Representation learning on temporal interaction graphs (TIG) is to model complex networks with the dynamic evolution of interactions arising in a broad spectrum of problems. Existing dynamic embedding methods on TIG discretely update node embeddings merely when an interaction occurs. They fail to capture the continuous dynamic evolution of embedding trajectories of nodes. In this paper, we propose a two-module framework named ConTIG, a continuous representation method that captures the continuous dynamic evolution of node embedding trajectories. With two essential modules, our model exploit three-fold factors in dynamic networks which include latest interaction, neighbor features and inherent characteristics. In the first update module, we employ a continuous inference block to learn the nodes' state trajectories by learning from time-adjacent interaction patterns between node pairs using ordinary differential equations. In the second transform module, we introduce a self-attention mechanism to predict future node embeddings by aggregating historical temporal interaction information. Experiments results demonstrate the superiority of ConTIG on temporal link prediction, temporal node recommendation and dynamic node classification tasks compared with a range of state-of-the-art baselines, especially for long-interval interactions prediction.
Graph Representation Learning (GRL) methods opened new avenues for addressing complex, real-world problems represented by graphs. However, many graphs used in these applications comprise millions of nodes and billions of edges and are beyond the capabilities of current methods and software implementations. We present GRAPE, a software resource for graph processing and embedding that can scale with big graphs by using specialized and smart data structures, algorithms, and a fast parallel implementation of random walk-based methods. Compared with state-of-the-art software resources, GRAPE shows an improvement of orders of magnitude in empirical space and time complexity, as well as a competitive edge and node label prediction performance. GRAPE comprises about 1.7 million well-documented lines of Python and Rust code and provides 69 node embedding methods, 25 inference models, a collection of efficient graph processing utilities and over 80,000 graphs from the literature and other sources. Standardized interfaces allow seamless integration of third-party libraries, while ready-to-use and modular pipelines permit an easy-to-use evaluation of GRL methods, therefore also positioning GRAPE as a software resource to perform a fair comparison between methods and libraries for graph processing and embedding.
Graph Convolutional Networks (GCNs) are a popular method from graph representation learning that have proved effective for tasks like node classification tasks. Although typical GCN models focus on classifying nodes within a static graph, several recent variants propose node classification in dynamic graphs whose topologies and node attributes change over time, e.g., social networks with dynamic relationships, or literature citation networks with changing co-authorships. These works, however, do not fully address the challenge of flexibly assigning different importance to snapshots of the graph at different times, which depending on the graph dynamics may have more or less predictive power on the labels. We address this challenge by proposing a new method, GCN-SE, that attaches a set of learnable attention weights to graph snapshots at different times, inspired by Squeeze and Excitation Net (SE-Net). We show that GCN-SE outperforms previously proposed node classification methods on a variety of graph datasets. To verify the effectiveness of the attention weight in determining the importance of different graph snapshots, we adapt perturbation-based methods from the field of explainable machine learning to graphical settings and evaluate the correlation between the attention weights learned by GCN-SE and the importance of different snapshots over time. These experiments demonstrate that GCN-SE can in fact identify different snapshots' predictive power for dynamic node classification.
Graph Convolutional Networks (GCNs) are widely used in a variety of applications, and can be seen as an unstructured version of standard Convolutional Neural Networks (CNNs). As in CNNs, the computational cost of GCNs for large input graphs (such as large point clouds or meshes) can be high and inhibit the use of these networks, especially in environments with low computational resources. To ease these costs, quantization can be applied to GCNs. However, aggressive quantization of the feature maps can lead to a significant degradation in performance. On a different note, Haar wavelet transforms are known to be one of the most effective and efficient approaches to compress signals. Therefore, instead of applying aggressive quantization to feature maps, we propose to utilize Haar wavelet compression and light quantization to reduce the computations and the bandwidth involved with the network. We demonstrate that this approach surpasses aggressive feature quantization by a significant margin, for a variety of problems ranging from node classification to point cloud classification and part and semantic segmentation.
