Embedding methods transform the knowledge graph into a continuous, low-dimensional space, facilitating inference and completion tasks. Existing methods are mainly divided into two types: translational distance models and semantic matching models. A key challenge in translational distance models is their inability to effectively differentiate between 'head' and 'tail' entities in graphs. To address this problem, a novel location-sensitive embedding (LSE) method has been developed. LSE innovatively modifies the head entity using relation-specific mappings, conceptualizing relations as linear transformations rather than mere translations. The theoretical foundations of LSE, including its representational capabilities and its connections to existing models, have been thoroughly examined. A more streamlined variant, LSEd, which employs a diagonal matrix for transformations to enhance practical efficiency, is also proposed. Experiments conducted on four large-scale KG datasets for link prediction show that LSEd either outperforms or is competitive with state-of-the-art related works.
As the Chinese stock market continues to evolve and its market structure grows increasingly complex, traditional quantitative trading methods are facing escalating challenges. Particularly, due to policy uncertainty and the frequent market fluctuations triggered by sudden economic events, existing models often struggle to accurately predict market dynamics. To address these challenges, this paper introduces Stockformer, a price-volume factor stock selection model that integrates wavelet transformation and a multitask self-attention network, aimed at enhancing responsiveness and predictive accuracy regarding market instabilities. Through discrete wavelet transform, Stockformer decomposes stock returns into high and low frequencies, meticulously capturing long-term market trends and short-term fluctuations, including abrupt events. Moreover, the model incorporates a Dual-Frequency Spatiotemporal Encoder and graph embedding techniques to effectively capture complex temporal and spatial relationships among stocks. Employing a multitask learning strategy, it simultaneously predicts stock returns and directional trends. Experimental results show that Stockformer outperforms existing advanced methods on multiple real stock market datasets. In strategy backtesting, Stockformer consistently demonstrates exceptional stability and reliability across market conditions-whether rising, falling, or fluctuating-particularly maintaining high performance during downturns or volatile periods, indicating a high adaptability to market fluctuations. To foster innovation and collaboration in the financial analysis sector, the Stockformer model's code has been open-sourced and is available on the GitHub repository: https://github.com/Eric991005/Multitask-Stockformer.
In a spoofing attack, a malicious actor impersonates a legitimate user to access or manipulate data without authorization. The vulnerability of cryptographic security mechanisms to compromised user credentials motivates spoofing attack detection in the physical layer, which traditionally relied on channel features, such as the received signal strength (RSS) measured by spatially distributed receivers or access points. However, existing methods cannot effectively cope with the dynamic nature of channels, which change over time as a result of user mobility and other factors. To address this limitation, this work builds upon the intuition that the temporal pattern of changes in RSS features can be used to detect the presence of concurrent transmissions from multiple (possibly changing) locations, which in turn indicates the existence of an attack. Since a localization-based approach would require costly data collection and would suffer from low spatial resolution due to multipath, the proposed algorithm employs a deep neural network to construct a graph embedding of a sequence of RSS features that reflects changes in the propagation conditions. A graph neural network then classifies these embeddings to detect spoofing attacks. The effectiveness and robustness of the proposed scheme are corroborated by experiments with real-data.
Graphs are a powerful representation tool in machine learning applications, with link prediction being a key task in graph learning. Temporal link prediction in dynamic networks is of particular interest due to its potential for solving complex scientific and real-world problems. Traditional approaches to temporal link prediction have focused on finding the aggregation of dynamics of the network as a unified output. In this study, we propose a novel perspective on temporal link prediction by defining nodes as Newtonian objects and incorporating the concept of velocity to predict network dynamics. By computing more specific dynamics of each node, rather than overall dynamics, we improve both accuracy and explainability in predicting future connections. We demonstrate the effectiveness of our approach using two datasets, including 17 years of co-authorship data from PubMed. Experimental results show that our temporal graph embedding dynamics approach improves downstream classification models' ability to predict future collaboration efficacy in co-authorship networks by 17.34% (AUROC improvement relative to the baseline model). Furthermore, our approach offers an interpretable layer over traditional approaches to address the temporal link prediction problem.
