Knowledge graph representation learning approaches provide a mapping between symbolic knowledge in the form of triples in a knowledge graph (KG) and their feature vectors. Knowledge graph embedding (KGE) models often represent relations in a KG as geometric transformations. Most state-of-the-art (SOTA) KGE models are derived from elementary geometric transformations (EGTs), such as translation, scaling, rotation, and reflection, or their combinations. These geometric transformations enable the models to effectively preserve specific structural and relational patterns of the KG. However, the current use of EGTs by KGEs remains insufficient without considering relation-specific transformations. Although recent models attempted to address this problem by ensembling SOTA baseline models in different ways, only a single or composite version of geometric transformations are used by such baselines to represent all the relations. In this paper, we propose a framework that evaluates how well each relation fits with different geometric transformations. Based on this ranking, the model can: (1) assign the best-matching transformation to each relation, or (2) use majority voting to choose one transformation type to apply across all relations. That is, the model learns a single relation-specific EGT in low dimensional vector space through an attention mechanism. Furthermore, we use the correlation between relations and EGTs, which are learned in a low dimension, for relation embeddings in a high dimensional vector space. The effectiveness of our models is demonstrated through comprehensive evaluations on three benchmark KGs as well as a real-world financial KG, witnessing a performance comparable to leading models
The hyperbolic space, characterized by a constant negative curvature and exponentially expanding space, aligns well with the structural properties of heterogeneous graphs. However, although heterogeneous graphs inherently possess diverse power-law structures, most hyperbolic heterogeneous graph embedding models rely on a single hyperbolic space. This approach may fail to effectively capture the diverse power-law structures within heterogeneous graphs. To address this limitation, we propose a Metapath-based Hyperbolic Contrastive Learning framework (MHCL), which uses multiple hyperbolic spaces to capture diverse complex structures within heterogeneous graphs. Specifically, by learning each hyperbolic space to describe the distribution of complex structures corresponding to each metapath, it is possible to capture semantic information effectively. Since metapath embeddings represent distinct semantic information, preserving their discriminability is important when aggregating them to obtain node representations. Therefore, we use a contrastive learning approach to optimize MHCL and improve the discriminability of metapath embeddings. In particular, our contrastive learning method minimizes the distance between embeddings of the same metapath and maximizes the distance between those of different metapaths in hyperbolic space, thereby improving the separability of metapath embeddings with distinct semantic information. We conduct comprehensive experiments to evaluate the effectiveness of MHCL. The experimental results demonstrate that MHCL outperforms state-of-the-art baselines in various graph machine learning tasks, effectively capturing the complex structures of heterogeneous graphs.
Continual Knowledge Graph Embedding (CKGE) seeks to integrate new knowledge while preserving past information. However, existing methods struggle with efficiency and scalability due to two key limitations: (1) suboptimal knowledge preservation between snapshots caused by manually designed node/relation importance scores that ignore graph dependencies relevant to the downstream task, and (2) computationally expensive graph traversal for node/relation importance calculation, leading to slow training and high memory overhead. To address these limitations, we introduce ETT-CKGE (Efficient, Task-driven, Tokens for Continual Knowledge Graph Embedding), a novel task-guided CKGE method that leverages efficient task-driven tokens for efficient and effective knowledge transfer between snapshots. Our method introduces a set of learnable tokens that directly capture task-relevant signals, eliminating the need for explicit node scoring or traversal. These tokens serve as consistent and reusable guidance across snapshots, enabling efficient token-masked embedding alignment between snapshots. Importantly, knowledge transfer is achieved through simple matrix operations, significantly reducing training time and memory usage. Extensive experiments across six benchmark datasets demonstrate that ETT-CKGE consistently achieves superior or competitive predictive performance, while substantially improving training efficiency and scalability compared to state-of-the-art CKGE methods. The code is available at: https://github.com/lijingzhu1/ETT-CKGE/tree/main
Knowledge graph embedding (KGE) models are extensively studied for knowledge graph completion, yet their evaluation remains constrained by unrealistic benchmarks. Standard evaluation metrics rely on the closed-world assumption, which penalizes models for correctly predicting missing triples, contradicting the fundamental goals of link prediction. These metrics often compress accuracy assessment into a single value, obscuring models' specific strengths and weaknesses. The prevailing evaluation protocol, link prediction, operates under the unrealistic assumption that an entity's properties, for which values are to be predicted, are known in advance. While alternative protocols such as property prediction, entity-pair ranking, and triple classification address some of these limitations, they remain underutilized. Moreover, commonly used datasets are either faulty or too small to reflect real-world data. Few studies examine the role of mediator nodes, which are essential for modeling n-ary relationships, or investigate model performance variation across domains. This paper conducts a comprehensive evaluation of four representative KGE models on large-scale datasets FB-CVT-REV and FB+CVT-REV. Our analysis reveals critical insights, including substantial performance variations between small and large datasets, both in relative rankings and absolute metrics, systematic overestimation of model capabilities when n-ary relations are binarized, and fundamental limitations in current evaluation protocols and metrics.