Graph neural networks (GNNs) have achieved superior performance on node classification tasks in the last few years. Commonly, this is framed in a transductive semi-supervised learning setup wherein the entire graph, including the target nodes to be labeled, is available for training. Driven in part by scalability, recent works have focused on the inductive case where only the labeled portion of a graph is available for training. In this context, our current work considers a challenging inductive setting where a set of labeled graphs are available for training while the unlabeled target graph is completely separate, i.e., there are no connections between labeled and unlabeled nodes. Under the implicit assumption that the testing and training graphs come from similar distributions, our goal is to develop a labeling function that generalizes to unobserved connectivity structures. To that end, we employ a graph neural tangent kernel (GNTK) that corresponds to infinitely wide GNNs to find correspondences between nodes in different graphs based on both the topology and the node features. We augment the capabilities of the GNTK with residual connections and empirically illustrate its performance gains on standard benchmarks.
The class imbalance problem, as an important issue in learning node representations, has drawn increasing attention from the community. Although the imbalance considered by existing studies roots from the unequal quantity of labeled examples in different classes (quantity imbalance), we argue that graph data expose a unique source of imbalance from the asymmetric topological properties of the labeled nodes, i.e., labeled nodes are not equal in terms of their structural role in the graph (topology imbalance). In this work, we first probe the previously unknown topology-imbalance issue, including its characteristics, causes, and threats to semi-supervised node classification learning. We then provide a unified view to jointly analyzing the quantity- and topology- imbalance issues by considering the node influence shift phenomenon with the Label Propagation algorithm. In light of our analysis, we devise an influence conflict detection -- based metric Totoro to measure the degree of graph topology imbalance and propose a model-agnostic method ReNode to address the topology-imbalance issue by re-weighting the influence of labeled nodes adaptively based on their relative positions to class boundaries. Systematic experiments demonstrate the effectiveness and generalizability of our method in relieving topology-imbalance issue and promoting semi-supervised node classification. The further analysis unveils varied sensitivity of different graph neural networks (GNNs) to topology imbalance, which may serve as a new perspective in evaluating GNN architectures.
Graph Neural Networks (GNNs) have shown advantages in various graph-based applications. Most existing GNNs assume strong homophily of graph structure and apply permutation-invariant local aggregation of neighbors to learn a representation for each node. However, they fail to generalize to heterophilic graphs, where most neighboring nodes have different labels or features, and the relevant nodes are distant. Few recent studies attempt to address this problem by combining multiple hops of hidden representations of central nodes (i.e., multi-hop-based approaches) or sorting the neighboring nodes based on attention scores (i.e., ranking-based approaches). As a result, these approaches have some apparent limitations. On the one hand, multi-hop-based approaches do not explicitly distinguish relevant nodes from a large number of multi-hop neighborhoods, leading to a severe over-smoothing problem. On the other hand, ranking-based models do not joint-optimize node ranking with end tasks and result in sub-optimal solutions. In this work, we present Graph Pointer Neural Networks (GPNN) to tackle the challenges mentioned above. We leverage a pointer network to select the most relevant nodes from a large amount of multi-hop neighborhoods, which constructs an ordered sequence according to the relationship with the central node. 1D convolution is then applied to extract high-level features from the node sequence. The pointer-network-based ranker in GPNN is joint-optimized with other parts in an end-to-end manner. Extensive experiments are conducted on six public node classification datasets with heterophilic graphs. The results show that GPNN significantly improves the classification performance of state-of-the-art methods. In addition, analyses also reveal the privilege of the proposed GPNN in filtering out irrelevant neighbors and reducing over-smoothing.