Accurate precipitation nowcasting is crucial for applications such as flood prediction, disaster management, agriculture optimization, and transportation management. While many studies have approached this task using sequence-to-sequence models, most focus on single regions, ignoring correlations between disjoint areas. We reformulate precipitation nowcasting as a spatiotemporal graph sequence problem. Specifically, we propose Graph Dual-stream Convolutional Attention Fusion, a novel extension of the graph attention network. Our model's dual-stream design employs distinct attention mechanisms for spatial and temporal interactions, capturing their unique dynamics. A gated fusion module integrates both streams, leveraging spatial and temporal information for improved predictive accuracy. Additionally, our framework enhances graph attention by directly processing three-dimensional tensors within graph nodes, removing the need for reshaping. This capability enables handling complex, high-dimensional data and exploiting higher-order correlations between data dimensions. Depthwise-separable convolutions are also incorporated to refine local feature extraction and efficiently manage high-dimensional inputs. We evaluate our model using seven years of precipitation data from Copernicus Climate Change Services, covering Europe and neighboring regions. Experimental results demonstrate superior performance of our approach compared to other models. Moreover, visualizations of seasonal spatial and temporal attention scores provide insights into the most significant connections between regions and time steps.
In the rapidly advancing information era, various human behaviors are being precisely recorded in the form of data, including identity information, criminal records, and communication data. Law enforcement agencies can effectively maintain social security and precisely combat criminal activities by analyzing the aforementioned data. In comparison to traditional data analysis methods, deep learning models, relying on the robust computational power in cloud centers, exhibit higher accuracy in extracting data features and inferring data. However, within the architecture of cloud centers, the transmission of data from end devices introduces significant latency, hindering real-time inference of data. Furthermore, low-latency edge computing architectures face limitations in direct deployment due to relatively weak computing and storage capacities of nodes. To address these challenges, a lightweight distributed knowledge graph completion architecture is proposed. Firstly, we introduce a lightweight distributed knowledge graph completion architecture that utilizes knowledge graph embedding for data analysis. Subsequently, to filter out substandard data, a personnel data quality assessment method named PDQA is proposed. Lastly, we present a model pruning algorithm that significantly reduces the model size while maximizing performance, enabling lightweight deployment. In experiments, we compare the effects of 11 advanced models on completing the knowledge graph of public security personnel information. The results indicate that the RotatE model outperforms other models significantly in knowledge graph completion, with the pruned model size reduced by 70\%, and hits@10 reaching 86.97\%.}
Some of the most successful knowledge graph embedding (KGE) models for link prediction -- CP, RESCAL, TuckER, ComplEx -- can be interpreted as energy-based models. Under this perspective they are not amenable for exact maximum-likelihood estimation (MLE), sampling and struggle to integrate logical constraints. This work re-interprets the score functions of these KGEs as circuits -- constrained computational graphs allowing efficient marginalisation. Then, we design two recipes to obtain efficient generative circuit models by either restricting their activations to be non-negative or squaring their outputs. Our interpretation comes with little or no loss of performance for link prediction, while the circuits framework unlocks exact learning by MLE, efficient sampling of new triples, and guarantee that logical constraints are satisfied by design. Furthermore, our models scale more gracefully than the original KGEs on graphs with millions of entities.
Representing graph data in a low-dimensional space for subsequent tasks is the purpose of attributed graph embedding. Most existing neural network approaches learn latent representations by minimizing reconstruction errors. Rare work considers the data distribution and the topological structure of latent codes simultaneously, which often results in inferior embeddings in real-world graph data. This paper proposes a novel Deep Manifold (Variational) Graph Auto-Encoder (DMVGAE/DMGAE) method for attributed graph data to improve the stability and quality of learned representations to tackle the crowding problem. The node-to-node geodesic similarity is preserved between the original and latent space under a pre-defined distribution. The proposed method surpasses state-of-the-art baseline algorithms by a significant margin on different downstream tasks across popular datasets, which validates our solutions. We promise to release the code after acceptance.
The primary aim of Knowledge Graph embeddings (KGE) is to learn low-dimensional representations of entities and relations for predicting missing facts. While rotation-based methods like RotatE and QuatE perform well in KGE, they face two challenges: limited model flexibility requiring proportional increases in relation size with entity dimension, and difficulties in generalizing the model for higher-dimensional rotations. To address these issues, we introduce OrthogonalE, a novel KGE model employing matrices for entities and block-diagonal orthogonal matrices with Riemannian optimization for relations. This approach enhances the generality and flexibility of KGE models. The experimental results indicate that our new KGE model, OrthogonalE, is both general and flexible, significantly outperforming state-of-the-art KGE models while substantially reducing the number of relation parameters.
