Knowledge graph (KG) embedding seeks to learn vector representations for entities and relations. Conventional models reason over graph structures, but they suffer from the issues of graph incompleteness and long-tail entities. Recent studies have used pre-trained language models to learn embeddings based on the textual information of entities and relations, but they cannot take advantage of graph structures. In the paper, we show empirically that these two kinds of features are complementary for KG embedding. To this end, we propose CoLE, a Co-distillation Learning method for KG Embedding that exploits the complementarity of graph structures and text information. Its graph embedding model employs Transformer to reconstruct the representation of an entity from its neighborhood subgraph. Its text embedding model uses a pre-trained language model to generate entity representations from the soft prompts of their names, descriptions, and relational neighbors. To let the two model promote each other, we propose co-distillation learning that allows them to distill selective knowledge from each other's prediction logits. In our co-distillation learning, each model serves as both a teacher and a student. Experiments on benchmark datasets demonstrate that the two models outperform their related baselines, and the ensemble method CoLE with co-distillation learning advances the state-of-the-art of KG embedding.
Spatiotemporal activity prediction, aiming to predict user activities at a specific location and time, is crucial for applications like urban planning and mobile advertising. Existing solutions based on tensor decomposition or graph embedding suffer from the following two major limitations: 1) ignoring the fine-grained similarities of user preferences; 2) user's modeling is entangled. In this work, we propose a hypergraph neural network model called DisenHCN to bridge the above gaps. In particular, we first unify the fine-grained user similarity and the complex matching between user preferences and spatiotemporal activity into a heterogeneous hypergraph. We then disentangle the user representations into different aspects (location-aware, time-aware, and activity-aware) and aggregate corresponding aspect's features on the constructed hypergraph, capturing high-order relations from different aspects and disentangles the impact of each aspect for final prediction. Extensive experiments show that our DisenHCN outperforms the state-of-the-art methods by 14.23% to 18.10% on four real-world datasets. Further studies also convincingly verify the rationality of each component in our DisenHCN.
Incomplete multi-view clustering, which aims to solve the clustering problem on the incomplete multi-view data with partial view missing, has received more and more attention in recent years. Although numerous methods have been developed, most of the methods either cannot flexibly handle the incomplete multi-view data with arbitrary missing views or do not consider the negative factor of information imbalance among views. Moreover, some methods do not fully explore the local structure of all incomplete views. To tackle these problems, this paper proposes a simple but effective method, named localized sparse incomplete multi-view clustering (LSIMVC). Different from the existing methods, LSIMVC intends to learn a sparse and structured consensus latent representation from the incomplete multi-view data by optimizing a sparse regularized and novel graph embedded multi-view matrix factorization model. Specifically, in such a novel model based on the matrix factorization, a l1 norm based sparse constraint is introduced to obtain the sparse low-dimensional individual representations and the sparse consensus representation. Moreover, a novel local graph embedding term is introduced to learn the structured consensus representation. Different from the existing works, our local graph embedding term aggregates the graph embedding task and consensus representation learning task into a concise term. Furthermore, to reduce the imbalance factor of incomplete multi-view learning, an adaptive weighted learning scheme is introduced to LSIMVC. Finally, an efficient optimization strategy is given to solve the optimization problem of our proposed model. Comprehensive experimental results performed on six incomplete multi-view databases verify that the performance of our LSIMVC is superior to the state-of-the-art IMC approaches. The code is available in https://github.com/justsmart/LSIMVC.