Graph neural networks (GNNs), which capture graph structures via a feature aggregation mechanism following the graph embedding framework, have demonstrated a powerful ability to support various tasks. According to the topology properties (e.g., structural roles or community memberships of nodes) to be preserved, graph embedding can be categorized into identity and position embedding. However, it is unclear for most GNN-based methods which property they can capture. Some of them may also suffer from low efficiency and scalability caused by several time- and space-consuming procedures (e.g., feature extraction and training). From a perspective of graph signal processing, we find that high- and low-frequency information in the graph spectral domain may characterize node identities and positions, respectively. Based on this investigation, we propose random feature aggregation (RFA) for efficient identity and position embedding, serving as an extreme ablation study regarding GNN feature aggregation. RFA (i) adopts a spectral-based GNN without learnable parameters as its backbone, (ii) only uses random noises as inputs, and (iii) derives embeddings via just one feed-forward propagation (FFP). Inspired by degree-corrected spectral clustering, we further introduce a degree correction mechanism to the GNN backbone. Surprisingly, our experiments demonstrate that two variants of RFA with high- and low-pass filters can respectively derive informative identity and position embeddings via just one FFP (i.e., without any training). As a result, RFA can achieve a better trade-off between quality and efficiency for both identity and position embedding over various baselines.
We focus on obtaining robust knowledge graph embedding under perturbation in the embedding space. To address these challenges, we introduce a novel framework, Robust Knowledge Graph Embedding via Denoising, which enhances the robustness of KGE models on noisy triples. By treating KGE methods as energy-based models, we leverage the established connection between denoising and score matching, enabling the training of a robust denoising KGE model. Furthermore, we propose certified robustness evaluation metrics for KGE methods based on the concept of randomized smoothing. Through comprehensive experiments on benchmark datasets, our framework consistently shows superior performance compared to existing state-of-the-art KGE methods when faced with perturbed entity embedding.
Uncertainty quantification in Knowledge Graph Embedding (KGE) methods is crucial for ensuring the reliability of downstream applications. A recent work applies conformal prediction to KGE methods, providing uncertainty estimates by generating a set of answers that is guaranteed to include the true answer with a predefined confidence level. However, existing methods provide probabilistic guarantees averaged over a reference set of queries and answers (marginal coverage guarantee). In high-stakes applications such as medical diagnosis, a stronger guarantee is often required: the predicted sets must provide consistent coverage per query (conditional coverage guarantee). We propose CondKGCP, a novel method that approximates predicate-conditional coverage guarantees while maintaining compact prediction sets. CondKGCP merges predicates with similar vector representations and augments calibration with rank information. We prove the theoretical guarantees and demonstrate empirical effectiveness of CondKGCP by comprehensive evaluations.