Graph convolutional neural networks (GCNNs) are popular deep learning architectures that, upon replacing regular convolutions with graph filters (GFs), generalize CNNs to irregular domains. However, classical GFs are prone to numerical errors since they consist of high-order polynomials. This problem is aggravated when several filters are applied in cascade, limiting the practical depth of GCNNs. To tackle this issue, we present the neighborhood graph filters (NGFs), a family of GFs that replaces the powers of the graph shift operator with $k$-hop neighborhood adjacency matrices. NGFs help to alleviate the numerical issues of traditional GFs, allow for the design of deeper GCNNs, and enhance the robustness to errors in the topology of the graph. To illustrate the advantage over traditional GFs in practical applications, we use NGFs in the design of deep neighborhood GCNNs to solve graph signal denoising and node classification problems over both synthetic and real-world data.
Network representation learning aims to generate an embedding for each node in a network, which facilitates downstream machine learning tasks such as node classification and link prediction. Current work mainly focuses on transductive network representation learning, i.e. generating fixed node embeddings, which is not suitable for real-world applications. Therefore, we propose a new inductive network representation learning method called MNCI by mining neighborhood and community influences in temporal networks. We propose an aggregator function that integrates neighborhood influence with community influence to generate node embeddings at any time. We conduct extensive experiments on several real-world datasets and compare MNCI with several state-of-the-art baseline methods on various tasks, including node classification and network visualization. The experimental results show that MNCI achieves better performance than baselines.
Graph auto-encoders have proved to be useful in network embedding task. However, current models only consider explicit structures and fail to explore the informative latent structures cohered in networks. To address this issue, we propose a latent network embedding model based on adversarial graph auto-encoders. Under this framework, the problem of discovering latent structures is formulated as inferring the latent ties from partial observations. A latent transmission matrix that describes the strengths of existing edges and latent ties is derived based on influence cascades sampled by simulating diffusion processes over networks. Besides, since the inference process may bring extra noises, we introduce an adversarial training that works as regularization to dislodge noises and improve the model robustness. Extensive experiments on link prediction and node classification tasks show that the proposed model achieves superior results compared with baseline models.
While deep neural networks have achieved great success in graph analysis, recent work has shown that they are vulnerable to adversarial attacks. Compared with adversarial attacks on image classification, performing adversarial attacks on graphs is more challenging because of the discrete and non-differential nature of the adjacent matrix for a graph. In this work, we propose Cluster Attack -- a Graph Injection Attack (GIA) on node classification, which injects fake nodes into the original graph to degenerate the performance of graph neural networks (GNNs) on certain victim nodes while affecting the other nodes as little as possible. We demonstrate that a GIA problem can be equivalently formulated as a graph clustering problem; thus, the discrete optimization problem of the adjacency matrix can be solved in the context of graph clustering. In particular, we propose to measure the similarity between victim nodes by a metric of Adversarial Vulnerability, which is related to how the victim nodes will be affected by the injected fake node, and to cluster the victim nodes accordingly. Our attack is performed in a practical and unnoticeable query-based black-box manner with only a few nodes on the graphs that can be accessed. Theoretical analysis and extensive experiments demonstrate the effectiveness of our method by fooling the node classifiers with only a small number of queries.
In this paper, we investigate the degree of explainability of graph neural networks (GNNs). Existing explainers work by finding global/local subgraphs to explain a prediction, but they are applied after a GNN has already been trained. Here, we propose a meta-learning framework for improving the level of explainability of a GNN directly at training time, by steering the optimization procedure towards what we call `interpretable minima'. Our framework (called MATE, MetA-Train to Explain) jointly trains a model to solve the original task, e.g., node classification, and to provide easily processable outputs for downstream algorithms that explain the model's decisions in a human-friendly way. In particular, we meta-train the model's parameters to quickly minimize the error of an instance-level GNNExplainer trained on-the-fly on randomly sampled nodes. The final internal representation relies upon a set of features that can be `better' understood by an explanation algorithm, e.g., another instance of GNNExplainer. Our model-agnostic approach can improve the explanations produced for different GNN architectures and use any instance-based explainer to drive this process. Experiments on synthetic and real-world datasets for node and graph classification show that we can produce models that are consistently easier to explain by different algorithms. Furthermore, this increase in explainability comes at no cost for the accuracy of the model.
