhy/FactorGCN.PyTorch.
Existing Graph Neural Network (GNN) methods that learn inductive unsupervised graph representations focus on learning node and edge representations by predicting observed edges in the graph. Although such approaches have shown advances in downstream node classification tasks, they are ineffective in jointly representing larger $k$-node sets, $k{>}2$. We propose MHM-GNN, an inductive unsupervised graph representation approach that combines joint $k$-node representations with energy-based models (hypergraph Markov networks) and GNNs. To address the intractability of the loss that arises from this combination, we endow our optimization with a loss upper bound using a finite-sample unbiased Markov Chain Monte Carlo estimator. Our experiments show that the unsupervised MHM-GNN representations of MHM-GNN produce better unsupervised representations than existing approaches from the literature.
The lack of anisotropic kernels in graph neural networks (GNNs) strongly limits their expressiveness, contributing to well-known issues such as over-smoothing. To overcome this limitation, we propose the first globally consistent anisotropic kernels for GNNs, allowing for graph convolutions that are defined according to topologicaly-derived directional flows. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then, we propose the use of the Laplacian eigenvectors as such vector field. We show that the method generalizes CNNs on an $n$-dimensional grid and is provably more discriminative than standard GNNs regarding the Weisfeiler-Lehman 1-WL test. We evaluate our method on different standard benchmarks and see a relative error reduction of 8% on the CIFAR10 graph dataset and 11% to 32% on the molecular ZINC dataset, and a relative increase in precision of 1.6% on the MolPCBA dataset. An important outcome of this work is that it enables graph networks to embed directions in an unsupervised way, thus allowing a better representation of the anisotropic features in different physical or biological problems.
Knowledge Graphs (KG) are of vital importance for multiple applications on the web, including information retrieval, recommender systems, and metadata annotation. Regardless of whether they are built manually by domain experts or with automatic pipelines, KGs are often incomplete. Recent work has begun to explore the use of textual descriptions available in knowledge graphs to learn vector representations of entities in order to preform link prediction. However, the extent to which these representations learned for link prediction generalize to other tasks is unclear. This is important given the cost of learning such representations. Ideally, we would prefer representations that do not need to be trained again when transferring to a different task, while retaining reasonable performance. In this work, we propose a holistic evaluation protocol for entity representations learned via a link prediction objective. We consider the inductive link prediction and entity classification tasks, which involve entities not seen during training. We also consider an information retrieval task for entity-oriented search. We evaluate an architecture based on a pretrained language model, that exhibits strong generalization to entities not observed during training, and outperforms related state-of-the-art methods (22% MRR improvement in link prediction on average). We further provide evidence that the learned representations transfer well to other tasks without fine-tuning. In the entity classification task we obtain an average improvement of 16% in accuracy compared with baselines that also employ pre-trained models. In the information retrieval task, we obtain significant improvements of up to 8.8% in NDCG@10 for natural language queries. We thus show that the learned representations are not limited KG-specific tasks, and have greater generalization properties than evaluated in previous work.
Graph Representation Learning (GRL) has become a key paradigm in network analysis, with a plethora of interdisciplinary applications. As the scale of networks increases, most of the widely used learning-based graph representation models also face computational challenges. While there is a recent effort toward designing algorithms that solely deal with scalability issues, most of them behave poorly in terms of accuracy on downstream tasks. In this paper, we aim to study models that balance the trade-off between efficiency and accuracy. In particular, we propose NodeSig, a scalable model that computes binary node representations. NodeSig exploits random walk diffusion probabilities via stable random projections towards efficiently computing embeddings in the Hamming space. Our extensive experimental evaluation on various networks has demonstrated that the proposed model achieves a good balance between accuracy and efficiency compared to well-known baseline models on the node classification and link prediction tasks.
