Despite the success of graph neural network models in node classification, edge prediction (the task of predicting missing or potential links between nodes in a graph) remains a challenging problem for these models. A common approach for edge prediction is to first obtain the embeddings of two nodes, and then a predefined scoring function is used to predict the existence of an edge between the two nodes. Here, we introduce a preliminary idea called Edge2Node which suggests to directly obtain an embedding for each edge, without the need for a scoring function. This idea wants to create a new graph H based on the graph G given for the edge prediction task, and then suggests reducing the edge prediction task on G to a node classification task on H. We anticipate that this introductory method could stimulate further investigations for edge prediction task.
A recently released Temporal Graph Benchmark is analyzed in the context of Dynamic Link Property Prediction. We outline our observations and propose a trivial optimization-free baseline of "recently popular nodes" outperforming other methods on medium and large-size datasets in the Temporal Graph Benchmark. We propose two measures based on Wasserstein distance which can quantify the strength of short-term and long-term global dynamics of datasets. By analyzing our unexpectedly strong baseline, we show how standard negative sampling evaluation can be unsuitable for datasets with strong temporal dynamics. We also show how simple negative-sampling can lead to model degeneration during training, resulting in impossible to rank, fully saturated predictions of temporal graph networks. We propose improved negative sampling schemes for both training and evaluation and prove their usefulness. We conduct a comparison with a model trained non-contrastively without negative sampling. Our results provide a challenging baseline and indicate that temporal graph network architectures need deep rethinking for usage in problems with significant global dynamics, such as social media, cryptocurrency markets or e-commerce. We open-source the code for baselines, measures and proposed negative sampling schemes.
In this paper, we propose a Path-aware Siamese Graph neural network(PSG) for link prediction tasks. First, PSG captures both nodes and edge features for given two nodes, namely the structure information of k-neighborhoods and relay paths information of the nodes. Furthermore, a novel multi-task GNN framework with self-supervised contrastive learning is proposed for differentiation of positive links and negative links while content and behavior of nodes can be captured simultaneously. We evaluate the proposed algorithm PSG on two link property prediction datasets, ogbl-ddi and ogbl-collab. PSG achieves top 1 performance on ogbl-ddi until submission and top 3 performance on ogbl-collab. The experimental results verify the superiority of our proposed PSG
Digraph Representation Learning (DRL) aims to learn representations for directed homogeneous graphs (digraphs). Prior work in DRL is largely constrained (e.g., limited to directed acyclic graphs), or has poor generalizability across tasks (e.g., evaluated solely on one task). Most Graph Neural Networks (GNNs) exhibit poor performance on digraphs due to the neglect of modeling neighborhoods and preserving asymmetry. In this paper, we address these notable challenges by leveraging hyperbolic collaborative learning from multi-ordered and partitioned neighborhoods, and regularizers inspired by socio-psychological factors. Our resulting formalism, Digraph Hyperbolic Networks (D-HYPR) - albeit conceptually simple - generalizes to digraphs where cycles and non-transitive relations are common, and is applicable to multiple downstream tasks including node classification, link presence prediction, and link property prediction. In order to assess the effectiveness of D-HYPR, extensive evaluations were performed across 8 real-world digraph datasets involving 21 prior techniques. D-HYPR statistically significantly outperforms the current state of the art. We release our code at https://github.com/hongluzhou/dhypr
In this paper, we aim at providing an effective Pairwise Learning Neural Link Prediction (PLNLP) framework. The framework treats link prediction as a pairwise learning to rank problem and consists of four main components, i.e., neighborhood encoder, link predictor, negative sampler and objective function. The framework is flexible that any generic graph neural convolution or link prediction specific neural architecture could be employed as neighborhood encoder. For link predictor, we design different scoring functions, which could be selected based on different types of graphs. In negative sampler, we provide several sampling strategies, which are problem specific. As for objective function, we propose to use an effective ranking loss, which approximately maximizes the standard ranking metric AUC. We evaluate the proposed PLNLP framework on 4 link property prediction datasets of Open Graph Benchmark, including ogbl-ddi, ogbl-collab, ogbl-ppa and ogbl-ciation2. PLNLP achieves top 1 performance on ogbl-ddi and ogbl-collab, and top 2 performance on ogbl-ciation2 only with basic neural architecture. The performance demonstrates the effectiveness of PLNLP.
Most state-of-the-art Graph Neural Networks (GNNs) can be defined as a form of graph convolution which can be realized by message passing between direct neighbors or beyond. To scale such GNNs to large graphs, various neighbor-, layer-, or subgraph-sampling techniques are proposed to alleviate the "neighbor explosion" problem by considering only a small subset of messages passed to the nodes in a mini-batch. However, sampling-based methods are difficult to apply to GNNs that utilize many-hops-away or global context each layer, show unstable performance for different tasks and datasets, and do not speed up model inference. We propose a principled and fundamentally different approach, VQ-GNN, a universal framework to scale up any convolution-based GNNs using Vector Quantization (VQ) without compromising the performance. In contrast to sampling-based techniques, our approach can effectively preserve all the messages passed to a mini-batch of nodes by learning and updating a small number of quantized reference vectors of global node representations, using VQ within each GNN layer. Our framework avoids the "neighbor explosion" problem of GNNs using quantized representations combined with a low-rank version of the graph convolution matrix. We show that such a compact low-rank version of the gigantic convolution matrix is sufficient both theoretically and experimentally. In company with VQ, we design a novel approximated message passing algorithm and a nontrivial back-propagation rule for our framework. Experiments on various types of GNN backbones demonstrate the scalability and competitive performance of our framework on large-graph node classification and link prediction benchmarks.