Nodes in networks may have one or more functions that determine their role in the system. As opposed to local proximity, which captures the local context of nodes, the role identity captures the functional "role" that nodes play in a network, such as being the center of a group, or the bridge between two groups. This means that nodes far apart in a network can have similar structural role identities. Several recent works have explored methods for embedding the roles of nodes in networks. However, these methods all rely on either approximating or indirect modeling of structural equivalence. In this paper, we present a novel and flexible framework using stress majorization, to transform the high-dimensional role identities in networks directly (without approximation or indirect modeling) to a low-dimensional embedding space. Our method is also flexible, in that it does not rely on specific structural similarity definitions. We evaluated our method on the tasks of node classification, clustering, and visualization, using three real-world and five synthetic networks. Our experiments show that our framework achieves superior results than existing methods in learning node role representations.
Many real-world graphs involve different types of nodes and relations between nodes, being heterogeneous by nature. The representation learning of heterogeneous graphs (HGs) embeds the rich structure and semantics of such graphs into a low-dimensional space and facilitates various data mining tasks, such as node classification, node clustering, and link prediction. In this paper, we propose a self-supervised method that learns HG representations by relying on knowledge exchange and discovery among different HG structural semantics (meta-paths). Specifically, by maximizing the mutual information of meta-path representations, we promote meta-path information fusion and consensus, and ensure that globally shared semantics are encoded. By extensive experiments on node classification, node clustering, and link prediction tasks, we show that the proposed self-supervision both outperforms and improves competing methods by 1% and up to 10% for all tasks.
Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using the graph structures based on the relational inductive bias (homophily assumption). Though GNNs are believed to outperform NNs in real-world tasks, performance advantages of GNNs over graph-agnostic NNs seem not generally satisfactory. Heterophily has been considered as a main cause and numerous works have been put forward to address it. In this paper, we first show that not all cases of heterophily are harmful for GNNs with aggregation operation. Then, we propose new metrics based on a similarity matrix which considers the influence of both graph structure and input features on GNNs. The metrics demonstrate advantages over the commonly used homophily metrics by tests on synthetic graphs. From the metrics and the observations, we find some cases of harmful heterophily can be addressed by diversification operation. With this fact and knowledge of filterbanks, we propose the Adaptive Channel Mixing (ACM) framework to adaptively exploit aggregation, diversification and identity channels in each GNN layer to address harmful heterophily. We validate the ACM-augmented baselines with 10 real-world node classification tasks. They consistently achieve significant performance gain and exceed the state-of-the-art GNNs on most of the tasks without incurring significant computational burden.
Random walk based node embedding algorithms learn vector representations of nodes by optimizing an objective function of node embedding vectors and skip-bigram statistics computed from random walks on the network. They have been applied to many supervised learning problems such as link prediction and node classification and have demonstrated state-of-the-art performance. Yet, their properties remain poorly understood. This paper studies properties of random walk based node embeddings in the unsupervised setting of discovering hidden block structure in the network, i.e., learning node representations whose cluster structure in Euclidean space reflects their adjacency structure within the network. We characterize the ergodic limits of the embedding objective, its generalization, and related convex relaxations to derive corresponding non-randomized versions of the node embedding objectives. We also characterize the optimal node embedding Grammians of the non-randomized objectives for the expected graph of a two-community Stochastic Block Model (SBM). We prove that the solution Grammian has rank $1$ for a suitable nuclear norm relaxation of the non-randomized objective. Comprehensive experimental results on SBM random networks reveal that our non-randomized ergodic objectives yield node embeddings whose distribution is Gaussian-like, centered at the node embeddings of the expected network within each community, and concentrate in the linear degree-scaling regime as the number of nodes increases.