Spectral embedding is a powerful graph embedding technique that has received a lot of attention recently due to its effectiveness on Graph Transformers. However, from a theoretical perspective, the universal expressive power of spectral embedding comes at the price of losing two important invariance properties of graphs, sign and basis invariance, which also limits its effectiveness on graph data. To remedy this issue, many previous methods developed costly approaches to learn new invariants and suffer from high computation complexity. In this work, we explore a minimal approach that resolves the ambiguity issues by directly finding canonical directions for the eigenvectors, named Laplacian Canonization (LC). As a pure pre-processing method, LC is light-weighted and can be applied to any existing GNNs. We provide a thorough investigation, from theory to algorithm, on this approach, and discover an efficient algorithm named Maximal Axis Projection (MAP) that works for both sign and basis invariance and successfully canonizes more than 90% of all eigenvectors. Experiments on real-world benchmark datasets like ZINC, MOLTOX21, and MOLPCBA show that MAP consistently outperforms existing methods while bringing minimal computation overhead. Code is available at https://github.com/PKU-ML/LaplacianCanonization.
Recent studies focus on embedding learning over knowledge graphs, which map entities and relations in knowledge graphs into low-dimensional vector spaces. While existing models mainly consider the aspect of graph structure, there exists a wealth of contextual and literal information that can be utilized for more effective embedding learning. This paper introduces a novel model that incorporates both contextual and literal information into entity and relation embeddings by utilizing graph convolutional networks. Specifically, for contextual information, we assess its significance through confidence and relatedness metrics. In addition, a unique rule-based method is developed to calculate the confidence metric, and the relatedness metric is derived from the literal information's representations. We validate our model performance with thorough experiments on two established benchmark datasets.
The multimodal recommendation has gradually become the infrastructure of online media platforms, enabling them to provide personalized service to users through a joint modeling of user historical behaviors (e.g., purchases, clicks) and item various modalities (e.g., visual and textual). The majority of existing studies typically focus on utilizing modal features or modal-related graph structure to learn user local interests. Nevertheless, these approaches encounter two limitations: (1) Shared updates of user ID embeddings result in the consequential coupling between collaboration and multimodal signals; (2) Lack of exploration into robust global user interests to alleviate the sparse interaction problems faced by local interest modeling. To address these issues, we propose a novel Local and Global Graph Learning-guided Multimodal Recommender (LGMRec), which jointly models local and global user interests. Specifically, we present a local graph embedding module to independently learn collaborative-related and modality-related embeddings of users and items with local topological relations. Moreover, a global hypergraph embedding module is designed to capture global user and item embeddings by modeling insightful global dependency relations. The global embeddings acquired within the hypergraph embedding space can then be combined with two decoupled local embeddings to improve the accuracy and robustness of recommendations. Extensive experiments conducted on three benchmark datasets demonstrate the superiority of our LGMRec over various state-of-the-art recommendation baselines, showcasing its effectiveness in modeling both local and global user interests.
We investigate the problem of multiplex graph embedding, that is, graphs in which nodes interact through multiple types of relations (dimensions). In recent years, several methods have been developed to address this problem. However, the need for more effective and specialized approaches grows with the production of graph data with diverse characteristics. In particular, real-world multiplex graphs may exhibit a high number of dimensions, making it difficult to construct a single consensus representation. Furthermore, important information can be hidden in complex latent structures scattered in multiple dimensions. To address these issues, we propose HMGE, a novel embedding method based on hierarchical aggregation for high-dimensional multiplex graphs. Hierarchical aggregation consists of learning a hierarchical combination of the graph dimensions and refining the embeddings at each hierarchy level. Non-linear combinations are computed from previous ones, thus uncovering complex information and latent structures hidden in the multiplex graph dimensions. Moreover, we leverage mutual information maximization between local patches and global summaries to train the model without supervision. This allows to capture of globally relevant information present in diverse locations of the graph. Detailed experiments on synthetic and real-world data illustrate the suitability of our approach to downstream supervised tasks, including link prediction and node classification.
