Multi-relational networks capture intricate relationships in data and have diverse applications across fields such as biomedical, financial, and social sciences. As networks derived from increasingly large datasets become more common, identifying efficient methods for representing and analyzing them becomes crucial. This work extends the Prime Adjacency Matrices (PAMs) framework, which employs prime numbers to represent distinct relations within a network uniquely. This enables a compact representation of a complete multi-relational graph using a single adjacency matrix, which, in turn, facilitates quick computation of multi-hop adjacency matrices. In this work, we enhance the framework by introducing a lossless algorithm for calculating the multi-hop matrices and propose the Bag of Paths (BoP) representation, a versatile feature extraction methodology for various graph analytics tasks, at the node, edge, and graph level. We demonstrate the efficiency of the framework across various tasks and datasets, showing that simple BoP-based models perform comparably to or better than commonly used neural models while offering improved speed and interpretability.
Heterogeneous graphs are ubiquitous to model complex data. There are urgent needs on powerful heterogeneous graph neural networks to effectively support important applications. We identify a potential semantic mixing issue in existing message passing processes, where the representations of the neighbors of a node $v$ are forced to be transformed to the feature space of $v$ for aggregation, though the neighbors are in different types. That is, the semantics in different node types are entangled together into node $v$'s representation. To address the issue, we propose SlotGAT with separate message passing processes in slots, one for each node type, to maintain the representations in their own node-type feature spaces. Moreover, in a slot-based message passing layer, we design an attention mechanism for effective slot-wise message aggregation. Further, we develop a slot attention technique after the last layer of SlotGAT, to learn the importance of different slots in downstream tasks. Our analysis indicates that the slots in SlotGAT can preserve different semantics in various feature spaces. The superiority of SlotGAT is evaluated against 13 baselines on 6 datasets for node classification and link prediction. Our code is at https://github.com/scottjiao/SlotGAT_ICML23/.
Heterogeneous Graph Neural Networks (HGNNs) are powerful tools for deep learning on heterogeneous graphs. Typical HGNNs require repetitive message passing during training, limiting efficiency for large-scale real-world graphs. Recent pre-computation-based HGNNs use one-time message passing to transform a heterogeneous graph into regular-shaped tensors, enabling efficient mini-batch training. Existing pre-computation-based HGNNs can be mainly categorized into two styles, which differ in how much information loss is allowed and efficiency. We propose a hybrid pre-computation-based HGNN, named Random Projection Heterogeneous Graph Neural Network (RpHGNN), which combines the benefits of one style's efficiency with the low information loss of the other style. To achieve efficiency, the main framework of RpHGNN consists of propagate-then-update iterations, where we introduce a Random Projection Squashing step to ensure that complexity increases only linearly. To achieve low information loss, we introduce a Relation-wise Neighbor Collection component with an Even-odd Propagation Scheme, which aims to collect information from neighbors in a finer-grained way. Experimental results indicate that our approach achieves state-of-the-art results on seven small and large benchmark datasets while also being 230% faster compared to the most effective baseline. Surprisingly, our approach not only surpasses pre-processing-based baselines but also outperforms end-to-end methods.
Heterogeneous graph neural networks (HGNNs) have powerful capability to embed rich structural and semantic information of a heterogeneous graph into node representations. Existing HGNNs inherit many mechanisms from graph neural networks (GNNs) over homogeneous graphs, especially the attention mechanism and the multi-layer structure. These mechanisms bring excessive complexity, but seldom work studies whether they are really effective on heterogeneous graphs. This paper conducts an in-depth and detailed study of these mechanisms and proposes Simple and Efficient Heterogeneous Graph Neural Network (SeHGNN). To easily capture structural information, SeHGNN pre-computes the neighbor aggregation using a light-weight mean aggregator, which reduces complexity by removing overused neighbor attention and avoiding repeated neighbor aggregation in every training epoch. To better utilize semantic information, SeHGNN adopts the single-layer structure with long metapaths to extend the receptive field, as well as a transformer-based semantic fusion module to fuse features from different metapaths. As a result, SeHGNN exhibits the characteristics of simple network structure, high prediction accuracy, and fast training speed. Extensive experiments on five real-world heterogeneous graphs demonstrate the superiority of SeHGNN over the state-of-the-arts on both accuracy and training speed.
Heterogeneous graph neural networks (HGNNs) have been blossoming in recent years, but the unique data processing and evaluation setups used by each work obstruct a full understanding of their advancements. In this work, we present a systematical reproduction of 12 recent HGNNs by using their official codes, datasets, settings, and hyperparameters, revealing surprising findings about the progress of HGNNs. We find that the simple homogeneous GNNs, e.g., GCN and GAT, are largely underestimated due to improper settings. GAT with proper inputs can generally match or outperform all existing HGNNs across various scenarios. To facilitate robust and reproducible HGNN research, we construct the Heterogeneous Graph Benchmark (HGB), consisting of 11 diverse datasets with three tasks. HGB standardizes the process of heterogeneous graph data splits, feature processing, and performance evaluation. Finally, we introduce a simple but very strong baseline Simple-HGN--which significantly outperforms all previous models on HGB--to accelerate the advancement of HGNNs in the future.