Knowledge Graphs, such as Wikidata, comprise structural and textual knowledge in order to represent knowledge. For each of the two modalities dedicated approaches for graph embedding and language models learn patterns that allow for predicting novel structural knowledge. Few approaches have integrated learning and inference with both modalities and these existing ones could only partially exploit the interaction of structural and textual knowledge. In our approach, we build on existing strong representations of single modalities and we use hypercomplex algebra to represent both, (i), single-modality embedding as well as, (ii), the interaction between different modalities and their complementary means of knowledge representation. More specifically, we suggest Dihedron and Quaternion representations of 4D hypercomplex numbers to integrate four modalities namely structural knowledge graph embedding, word-level representations (e.g.\ Word2vec, Fasttext), sentence-level representations (Sentence transformer), and document-level representations (sentence transformer, Doc2vec). Our unified vector representation scores the plausibility of labelled edges via Hamilton and Dihedron products, thus modeling pairwise interactions between different modalities. Extensive experimental evaluation on standard benchmark datasets shows the superiority of our two new models using abundant textual information besides sparse structural knowledge to enhance performance in link prediction tasks.
We study a simple embedding technique based on a matrix of personalized PageRank vectors seeded on a random set of nodes. We show that the embedding produced by the element-wise logarithm of this matrix (1) are related to the spectral embedding for a class of graphs where spectral embeddings are significant, and hence useful representation of the data, (2) can be done for the entire network or a smaller part of it, which enables precise local representation, and (3) uses a relatively small number of PageRank vectors compared to the size of the networks. Most importantly, the general nature of this embedding strategy opens up many emerging applications, where eigenvector and spectral techniques may not be well established, to the PageRank-based relatives. For instance, similar techniques can be used on PageRank vectors from hypergraphs to get "spectral-like" embeddings.
This paper presents $\mu\text{KG}$, an open-source Python library for representation learning over knowledge graphs. $\mu\text{KG}$ supports joint representation learning over multi-source knowledge graphs (and also a single knowledge graph), multiple deep learning libraries (PyTorch and TensorFlow2), multiple embedding tasks (link prediction, entity alignment, entity typing, and multi-source link prediction), and multiple parallel computing modes (multi-process and multi-GPU computing). It currently implements 26 popular knowledge graph embedding models and supports 16 benchmark datasets. $\mu\text{KG}$ provides advanced implementations of embedding techniques with simplified pipelines of different tasks. It also comes with high-quality documentation for ease of use. $\mu\text{KG}$ is more comprehensive than existing knowledge graph embedding libraries. It is useful for a thorough comparison and analysis of various embedding models and tasks. We show that the jointly learned embeddings can greatly help knowledge-powered downstream tasks, such as multi-hop knowledge graph question answering. We will stay abreast of the latest developments in the related fields and incorporate them into $\mu\text{KG}$.
Recent advances in data processing have stimulated the demand for learning graphs of very large scales. Graph Neural Networks (GNNs), being an emerging and powerful approach in solving graph learning tasks, are known to be difficult to scale up. Most scalable models apply node-based techniques in simplifying the expensive graph message-passing propagation procedure of GNN. However, we find such acceleration insufficient when applied to million- or even billion-scale graphs. In this work, we propose SCARA, a scalable GNN with feature-oriented optimization for graph computation. SCARA efficiently computes graph embedding from node features, and further selects and reuses feature computation results to reduce overhead. Theoretical analysis indicates that our model achieves sub-linear time complexity with a guaranteed precision in propagation process as well as GNN training and inference. We conduct extensive experiments on various datasets to evaluate the efficacy and efficiency of SCARA. Performance comparison with baselines shows that SCARA can reach up to 100x graph propagation acceleration than current state-of-the-art methods with fast convergence and comparable accuracy. Most notably, it is efficient to process precomputation on the largest available billion-scale GNN dataset Papers100M (111M nodes, 1.6B edges) in 100 seconds.
Distributed power allocation is important for interference-limited wireless networks with dense transceiver pairs. In this paper, we aim to design low signaling overhead distributed power allocation schemes by using graph neural networks (GNNs), which are scalable to the number of wireless links. We first apply the message passing neural network (MPNN), a unified framework of GNN, to solve the problem. We show that the signaling overhead grows quadratically as the network size increases. Inspired from the over-the-air computation (AirComp), we then propose an Air-MPNN framework, where the messages from neighboring nodes are represented by the transmit power of pilots and can be aggregated efficiently by evaluating the total interference power. The signaling overhead of Air-MPNN grows linearly as the network size increases, and we prove that Air-MPNN is permutation invariant. To further reduce the signaling overhead, we propose the Air message passing recurrent neural network (Air-MPRNN), where each node utilizes the graph embedding and local state in the previous frame to update the graph embedding in the current frame. Since existing communication systems send a pilot during each frame, Air-MPRNN can be integrated into the existing standards by adjusting pilot power. Simulation results validate the scalability of the proposed frameworks, and show that they outperform the existing power allocation algorithms in terms of sum-rate for various system parameters.