Representation learning using network embedding has received tremendous attention due to its efficacy to solve downstream tasks. Popular embedding methods (such as deepwalk, node2vec, LINE) are based on a neural architecture, thus unable to scale on large networks both in terms of time and space usage. Recently, we proposed BinSketch, a sketching technique for compressing binary vectors to binary vectors. In this paper, we show how to extend BinSketch and use it for network hashing. Our proposal named QUINT is built upon BinSketch, and it embeds nodes of a sparse network onto a low-dimensional space using simple bi-wise operations. QUINT is the first of its kind that provides tremendous gain in terms of speed and space usage without compromising much on the accuracy of the downstream tasks. Extensive experiments are conducted to compare QUINT with seven state-of-the-art network embedding methods for two end tasks - link prediction and node classification. We observe huge performance gain for QUINT in terms of speedup (up to 7000x) and space saving (up to 80x) due to its bit-wise nature to obtain node embedding. Moreover, QUINT is a consistent top-performer for both the tasks among the baselines across all the datasets. Our empirical observations are backed by rigorous theoretical analysis to justify the effectiveness of QUINT. In particular, we prove that QUINT retains enough structural information which can be used further to approximate many topological properties of networks with high confidence.
Many real-world data can be represented as heterogeneous graphs with different types of nodes and connections. Heterogeneous graph neural network model aims to embed nodes or subgraphs into low-dimensional vector space for various downstream tasks such as node classification, link prediction, etc. Although several models were proposed recently, they either only aggregate information from the same type of neighbors, or just indiscriminately treat homogeneous and heterogeneous neighbors in the same way. Based on these observations, we propose a new heterogeneous graph neural network model named HMSG to comprehensively capture structural, semantic and attribute information from both homogeneous and heterogeneous neighbors. Specifically, we first decompose the heterogeneous graph into multiple metapath-based homogeneous and heterogeneous subgraphs, and each subgraph associates specific semantic and structural information. Then message aggregation methods are applied to each subgraph independently, so that information can be learned in a more targeted and efficient manner. Through a type-specific attribute transformation, node attributes can also be transferred among different types of nodes. Finally, we fuse information from subgraphs together to get the complete representation. Extensive experiments on several datasets for node classification, node clustering and link prediction tasks show that HMSG achieves the best performance in all evaluation metrics than state-of-the-art baselines.
The robustness of the much-used Graph Convolutional Networks (GCNs) to perturbations of their input is becoming a topic of increasing importance. In this paper, the random GCN is introduced for which a random matrix theory analysis is possible. This analysis suggests that if the graph is sufficiently perturbed, or in the extreme case random, then the GCN fails to benefit from the node features. It is furthermore observed that enhancing the message passing step in GCNs by adding the node feature kernel to the adjacency matrix of the graph structure solves this problem. An empirical study of a GCN utilised for node classification on six real datasets further confirms the theoretical findings and demonstrates that perturbations of the graph structure can result in GCNs performing significantly worse than Multi-Layer Perceptrons run on the node features alone. In practice, adding a node feature kernel to the message passing of perturbed graphs results in a significant improvement of the GCN's performance, thereby rendering it more robust to graph perturbations. Our code is publicly available at:https://github.com/ChangminWu/RobustGCN.
Graph Contrastive Learning (GCL) establishes a new paradigm for learning graph representations without human annotations. Although remarkable progress has been witnessed recently, the success behind GCL is still left somewhat mysterious. In this work, we first identify several critical design considerations within a general GCL paradigm, including augmentation functions, contrasting modes, contrastive objectives, and negative mining techniques. Then, to understand the interplay of different GCL components, we conduct extensive, controlled experiments over a set of benchmark tasks on datasets across various domains. Our empirical studies suggest a set of general receipts for effective GCL, e.g., simple topology augmentations that produce sparse graph views bring promising performance improvements; contrasting modes should be aligned with the granularities of end tasks. In addition, to foster future research and ease the implementation of GCL algorithms, we develop an easy-to-use library PyGCL, featuring modularized CL components, standardized evaluation, and experiment management. We envision this work to provide useful empirical evidence of effective GCL algorithms and offer several insights for future research.