A graph embedding is an emerging approach that can represent a graph structure with a fixed-length low-dimensional vector. node2vec is a well-known algorithm to obtain such a graph embedding by sampling neighboring nodes on a given graph with a random walk technique. However, the original node2vec algorithm typically relies on a batch training of graph structures; thus, it is not suited for applications in which the graph structure changes after the deployment. In this paper, we focus on node2vec applications for IoT (Internet of Things) environments. To handle the changes of graph structures after the IoT devices have been deployed in edge environments, in this paper we propose to combine an online sequential training algorithm with node2vec. The proposed sequentially-trainable model is implemented on an FPGA (Field-Programmable Gate Array) device to demonstrate the benefits of our approach. The proposed FPGA implementation achieves up to 205.25 times speedup compared to the original model on ARM Cortex-A53 CPU. Evaluation results using dynamic graphs show that although the accuracy is decreased in the original model, the proposed sequential model can obtain better graph embedding that achieves a higher accuracy even when the graph structure is changed.
Knowledge Graphs (KGs) such as Resource Description Framework (RDF) data represent relationships between various entities through the structure of triples (<subject, predicate, object>). Knowledge graph embedding (KGE) is crucial in machine learning applications, specifically in node classification and link prediction tasks. KGE remains a vital research topic within the semantic web community. RDF-star introduces the concept of a quoted triple (QT), a specific form of triple employed either as the subject or object within another triple. Moreover, RDF-star permits a QT to act as compositional entities within another QT, thereby enabling the representation of recursive, hyper-relational KGs with nested structures. However, existing KGE models fail to adequately learn the semantics of QTs and entities, primarily because they do not account for RDF-star graphs containing multi-leveled nested QTs and QT-QT relationships. This study introduces RDF-star2Vec, a novel KGE model specifically designed for RDF-star graphs. RDF-star2Vec introduces graph walk techniques that enable probabilistic transitions between a QT and its compositional entities. Feature vectors for QTs, entities, and relations are derived from generated sequences through the structured skip-gram model. Additionally, we provide a dataset and a benchmarking framework for data mining tasks focused on complex RDF-star graphs. Evaluative experiments demonstrated that RDF-star2Vec yielded superior performance compared to recent extensions of RDF2Vec in various tasks including classification, clustering, entity relatedness, and QT similarity.
Hierarchy is an important and commonly observed topological property in real-world graphs that indicate the relationships between supervisors and subordinates or the organizational behavior of human groups. As hierarchy is introduced as a new inductive bias into the Graph Neural Networks (GNNs) in various tasks, it implies latent topological relations for attackers to improve their inference attack performance, leading to serious privacy leakage issues. In addition, existing privacy-preserving frameworks suffer from reduced protection ability in hierarchical propagation due to the deficiency of adaptive upper-bound estimation of the hierarchical perturbation boundary. It is of great urgency to effectively leverage the hierarchical property of data while satisfying privacy guarantees. To solve the problem, we propose the Poincar\'e Differential Privacy framework, named PoinDP, to protect the hierarchy-aware graph embedding based on hyperbolic geometry. Specifically, PoinDP first learns the hierarchy weights for each entity based on the Poincar\'e model in hyperbolic space. Then, the Personalized Hierarchy-aware Sensitivity is designed to measure the sensitivity of the hierarchical structure and adaptively allocate the privacy protection strength. Besides, the Hyperbolic Gaussian Mechanism (HGM) is proposed to extend the Gaussian mechanism in Euclidean space to hyperbolic space to realize random perturbations that satisfy differential privacy under the hyperbolic space metric. Extensive experiment results on five real-world datasets demonstrate the proposed PoinDP's advantages of effective privacy protection while maintaining good performance on the node classification task.
Knowledge graph embedding models (KGEMs) developed for link prediction learn vector representations for entities in a knowledge graph, known as embeddings. A common tacit assumption is the KGE entity similarity assumption, which states that these KGEMs retain the graph's structure within their embedding space, \textit{i.e.}, position similar entities within the graph close to one another. This desirable property make KGEMs widely used in downstream tasks such as recommender systems or drug repurposing. Yet, the relation of entity similarity and similarity in the embedding space has rarely been formally evaluated. Typically, KGEMs are assessed based on their sole link prediction capabilities, using ranked-based metrics such as Hits@K or Mean Rank. This paper challenges the prevailing assumption that entity similarity in the graph is inherently mirrored in the embedding space. Therefore, we conduct extensive experiments to measure the capability of KGEMs to cluster similar entities together, and investigate the nature of the underlying factors. Moreover, we study if different KGEMs expose a different notion of similarity. Datasets, pre-trained embeddings and code are available at: https://github.com/nicolas-hbt/similar-embeddings/.