Traffic forecasting is a key task in the field of Intelligent Transportation Systems. Recent research on traffic forecasting has mainly focused on combining graph neural networks (GNNs) with other models. However, GNNs only consider short-range spatial information. In this study, we present a novel model termed LSTAN-GERPE (Lightweight Spatio-Temporal Attention Network with Graph Embedding and Rotational Position Encoding). This model leverages both Temporal and Spatial Attention mechanisms to effectively capture long-range traffic dynamics. Additionally, the optimal frequency for rotational position encoding is determined through a grid search approach in both the spatial and temporal attention mechanisms. This systematic optimization enables the model to effectively capture complex traffic patterns. The model also enhances feature representation by incorporating geographical location maps into the spatio-temporal embeddings. Without extensive feature engineering, the proposed method in this paper achieves advanced accuracy on the real-world traffic forecasting datasets PeMS04 and PeMS08.
Integrating structured knowledge from Knowledge Graphs (KGs) into Large Language Models (LLMs) remains a key challenge for symbolic reasoning. Existing methods mainly rely on prompt engineering or fine-tuning, which lose structural fidelity or incur high computational costs. Building on recent encoding techniques which integrate graph embeddings within the LLM input as tokens, we extend this paradigm to the KG domain by leveraging Knowledge Graph Embedding (KGE) models, thus enabling graph-aware reasoning. Our approach is model-agnostic, resource-efficient, and compatible with any LLMs. Extensive experimentation on synthetic and real-world datasets shows that our method improves reasoning performance over established baselines, further achieving the best trade-off in terms of accuracy and efficiency against state-of-the-art LLMs.
Worldwide, Geo-distributed Data Centers (GDCs) provide computing and storage services for massive workflow applications, resulting in high electricity costs that vary depending on geographical locations and time. How to reduce electricity costs while satisfying the deadline constraints of workflow applications is important in GDCs, which is determined by the execution time of servers, power, and electricity price. Determining the completion time of workflows with different server frequencies can be challenging, especially in scenarios with heterogeneous computing resources in GDCs. Moreover, the electricity price is also different in geographical locations and may change dynamically. To address these challenges, we develop a geo-distributed system architecture and propose an Electricity Cost aware Multiple Workflows Scheduling algorithm (ECMWS) for servers of GDCs with fixed frequency and power. ECMWS comprises four stages, namely workflow sequencing, deadline partitioning, task sequencing, and resource allocation where two graph embedding models and a policy network are constructed to solve the Markov Decision Process (MDP). After statistically calibrating parameters and algorithm components over a comprehensive set of workflow instances, the proposed algorithms are compared with the state-of-the-art methods over two types of workflow instances. The experimental results demonstrate that our proposed algorithm significantly outperforms other algorithms, achieving an improvement of over 15\% while maintaining an acceptable computational time. The source codes are available at https://gitee.com/public-artifacts/ecmws-experiments.
Knowledge graph embedding (KGE) methods aim to represent entities and relations in a continuous space while preserving their structural and semantic properties. Quaternion-based KGEs have demonstrated strong potential in capturing complex relational patterns. In this work, we propose QuatE-D, a novel quaternion-based model that employs a distance-based scoring function instead of traditional inner-product approaches. By leveraging Euclidean distance, QuatE-D enhances interpretability and provides a more flexible representation of relational structures. Experimental results demonstrate that QuatE-D achieves competitive performance while maintaining an efficient parameterization, particularly excelling in Mean Rank reduction. These findings highlight the effectiveness of distance-based scoring in quaternion embeddings, offering a promising direction for knowledge graph completion.
Self-supervised learning (SSL) in graphs has garnered significant attention, particularly in employing Graph Neural Networks (GNNs) with pretext tasks initially designed for other domains, such as contrastive learning and feature reconstruction. However, it remains uncertain whether these methods effectively reflect essential graph properties, precisely representation similarity with its neighbors. We observe that existing methods position opposite ends of a spectrum driven by the graph embedding smoothness, with each end corresponding to outperformance on specific downstream tasks. Decomposing the SSL objective into three terms via an information-theoretic framework with a neighbor representation variable reveals that this polarization stems from an imbalance among the terms, which existing methods may not effectively maintain. Further insights suggest that balancing between the extremes can lead to improved performance across a wider range of downstream tasks. A framework, BSG (Balancing Smoothness in Graph SSL), introduces novel loss functions designed to supplement the representation quality in graph-based SSL by balancing the derived three terms: neighbor loss, minimal loss, and divergence loss. We present a theoretical analysis of the effects of these loss functions, highlighting their significance from both the SSL and graph smoothness perspectives. Extensive experiments on multiple real-world datasets across node classification and link prediction consistently demonstrate that BSG achieves state-of-the-art performance, outperforming existing methods. Our implementation code is available at https://github.com/steve30572/BSG.