Self-attention mechanism in graph neural networks (GNNs) led to state-of-the-art performance on many graph representation learning tasks. Currently, at every layer, attention is computed between connected pairs of nodes and depends solely on the representation of the two nodes. However, such attention mechanism does not account for nodes that are not directly connected but provide important network context. Here we propose Multi-hop Attention Graph Neural Network (MAGNA), a principled way to incorporate multi-hop context information into every layer of attention computation. MAGNA diffuses the attention scores across the network, which increases the receptive field for every layer of the GNN. Unlike previous approaches, MAGNA uses a diffusion prior on attention values, to efficiently account for all paths between the pair of disconnected nodes. We demonstrate in theory and experiments that MAGNA captures large-scale structural information in every layer, and has a low-pass effect that eliminates noisy high-frequency information from graph data. Experimental results on node classification as well as the knowledge graph completion benchmarks show that MAGNA achieves state-of-the-art results: MAGNA achieves up to 5.7 percent relative error reduction over the previous state-of-the-art on Cora, Citeseer, and Pubmed. MAGNA also obtains the best performance on a large-scale Open Graph Benchmark dataset. On knowledge graph completion MAGNA advances state-of-the-art on WN18RR and FB15k-237 across four different performance metrics.
Graph Neural Networks (GNNs), a generalization of neural networks to graph-structured data, are often implemented using message passes between entities of a graph. While GNNs are effective for node classification, link prediction and graph classification, they are vulnerable to adversarial attacks, i.e., a small perturbation to the structure can lead to a non-trivial performance degradation. In this work, we propose Uncertainty Matching GNN (UM-GNN), that is aimed at improving the robustness of GNN models, particularly against poisoning attacks to the graph structure, by leveraging epistemic uncertainties from the message passing framework. More specifically, we propose to build a surrogate predictor that does not directly access the graph structure, but systematically extracts reliable knowledge from a standard GNN through a novel uncertainty-matching strategy. Interestingly, this uncoupling makes UM-GNN immune to evasion attacks by design, and achieves significantly improved robustness against poisoning attacks. Using empirical studies with standard benchmarks and a suite of global and target attacks, we demonstrate the effectiveness of UM-GNN, when compared to existing baselines including the state-of-the-art robust GCN.
We introduce an unsupervised graph embedding that trades off local node similarity and connectivity, and global structure. The embedding is based on a generalized graph Laplacian, whose eigenvectors compactly capture both network structure and neighborhood proximity in a single representation. The key idea is to transform the given graph into one whose weights measure the centrality of an edge by the fraction of the number of shortest paths that pass through that edge, and employ its spectral proprieties in the representation. Testing the resulting graph network representation shows significant improvement over the sate of the art in data analysis tasks including social networks and material science. We also test our method on node classification from the human-SARS CoV-2 protein-protein interactome.
Graph convolutional neural networks (GCNNs) have been widely used in graph learning. It has been observed that the smoothness functional on graphs can be defined in terms of the graph Laplacian. This fact points out in the direction of using Laplacian in deriving regularization operators on graphs and its consequent use with spectral GCNN filter designs. In this work, we explore the regularization properties of graph Laplacian and proposed a generalized framework for regularized filter designs in spectral GCNNs. We found that the filters used in many state-of-the-art GCNNs can be derived as a special case of the framework we developed. We designed new filters that are associated with well-defined regularization behavior and tested their performance on semi-supervised node classification tasks. Their performance was found to be superior to that of the other state-of-the-art techniques.
The nodes of a graph existing in a cluster are more likely to connect to each other than with other nodes in the graph. Then revealing some information about some nodes, the structure of the graph (graph edges) provides this opportunity to know more information about other nodes. From this perspective, this paper revisits the node classification task in a semi-supervised scenario by graph convolutional networks (GCNs). The goal is to benefit from the flow of information that circulates around the revealed node labels. The contribution of this paper is twofold. First, this paper provides a method for extracting side information from a graph realization. Then a new GCN architecture is presented that combines the output of traditional GCN and the extracted side information. Another contribution of this paper is relevant to non-graph observations (independent side information) that exists beside a graph realization in many applications. Indeed, the extracted side information can be replaced by a sequence of side information that is independent of the graph structure. For both cases, the experiments on synthetic and real-world datasets demonstrate that the proposed model achieves a higher prediction accuracy in comparison to the existing state-of-the-art methods for the node classification task.