Knowledge graph embedding research has mainly focused on learning continuous representations of knowledge graphs towards the link prediction problem. Recently developed frameworks can be effectively applied in research related applications. Yet, these frameworks do not fulfill many requirements of real-world applications. As the size of the knowledge graph grows, moving computation from a commodity computer to a cluster of computers in these frameworks becomes more challenging. Finding suitable hyperparameter settings w.r.t. time and computational budgets are left to practitioners. In addition, the continual learning aspect in knowledge graph embedding frameworks is often ignored, although continual learning plays an important role in many real-world (deep) learning-driven applications. Arguably, these limitations explain the lack of publicly available knowledge graph embedding models for large knowledge graphs. We developed a framework based on the frameworks DASK, Pytorch Lightning and Hugging Face to compute embeddings for large-scale knowledge graphs in a hardware-agnostic manner, which is able to address real-world challenges pertaining to the scale of real application. We provide an open-source version of our framework along with a hub of pre-trained models having more than 11.4 B parameters.
Personalized PageRank (PPR) is a fundamental tool in unsupervised learning of graph representations such as node ranking, labeling, and graph embedding. However, while data privacy is one of the most important recent concerns, existing PPR algorithms are not designed to protect user privacy. PPR is highly sensitive to the input graph edges: the difference of only one edge may cause a big change in the PPR vector, potentially leaking private user data. In this work, we propose an algorithm which outputs an approximate PPR and has provably bounded sensitivity to input edges. In addition, we prove that our algorithm achieves similar accuracy to non-private algorithms when the input graph has large degrees. Our sensitivity-bounded PPR directly implies private algorithms for several tools of graph learning, such as, differentially private (DP) PPR ranking, DP node classification, and DP node embedding. To complement our theoretical analysis, we also empirically verify the practical performances of our algorithms.
Knowledge graph embedding (KGE) models are an effective and popular approach to represent and reason with multi-relational data. Prior studies have shown that KGE models are sensitive to hyperparameter settings, however, and that suitable choices are dataset-dependent. In this paper, we explore hyperparameter optimization (HPO) for very large knowledge graphs, where the cost of evaluating individual hyperparameter configurations is excessive. Prior studies often avoided this cost by using various heuristics; e.g., by training on a subgraph or by using fewer epochs. We systematically discuss and evaluate the quality and cost savings of such heuristics and other low-cost approximation techniques. Based on our findings, we introduce GraSH, an efficient multi-fidelity HPO algorithm for large-scale KGEs that combines both graph and epoch reduction techniques and runs in multiple rounds of increasing fidelities. We conducted an experimental study and found that GraSH obtains state-of-the-art results on large graphs at a low cost (three complete training runs in total).
The Weisfeiler-Lehman (WL) test is a widely used algorithm in graph machine learning, including graph kernels, graph metrics, and graph neural networks. However, it focuses only on the consistency of the graph, which means that it is unable to detect slight structural differences. Consequently, this limits its ability to capture structural information, which also limits the performance of existing models that rely on the WL test. This limitation is particularly severe for traditional metrics defined by the WL test, which cannot precisely capture slight structural differences. In this paper, we propose a novel graph metric called the Wasserstein WL Subtree (WWLS) distance to address this problem. Our approach leverages the WL subtree as structural information for node neighborhoods and defines node metrics using the $L_1$-approximated tree edit distance ($L_1$-TED) between WL subtrees of nodes. Subsequently, we combine the Wasserstein distance and the $L_1$-TED to define the WWLS distance, which can capture slight structural differences that may be difficult to detect using conventional metrics. We demonstrate that the proposed WWLS distance outperforms baselines in both metric validation and graph classification experiments.