Knowledge graph embedding (KGE) models encode the structural information of knowledge graphs to predicting new links. Effective training of these models requires distinguishing between positive and negative samples with high precision. Although prior research has shown that improving the quality of negative samples can significantly enhance model accuracy, identifying high-quality negative samples remains a challenging problem. This paper theoretically investigates the condition under which negative samples lead to optimal KG embedding and identifies a sufficient condition for an effective negative sample distribution. Based on this theoretical foundation, we propose \textbf{E}mbedding \textbf{MU}tation (\textsc{EMU}), a novel framework that \emph{generates} negative samples satisfying this condition, in contrast to conventional methods that focus on \emph{identifying} challenging negative samples within the training data. Importantly, the simplicity of \textsc{EMU} ensures seamless integration with existing KGE models and negative sampling methods. To evaluate its efficacy, we conducted comprehensive experiments across multiple datasets. The results consistently demonstrate significant improvements in link prediction performance across various KGE models and negative sampling methods. Notably, \textsc{EMU} enables performance improvements comparable to those achieved by models with embedding dimension five times larger. An implementation of the method and experiments are available at https://github.com/nec-research/EMU-KG.
Knowledge graph embedding (KGE) is a technique that enhances knowledge graphs by addressing incompleteness and improving knowledge retrieval. A limitation of the existing KGE models is their underutilization of ontologies, specifically the relationships between properties. This study proposes a KGE model, TransU, designed for knowledge graphs with well-defined ontologies that incorporate relationships between properties. The model treats properties as a subset of entities, enabling a unified representation. We present experimental results using a standard dataset and a practical dataset.
Protein-protein interaction (PPI) prediction plays a pivotal role in deciphering cellular functions and disease mechanisms. To address the limitations of traditional experimental methods and existing computational approaches in cross-modal feature fusion and false-negative suppression, we propose SCMPPI-a novel supervised contrastive multimodal framework. By effectively integrating sequence-based features (AAC, DPC, ESMC-CKSAAP) with network topology (Node2Vec embeddings) and incorporating an enhanced contrastive learning strategy with negative sample filtering, SCMPPI achieves superior prediction performance. Extensive experiments on eight benchmark datasets demonstrate its state-of-the-art accuracy(98.13%) and AUC(99.69%), along with excellent cross-species generalization (AUC>99%). Successful applications in CD9 networks, Wnt pathway analysis, and cancer-specific networks further highlight its potential for disease target discovery, establishing SCMPPI as a powerful tool for multimodal biological data analysis.
Current Continual Knowledge Graph Embedding (CKGE) methods primarily rely on translation-based embedding methods, leveraging previously acquired knowledge to initialize new facts. To enhance learning efficiency, these methods often integrate fine-tuning or continual learning strategies. However, this compromises the model's prediction accuracy and the translation-based methods lack support for complex relational structures (multi-hop relations). To tackle this challenge, we propose a novel CKGE framework SoTCKGE grounded in Spatial Offset Transformation. Within this framework, entity positions are defined as being jointly determined by base position vectors and offset vectors. This not only enhances the model's ability to represent complex relational structures but also allows for the embedding update of both new and old knowledge through simple spatial offset transformations, without the need for continuous learning methods. Furthermore, we introduce a hierarchical update strategy and a balanced embedding method to refine the parameter update process, effectively minimizing training costs and augmenting model accuracy. To comprehensively assess the performance of our model, we have conducted extensive experimlents on four publicly accessible datasets and a new dataset constructed by us. Experimental results demonstrate the advantage of our model in enhancing multi-hop relationship learning and further improving prediction accuracy.