Learning embeddings from large-scale networks is an open challenge. Despite the overwhelming number of existing methods, is is unclear how to exploit network structure in a way that generalizes easily to unseen nodes, edges or graphs. In this work, we look at the problem of finding inductive network embeddings in large networks without domain-dependent node/edge attributes. We propose to use a set of basic predefined local encodings as the basis of a learning algorithm. In particular, we consider the degree frequencies at different distances from a node, which can be computed efficiently for relatively short distances and a large number of nodes. Interestingly, the resulting embeddings generalize well across unseen or distant regions in the network, both in unsupervised settings, when combined with language model learning, as well as in supervised tasks, when used as additional features in a neural network. Despite its simplicity, this method achieves state-of-the-art performance in tasks such as role detection, link prediction and node classification, and represents an inductive network embedding method directly applicable to large unattributed networks.
Network embedding is a highly effective method to learn low-dimensional node vector representations with original network structures being well preserved. However, existing network embedding algorithms are mostly developed for a single network, which fail to learn generalized feature representations across different networks. In this paper, we study a cross-network node classification problem, which aims at leveraging the abundant labeled information from a source network to help classify the unlabeled nodes in a target network. To succeed in such a task, transferable features should be learned for nodes across different networks. To this end, a novel cross-network deep network embedding (CDNE) model is proposed to incorporate domain adaptation into deep network embedding so as to learn label-discriminative and network-invariant node vector representations. On one hand, CDNE leverages network structures to capture the proximities between nodes within a network, by mapping more strongly connected nodes to have more similar latent vector representations. On the other hand, node attributes and labels are leveraged to capture the proximities between nodes across different networks by making the same labeled nodes across networks have aligned latent vector representations. Extensive experiments have been conducted, demonstrating that the proposed CDNE model significantly outperforms the state-of-the-art network embedding algorithms in cross-network node classification.
Graph convolutional networks (GCNs) have achieved promising performance on various graph-based tasks. However they suffer from over-smoothing when stacking more layers. In this paper, we present a quantitative study on this observation and develop novel insights towards the deeper GCN. First, we interpret the current graph convolutional operations from an optimization perspective and argue that over-smoothing is mainly caused by the naive first-order approximation of the solution to the optimization problem. Subsequently, we introduce two metrics to measure the over-smoothing on node-level tasks. Specifically, we calculate the fraction of the pairwise distance between connected and disconnected nodes to the overall distance respectively. Based on our theoretical and empirical analysis, we establish a universal theoretical framework of GCN from an optimization perspective and derive a novel convolutional kernel named GCN+ which has lower parameter amount while relieving the over-smoothing inherently. Extensive experiments on real-world datasets demonstrate the superior performance of GCN+ over state-of-the-art baseline methods on the node classification tasks.
Graph Neural Networks (GNNs) have attracted considerable attention and have emerged as a new promising paradigm to process graph-structured data. GNNs are usually stacked to multiple layers and the node representations in each layer are computed through propagating and aggregating the neighboring node features with respect to the graph. By stacking to multiple layers, GNNs are able to capture the long-range dependencies among the data on the graph and thus bring performance improvements. To train a GNN with multiple layers effectively, some normalization techniques (e.g., node-wise normalization, batch-wise normalization) are necessary. However, the normalization techniques for GNNs are highly task-relevant and different application tasks prefer to different normalization techniques, which is hard to know in advance. To tackle this deficiency, in this paper, we propose to learn graph normalization by optimizing a weighted combination of normalization techniques at four different levels, including node-wise normalization, adjacency-wise normalization, graph-wise normalization, and batch-wise normalization, in which the adjacency-wise normalization and the graph-wise normalization are newly proposed in this paper to take into account the local structure and the global structure on the graph, respectively. By learning the optimal weights, we are able to automatically select a single best or a best combination of multiple normalizations for a specific task. We conduct extensive experiments on benchmark datasets for different tasks, including node classification, link prediction, graph classification and graph regression, and confirm that the learned graph normalization leads to competitive results and that the learned weights suggest the appropriate normalization techniques for the specific task. Source code is released here https://github.com/cyh1112/GraphNormalization.