Learning good representations on multi-relational graphs is essential to knowledge base completion (KBC). In this paper, we propose a new self-supervised training objective for multi-relational graph representation learning, via simply incorporating relation prediction into the commonly used 1vsAll objective. The new training objective contains not only terms for predicting the subject and object of a given triple, but also a term for predicting the relation type. We analyse how this new objective impacts multi-relational learning in KBC: experiments on a variety of datasets and models show that relation prediction can significantly improve entity ranking, the most widely used evaluation task for KBC, yielding a 6.1% increase in MRR and 9.9% increase in Hits@1 on FB15k-237 as well as a 3.1% increase in MRR and 3.4% in Hits@1 on Aristo-v4. Moreover, we observe that the proposed objective is especially effective on highly multi-relational datasets, i.e. datasets with a large number of predicates, and generates better representations when larger embedding sizes are used.
Link prediction is a very fundamental task on graphs. Inspired by traditional path-based methods, in this paper we propose a general and flexible representation learning framework based on paths for link prediction. Specifically, we define the representation of a pair of nodes as the generalized sum of all path representations, with each path representation as the generalized product of the edge representations in the path. Motivated by the Bellman-Ford algorithm for solving the shortest path problem, we show that the proposed path formulation can be efficiently solved by the generalized Bellman-Ford algorithm. To further improve the capacity of the path formulation, we propose the Neural Bellman-Ford Network (NBFNet), a general graph neural network framework that solves the path formulation with learned operators in the generalized Bellman-Ford algorithm. The NBFNet parameterizes the generalized Bellman-Ford algorithm with 3 neural components, namely INDICATOR, MESSAGE and AGGREGATE functions, which corresponds to the boundary condition, multiplication operator, and summation operator respectively. The NBFNet is very general, covers many traditional path-based methods, and can be applied to both homogeneous graphs and multi-relational graphs (e.g., knowledge graphs) in both transductive and inductive settings. Experiments on both homogeneous graphs and knowledge graphs show that the proposed NBFNet outperforms existing methods by a large margin in both transductive and inductive settings, achieving new state-of-the-art results.
In this paper, we provide a theory of using graph neural networks (GNNs) for multi-node representation learning (where we are interested in learning a representation for a set of more than one node, such as link). We know that GNN is designed to learn single-node representations. When we want to learn a node set representation involving multiple nodes, a common practice in previous works is to directly aggregate the single-node representations obtained by a GNN into a joint node set representation. In this paper, we show a fundamental constraint of such an approach, namely the inability to capture the dependence between nodes in the node set, and argue that directly aggregating individual node representations does not lead to an effective joint representation for multiple nodes. Then, we notice that a few previous successful works for multi-node representation learning, including SEAL, Distance Encoding, and ID-GNN, all used node labeling. These methods first label nodes in the graph according to their relationships with the target node set before applying a GNN. Then, the node representations obtained in the labeled graph are aggregated into a node set representation. By investigating their inner mechanisms, we unify these node labeling techniques into a single and most general form -- labeling trick. We prove that with labeling trick a sufficiently expressive GNN learns the most expressive node set representations, thus in principle solves any joint learning tasks over node sets. Experiments on one important two-node representation learning task, link prediction, verified our theory. Our work explains the superior performance of previous node-labeling-based methods, and establishes a theoretical foundation of using GNNs for multi-node representation learning.
Scoring functions (SFs), which measure the plausibility of triplets in knowledge graph (KG), have become the crux of KG embedding. Lots of SFs, which target at capturing different kinds of relations in KGs, have been designed by humans in recent years. However, as relations can exhibit complex patterns that are hard to infer before training, none of them can consistently perform better than others on existing benchmark data sets. In this paper, inspired by the recent success of automated machine learning (AutoML), we propose to automatically design SFs (AutoSF) for distinct KGs by the AutoML techniques. However, it is non-trivial to explore domain-specific information here to make AutoSF efficient and effective. We firstly identify a unified representation over popularly used SFs, which helps to set up a search space for AutoSF. Then, we propose a greedy algorithm to search in such a space efficiently. The algorithm is further sped up by a filter and a predictor, which can avoid repeatedly training SFs with same expressive ability and help removing bad candidates during the search before model training. Finally, we perform extensive experiments on benchmark data sets. Results on link prediction and triplets classification show that the searched SFs by AutoSF, are KG dependent, new to the literature, and outperform the state-of-the-art SFs designed by humans.
Low-dimensional embeddings of nodes in large graphs have proved extremely useful in a variety of prediction tasks, from content recommendation to identifying protein functions. However, most existing approaches require that all nodes in the graph are present during training of the embeddings; these previous approaches are inherently transductive and do not naturally generalize to unseen nodes. Here we present GraphSAGE, a general, inductive framework that leverages node feature information (e.g., text attributes) to efficiently generate node embeddings for previously unseen data. Instead of training individual embeddings for each node, we learn a function that generates embeddings by sampling and aggregating features from a node's local neighborhood. Our algorithm outperforms strong baselines on three inductive node-classification benchmarks: we classify the category of unseen nodes in evolving information graphs based on citation and Reddit post data, and we show that our algorithm generalizes to completely unseen graphs using a multi-graph dataset of protein-protein interactions.