The skip-gram model (SGM), which employs a neural network to generate node vectors, serves as the basis for numerous popular graph embedding techniques. However, since the training datasets contain sensitive linkage information, the parameters of a released SGM may encode private information and pose significant privacy risks. Differential privacy (DP) is a rigorous standard for protecting individual privacy in data analysis. Nevertheless, when applying differential privacy to skip-gram in graphs, it becomes highly challenging due to the complex link relationships, which potentially result in high sensitivity and necessitate substantial noise injection. To tackle this challenge, we present AdvSGM, a differentially private skip-gram for graphs via adversarial training. Our core idea is to leverage adversarial training to privatize skip-gram while improving its utility. Towards this end, we develop a novel adversarial training module by devising two optimizable noise terms that correspond to the parameters of a skip-gram. By fine-tuning the weights between modules within AdvSGM, we can achieve differentially private gradient updates without additional noise injection. Extensive experimental results on six real-world graph datasets show that AdvSGM preserves high data utility across different downstream tasks.
Gene expression datasets offer insights into gene regulation mechanisms, biochemical pathways, and cellular functions. Additionally, comparing gene expression profiles between disease and control patients can deepen the understanding of disease pathology. Therefore, machine learning has been used to process gene expression data, with patient diagnosis emerging as one of the most popular applications. Although gene expression data can provide valuable insights, challenges arise because the number of patients in expression datasets is usually limited, and the data from different datasets with different gene expressions cannot be easily combined. This work proposes a novel methodology to address these challenges by integrating multiple gene expression datasets and domain-specific knowledge using knowledge graphs, a unique tool for biomedical data integration. Then, vector representations are produced using knowledge graph embedding techniques, which are used as inputs for a graph neural network and a multi-layer perceptron. We evaluate the efficacy of our methodology in three settings: single-dataset learning, multi-dataset learning, and transfer learning. The experimental results show that combining gene expression datasets and domain-specific knowledge improves patient diagnosis in all three settings.
In the real world, trajectory data is often sparse and incomplete due to low collection frequencies or limited device coverage. Trajectory recovery aims to recover these missing trajectory points, making the trajectories denser and more complete. However, this task faces two key challenges: 1) The excessive sparsity of individual trajectories makes it difficult to effectively leverage historical information for recovery; 2) Sparse trajectories make it harder to capture complex individual mobility preferences. To address these challenges, we propose a novel method called DiffMove. Firstly, we harness crowd wisdom for trajectory recovery. Specifically, we construct a group tendency graph using the collective trajectories of all users and then integrate the group mobility trends into the location representations via graph embedding. This solves the challenge of sparse trajectories being unable to rely on individual historical trajectories for recovery. Secondly, we capture individual mobility preferences from both historical and current perspectives. Finally, we integrate group mobility tendencies and individual preferences into the spatiotemporal distribution of the trajectory to recover high-quality trajectories. Extensive experiments on two real-world datasets demonstrate that DiffMove outperforms existing state-of-the-art methods. Further analysis validates the robustness of our method.
Dimensionality reduction is a fundamental task that aims to simplify complex data by reducing its feature dimensionality while preserving essential patterns, with core applications in data analysis and visualisation. To preserve the underlying data structure, multi-dimensional scaling (MDS) methods focus on preserving pairwise dissimilarities, such as distances. They optimise the embedding to have pairwise distances as close as possible to the data dissimilarities. However, the current standard is limited to embedding data in Riemannian manifolds. Motivated by the lack of asymmetry in the Riemannian metric of the embedding space, this paper extends the MDS problem to a natural asymmetric generalisation of Riemannian manifolds called Finsler manifolds. Inspired by Euclidean space, we define a canonical Finsler space for embedding asymmetric data. Due to its simplicity with respect to geodesics, data representation in this space is both intuitive and simple to analyse. We demonstrate that our generalisation benefits from the same theoretical convergence guarantees. We reveal the effectiveness of our Finsler embedding across various types of non-symmetric data, highlighting its value in applications such as data visualisation, dimensionality reduction, directed graph embedding, and link prediction.