Graph neural networks (GNNs) have achieved strong performance in various applications. In the real world, network data is usually formed in a streaming fashion. The distributions of patterns that refer to neighborhood information of nodes may shift over time. The GNN model needs to learn the new patterns that cannot yet be captured. But learning incrementally leads to the catastrophic forgetting problem that historical knowledge is overwritten by newly learned knowledge. Therefore, it is important to train GNN model to learn new patterns and maintain existing patterns simultaneously, which few works focus on. In this paper, we propose a streaming GNN model based on continual learning so that the model is trained incrementally and up-to-date node representations can be obtained at each time step. Firstly, we design an approximation algorithm to detect new coming patterns efficiently based on information propagation. Secondly, we combine two perspectives of data replaying and model regularization for existing pattern consolidation. Specially, a hierarchy-importance sampling strategy for nodes is designed and a weighted regularization term for GNN parameters is derived, achieving greater stability and generalization of knowledge consolidation. Our model is evaluated on real and synthetic data sets and compared with multiple baselines. The results of node classification prove that our model can efficiently update model parameters and achieve comparable performance to model retraining. In addition, we also conduct a case study on the synthetic data, and carry out some specific analysis for each part of our model, illustrating its ability to learn new knowledge and maintain existing knowledge from different perspectives.
A graph embedding algorithm embeds a graph into a low-dimensional space such that the embedding preserves the inherent properties of the graph. While graph embedding is fundamentally related to graph visualization, prior work did not exploit this connection explicitly. We develop Force2Vec that uses force-directed graph layout models in a graph embedding setting with an aim to excel in both machine learning (ML) and visualization tasks. We make Force2Vec highly parallel by mapping its core computations to linear algebra and utilizing multiple levels of parallelism available in modern processors. The resultant algorithm is an order of magnitude faster than existing methods (43x faster than DeepWalk, on average) and can generate embeddings from graphs with billions of edges in a few hours. In comparison to existing methods, Force2Vec is better in graph visualization and performs comparably or better in ML tasks such as link prediction, node classification, and clustering. Source code is available at https://github.com/HipGraph/Force2Vec.
Embedding is a useful technique to project a high-dimensional feature into a low-dimensional space, and it has many successful applications including link prediction, node classification and natural language processing. Current approaches mainly focus on static data, which usually lead to unsatisfactory performance in applications involving large changes over time. How to dynamically characterize the variation of the embedded features is still largely unexplored. In this paper, we introduce a dynamic variational embedding (DVE) approach for sequence-aware data based on recent advances in recurrent neural networks. DVE can model the node's intrinsic nature and temporal variation explicitly and simultaneously, which are crucial for exploration. We further apply DVE to sequence-aware recommender systems, and develop an end-to-end neural architecture for link prediction.
The heterogeneous network is a robust data abstraction that can model entities of different types interacting in various ways. Such heterogeneity brings rich semantic information but presents nontrivial challenges in aggregating the heterogeneous relationships between objects - especially those of higher-order indirect relations. Recent graph neural network approaches for representation learning on heterogeneous networks typically employ the attention mechanism, which is often only optimized for predictions based on direct links. Furthermore, even though most deep learning methods can aggregate higher-order information by building deeper models, such a scheme can diminish the degree of interpretability. To overcome these challenges, we explore an architecture - Layer-stacked ATTention Embedding (LATTE) - that automatically decomposes higher-order meta relations at each layer to extract the relevant heterogeneous neighborhood structures for each node. Additionally, by successively stacking layer representations, the learned node embedding offers a more interpretable aggregation scheme for nodes of different types at different neighborhood ranges. We conducted experiments on several benchmark heterogeneous network datasets. In both transductive and inductive node classification tasks, LATTE can achieve state-of-the-art performance compared to existing approaches, all while offering a lightweight model. With extensive experimental analyses and visualizations, the framework can demonstrate the ability to extract informative insights on heterogeneous networks.