Embedding knowledge graphs into low-dimensional spaces is a popular method for applying approaches, such as link prediction or node classification, to these databases. This embedding process is very costly in terms of both computational time and space. Part of the reason for this is the optimisation of hyperparameters, which involves repeatedly sampling, by random, guided, or brute-force selection, from a large hyperparameter space and testing the resulting embeddings for their quality. However, not all hyperparameters in this search space will be equally important. In fact, with prior knowledge of the relative importance of the hyperparameters, some could be eliminated from the search altogether without significantly impacting the overall quality of the outputted embeddings. To this end, we ran a Sobol sensitivity analysis to evaluate the effects of tuning different hyperparameters on the variance of embedding quality. This was achieved by performing thousands of embedding trials, each time measuring the quality of embeddings produced by different hyperparameter configurations. We regressed the embedding quality on those hyperparameter configurations, using this model to generate Sobol sensitivity indices for each of the hyperparameters. By evaluating the correlation between Sobol indices, we find substantial variability in the hyperparameter sensitivities between knowledge graphs, with differing dataset characteristics being the probable cause of these inconsistencies. As an additional contribution of this work we identify several relations in the UMLS knowledge graph that may cause data leakage via inverse relations, and derive and present UMLS-43, a leakage-robust variant of that graph.
Representation learning on graphs, also called graph embedding, has demonstrated its significant impact on a series of machine learning applications such as classification, prediction and recommendation. However, existing work has largely ignored the rich information contained in the properties (or attributes) of both nodes and edges of graphs in modern applications, e.g., those represented by property graphs. To date, most existing graph embedding methods either focus on plain graphs with only the graph topology, or consider properties on nodes only. We propose PGE, a graph representation learning framework that incorporates both node and edge properties into the graph embedding procedure. PGE uses node clustering to assign biases to differentiate neighbors of a node and leverages multiple data-driven matrices to aggregate the property information of neighbors sampled based on a biased strategy. PGE adopts the popular inductive model for neighborhood aggregation. We provide detailed analyses on the efficacy of our method and validate the performance of PGE by showing how PGE achieves better embedding results than the state-of-the-art graph embedding methods on benchmark applications such as node classification and link prediction over real-world datasets.
Negative sampling (NS) loss plays an important role in learning knowledge graph embedding (KGE) to handle a huge number of entities. However, the performance of KGE degrades without hyperparameters such as the margin term and number of negative samples in NS loss being appropriately selected. Currently, empirical hyperparameter tuning addresses this problem at the cost of computational time. To solve this problem, we theoretically analyzed NS loss to assist hyperparameter tuning and understand the better use of the NS loss in KGE learning. Our theoretical analysis showed that scoring methods with restricted value ranges, such as TransE and RotatE, require appropriate adjustment of the margin term or the number of negative samples different from those without restricted value ranges, such as RESCAL, ComplEx, and DistMult. We also propose subsampling methods specialized for the NS loss in KGE studied from a theoretical aspect. Our empirical analysis on the FB15k-237, WN18RR, and YAGO3-10 datasets showed that the results of actually trained models agree with our theoretical findings.
Graph embedding techniques are a staple of modern graph learning research. When using embeddings for downstream tasks such as classification, information about their stability and robustness, i.e., their susceptibility to sources of noise, stochastic effects, or specific parameter choices, becomes increasingly important. As one of the most prominent graph embedding schemes, we focus on node2vec and analyse its embedding quality from multiple perspectives. Our findings indicate that embedding quality is unstable with respect to parameter choices, and we propose strategies to remedy this in practice.