Graph neural networks (GNNs) are a popular class of parametric model for learning over graph-structured data. Recent work has argued that GNNs primarily use the graph for feature smoothing, and have shown competitive results on benchmark tasks by simply operating on graph-smoothed node features, rather than using end-to-end learned feature hierarchies that are challenging to scale to large graphs. In this work, we ask whether these results can be extended to heterogeneous graphs, which encode multiple types of relationship between different entities. We propose Neighbor Averaging over Relation Subgraphs (NARS), which trains a classifier on neighbor-averaged features for randomly-sampled subgraphs of the "metagraph" of relations. We describe optimizations to allow these sets of node features to be computed in a memory-efficient way, both at training and inference time. NARS achieves a new state of the art accuracy on several benchmark datasets, outperforming more expensive GNN-based methods
Heterogeneous information network (HIN) summarizes rich structural information in real-world datasets and plays an important role in many big data applications. Recently, graph neural networks have been extended to the representation learning of HIN. One very recent advancement is the hierarchical attention mechanism which incorporates both nodewise and semantic-wise attention. However, since HIN is more likely to be densely connected given its diverse types of edges, repeatedly applying graph convolutional layers can make the node embeddings indistinguishable very quickly. In order to avoid oversmoothness, existing graph neural networks targeting HIN generally suffer from a shallow structure. Consequently, those approaches ignore information beyond the local neighborhood. This design flaw violates the concept of non-local learning, which emphasizes the importance of capturing long-range dependencies. To properly address this limitation, we propose a novel framework of non-local attention in heterogeneous information networks (NLAH). Our framework utilizes a non-local attention structure to complement the hierarchical attention mechanism. In this way, it leverages both local and non-local information simultaneously. Moreover, a weighted sampling schema is designed for NLAH to reduce the computation cost for largescale datasets. Extensive experiments on three different realworld heterogeneous information networks illustrate that our framework exhibits extraordinary scalability and outperforms state-of-the-art baselines with significant margins.
Recent years have witnessed the emerging success of graph neural networks (GNNs) for modeling structured data. However, most GNNs are designed for homogeneous graphs, in which all nodes and edges belong to the same types, making them infeasible to represent heterogeneous structures. In this paper, we present the Heterogeneous Graph Transformer (HGT) architecture for modeling Web-scale heterogeneous graphs. To model heterogeneity, we design node- and edge-type dependent parameters to characterize the heterogeneous attention over each edge, empowering HGT to maintain dedicated representations for different types of nodes and edges. To handle dynamic heterogeneous graphs, we introduce the relative temporal encoding technique into HGT, which is able to capture the dynamic structural dependency with arbitrary durations. To handle Web-scale graph data, we design the heterogeneous mini-batch graph sampling algorithm---HGSampling---for efficient and scalable training. Extensive experiments on the Open Academic Graph of 179 million nodes and 2 billion edges show that the proposed HGT model consistently outperforms all the state-of-the-art GNN baselines by 9%--21% on various downstream tasks.
In this paper, we focus on graph representation learning of heterogeneous information network (HIN), in which various types of vertices are connected by various types of relations. Most of the existing methods conducted on HIN revise homogeneous graph embedding models via meta-paths to learn low-dimensional vector space of HIN. In this paper, we propose a novel Heterogeneous Graph Structural Attention Neural Network (HetSANN) to directly encode structural information of HIN without meta-path and achieve more informative representations. With this method, domain experts will not be needed to design meta-path schemes and the heterogeneous information can be processed automatically by our proposed model. Specifically, we implicitly represent heterogeneous information using the following two methods: 1) we model the transformation between heterogeneous vertices through a projection in low-dimensional entity spaces; 2) afterwards, we apply the graph neural network to aggregate multi-relational information of projected neighborhood by means of attention mechanism. We also present three extensions of HetSANN, i.e., voices-sharing product attention for the pairwise relationships in HIN, cycle-consistency loss to retain the transformation between heterogeneous entity spaces, and multi-task learning with full use of information. The experiments conducted on three public datasets demonstrate that our proposed models achieve significant and consistent improvements compared to state-of-the-art solutions.