Natural language understanding (NLU) using neural network pipelines often requires additional context that is not solely present in the input data. Through Prior research, it has been evident that NLU benchmarks are susceptible to manipulation by neural models, wherein these models exploit statistical artifacts within the encoded external knowledge to artificially inflate performance metrics for downstream tasks. Our proposed approach, known as the Recap, Deliberate, and Respond (RDR) paradigm, addresses this issue by incorporating three distinct objectives within the neural network pipeline. Firstly, the Recap objective involves paraphrasing the input text using a paraphrasing model in order to summarize and encapsulate its essence. Secondly, the Deliberation objective entails encoding external graph information related to entities mentioned in the input text, utilizing a graph embedding model. Finally, the Respond objective employs a classification head model that utilizes representations from the Recap and Deliberation modules to generate the final prediction. By cascading these three models and minimizing a combined loss, we mitigate the potential for gaming the benchmark and establish a robust method for capturing the underlying semantic patterns, thus enabling accurate predictions. To evaluate the effectiveness of the RDR method, we conduct tests on multiple GLUE benchmark tasks. Our results demonstrate improved performance compared to competitive baselines, with an enhancement of up to 2\% on standard metrics. Furthermore, we analyze the observed evidence for semantic understanding exhibited by RDR models, emphasizing their ability to avoid gaming the benchmark and instead accurately capture the true underlying semantic patterns.
Theoretical results from discrete geometry suggest that normed spaces can abstractly embed finite metric spaces with surprisingly low theoretical bounds on distortion in low dimensions. In this paper, inspired by this theoretical insight, we highlight normed spaces as a more flexible and computationally efficient alternative to several popular Riemannian manifolds for learning graph embeddings. Normed space embeddings significantly outperform several popular manifolds on a large range of synthetic and real-world graph reconstruction benchmark datasets while requiring significantly fewer computational resources. We also empirically verify the superiority of normed space embeddings on growing families of graphs associated with negative, zero, and positive curvature, further reinforcing the flexibility of normed spaces in capturing diverse graph structures as graph sizes increase. Lastly, we demonstrate the utility of normed space embeddings on two applied graph embedding tasks, namely, link prediction and recommender systems. Our work highlights the potential of normed spaces for geometric graph representation learning, raises new research questions, and offers a valuable tool for experimental mathematics in the field of finite metric space embeddings. We make our code and data publically available.
Graph-based data present unique challenges and opportunities for machine learning. Graph Neural Networks (GNNs), and especially those algorithms that capture graph topology through message passing for neighborhood aggregation, have been a leading solution. However, these networks often require substantial computational resources and may not optimally leverage the information contained in the graph's topology, particularly for large-scale or complex graphs. We propose Topology Coordinate Neural Network (TCNN) and Directional Virtual Coordinate Neural Network (DVCNN) as novel and efficient alternatives to message passing GNNs, that directly leverage the graph's topology, sidestepping the computational challenges presented by competing algorithms. Our proposed methods can be viewed as a reprise of classic techniques for graph embedding for neural network feature engineering, but they are novel in that our embedding techniques leverage ideas in Graph Coordinates (GC) that are lacking in current practice. Experimental results, benchmarked against the Open Graph Benchmark Leaderboard, demonstrate that TCNN and DVCNN achieve competitive or superior performance to message passing GNNs. For similar levels of accuracy and ROC-AUC, TCNN and DVCNN need far fewer trainable parameters than contenders of the OGBN Leaderboard. The proposed TCNN architecture requires fewer parameters than any neural network method currently listed in the OGBN Leaderboard for both OGBN-Proteins and OGBN-Products datasets. Conversely, our methods achieve higher performance for a similar number of trainable parameters. By providing an efficient and effective alternative to message passing GNNs, our work expands the toolbox of techniques for graph-based machine learning.