Learning efficient graph representation is the key to favorably addressing downstream tasks on graphs, such as node or graph property prediction. Given the non-Euclidean structural property of graphs, preserving the original graph data's similarity relationship in the embedded space needs specific tools and a similarity metric. This paper develops a new graph representation learning scheme, namely EGG, which embeds approximated second-order graph characteristics into a Grassmann manifold. The proposed strategy leverages graph convolutions to learn hidden representations of the corresponding subspace of the graph, which is then mapped to a Grassmann point of a low dimensional manifold through truncated singular value decomposition (SVD). The established graph embedding approximates denoised correlationship of node attributes, as implemented in the form of a symmetric matrix space for Euclidean calculation. The effectiveness of EGG is demonstrated using both clustering and classification tasks at the node level and graph level. It outperforms baseline models on various benchmarks.
Knowledge graph embedding research has mainly focused on learning continuous representations of entities and relations tailored towards the link prediction problem. Recent results indicate an ever increasing predictive ability of current approaches on benchmark datasets. However, this effectiveness often comes with the cost of over-parameterization and increased computationally complexity. The former induces extensive hyperparameter optimization to mitigate malicious overfitting. The latter magnifies the importance of winning the hardware lottery. Here, we investigate a remedy for the first problem. We propose a technique based on Kronecker decomposition to reduce the number of parameters in a knowledge graph embedding model, while retaining its expressiveness. Through Kronecker decomposition, large embedding matrices are split into smaller embedding matrices during the training process. Hence, embeddings of knowledge graphs are not plainly retrieved but reconstructed on the fly. The decomposition ensures that elementwise interactions between three embedding vectors are extended with interactions within each embedding vector. This implicitly reduces redundancy in embedding vectors and encourages feature reuse. To quantify the impact of applying Kronecker decomposition on embedding matrices, we conduct a series of experiments on benchmark datasets. Our experiments suggest that applying Kronecker decomposition on embedding matrices leads to an improved parameter efficiency on all benchmark datasets. Moreover, empirical evidence suggests that reconstructed embeddings entail robustness against noise in the input knowledge graph. To foster reproducible research, we provide an open-source implementation of our approach, including training and evaluation scripts as well as pre-trained models in our knowledge graph embedding framework (https://github.com/dice-group/dice-embeddings).
Learned knowledge graph representations supporting robots contain a wealth of domain knowledge that drives robot behavior. However, there does not exist an inference reconciliation framework that expresses how a knowledge graph representation affects a robot's sequential decision making. We use a pedagogical approach to explain the inferences of a learned, black-box knowledge graph representation, a knowledge graph embedding. Our interpretable model, uses a decision tree classifier to locally approximate the predictions of the black-box model, and provides natural language explanations interpretable by non-experts. Results from our algorithmic evaluation affirm our model design choices, and the results of our user studies with non-experts support the need for the proposed inference reconciliation framework. Critically, results from our simulated robot evaluation indicate that our explanations enable non-experts to correct erratic robot behaviors due to nonsensical beliefs within the black-box.
Knowledge graph (KG) embedding methods which map entities and relations to unique embeddings in the KG have shown promising results on many reasoning tasks. However, the same embedding dimension for both dense entities and sparse entities will cause either over parameterization (sparse entities) or under fitting (dense entities). Normally, a large dimension is set to get better performance. Meanwhile, the inference time grows log-linearly with the number of entities for all entities are traversed and compared. Both the parameter and inference become challenges when working with huge amounts of entities. Thus, we propose PIE, a \textbf{p}arameter and \textbf{i}nference \textbf{e}fficient solution. Inspired from tensor decomposition methods, we find that decompose entity embedding matrix into low rank matrices can reduce more than half of the parameters while maintaining comparable performance. To accelerate model inference, we propose a self-supervised auxiliary task, which can be seen as fine-grained entity typing. By randomly masking and recovering entities' connected relations, the task learns the co-occurrence of entity and relations. Utilizing the fine grained typing, we can filter unrelated entities during inference and get targets with possibly sub-linear time requirement. Experiments on link prediction benchmarks demonstrate the proposed key capabilities. Moreover, we prove effectiveness of the proposed solution on the Open Graph Benchmark large scale challenge dataset WikiKG90Mv2 and achieve the state of the art performance.