Graph representation learning is to learn universal node representations that preserve both node attributes and structural information. The derived node representations can be used to serve various downstream tasks, such as node classification and node clustering. When a graph is heterogeneous, the problem becomes more challenging than the homogeneous graph node learning problem. Inspired by the emerging information theoretic-based learning algorithm, in this paper we propose an unsupervised graph neural network Heterogeneous Deep Graph Infomax (HDGI) for heterogeneous graph representation learning. We use the meta-path structure to analyze the connections involving semantics in heterogeneous graphs and utilize graph convolution module and semantic-level attention mechanism to capture local representations. By maximizing local-global mutual information, HDGI effectively learns high-level node representations that can be utilized in downstream graph-related tasks. Experiment results show that HDGI remarkably outperforms state-of-the-art unsupervised graph representation learning methods on both classification and clustering tasks. By feeding the learned representations into a parametric model, such as logistic regression, we even achieve comparable performance in node classification tasks when comparing with state-of-the-art supervised end-to-end GNN models.
Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved state-of-the-art performance in tasks such as node classification and link prediction. However, most existing GNNs are designed to learn node representations on the fixed and homogeneous graphs. The limitations especially become problematic when learning representations on a misspecified graph or a heterogeneous graph that consists of various types of nodes and edges. In this paper, we propose Graph Transformer Networks (GTNs) that are capable of generating new graph structures, which involve identifying useful connections between unconnected nodes on the original graph, while learning effective node representation on the new graphs in an end-to-end fashion. Graph Transformer layer, a core layer of GTNs, learns a soft selection of edge types and composite relations for generating useful multi-hop connections so-called meta-paths. Our experiments show that GTNs learn new graph structures, based on data and tasks without domain knowledge, and yield powerful node representation via convolution on the new graphs. Without domain-specific graph preprocessing, GTNs achieved the best performance in all three benchmark node classification tasks against the state-of-the-art methods that require pre-defined meta-paths from domain knowledge.
Latent factor models (LFMs) such as matrix factorization have achieved the state-of-the-art performance among various collaborative filtering approaches for recommendation. Despite the high recommendation accuracy of LFMs, a critical issue to be resolved is their lack of interpretability. Extensive efforts have been devoted to interpreting the prediction results of LFMs. However, they either rely on auxiliary information which may not be available in practice, or sacrifice recommendation accuracy for interpretability. Influence functions, stemming from robust statistics, have been developed to understand the effect of training points on the predictions of black-box models. Inspired by this, we propose a novel explanation method named FIA (Fast Influence Analysis) to understand the prediction of trained LFMs by tracing back to the training data with influence functions. We present how to employ influence functions to measure the impact of historical user-item interactions on the prediction results of LFMs and provide intuitive neighbor-style explanations based on the most influential interactions. Our proposed FIA exploits the characteristics of two important LFMs, matrix factorization and neural collaborative filtering, and is capable of accelerating the overall influence analysis process. We provide a detailed complexity analysis for FIA over LFMs and conduct extensive experiments to evaluate its performance using real-world datasets. The results demonstrate the effectiveness and efficiency of FIA, and the usefulness of the generated explanations for the recommendation results.
We present a scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs. We motivate the choice of our convolutional architecture via a localized first-order approximation of spectral graph convolutions. Our model scales linearly in the number of graph edges and learns hidden layer representations that encode both local graph structure and features of nodes. In a number of experiments on citation networks and on a knowledge graph dataset we demonstrate that our approach outperforms related methods by a significant margin.
Knowledge graphs enable a wide variety of applications, including question answering and information retrieval. Despite the great effort invested in their creation and maintenance, even the largest (e.g., Yago, DBPedia or Wikidata) remain incomplete. We introduce Relational Graph Convolutional Networks (R-GCNs) and apply them to two standard knowledge base completion tasks: Link prediction (recovery of missing facts, i.e. subject-predicate-object triples) and entity classification (recovery of missing entity attributes). R-GCNs are related to a recent class of neural networks operating on graphs, and are developed specifically to deal with the highly multi-relational data characteristic of realistic knowledge bases. We demonstrate the effectiveness of R-GCNs as a stand-alone model for entity classification. We further show that factorization models for link prediction such as DistMult can be significantly improved by enriching them with an encoder model to accumulate evidence over multiple inference steps in the relational graph, demonstrating a large improvement of 29.8% on FB15k-237 over a decoder-only baseline.
We present graph attention networks (GATs), novel neural network architectures that operate on graph-structured data, leveraging masked self-attentional layers to address the shortcomings of prior methods based on graph convolutions or their approximations. By stacking layers in which nodes are able to attend over their neighborhoods' features, we enable (implicitly) specifying different weights to different nodes in a neighborhood, without requiring any kind of costly matrix operation (such as inversion) or depending on knowing the graph structure upfront. In this way, we address several key challenges of spectral-based graph neural networks simultaneously, and make our model readily applicable to inductive as well as transductive problems. Our GAT models have achieved or matched state-of-the-art results across four established transductive and inductive graph benchmarks: the Cora, Citeseer and Pubmed citation network datasets, as well as a protein-protein interaction dataset (wherein test graphs remain unseen during training).