Graph Mamba, a powerful graph embedding technique, has emerged as a cornerstone in various domains, including bioinformatics, social networks, and recommendation systems. This survey represents the first comprehensive study devoted to Graph Mamba, to address the critical gaps in understanding its applications, challenges, and future potential. We start by offering a detailed explanation of the original Graph Mamba architecture, highlighting its key components and underlying mechanisms. Subsequently, we explore the most recent modifications and enhancements proposed to improve its performance and applicability. To demonstrate the versatility of Graph Mamba, we examine its applications across diverse domains. A comparative analysis of Graph Mamba and its variants is conducted to shed light on their unique characteristics and potential use cases. Furthermore, we identify potential areas where Graph Mamba can be applied in the future, highlighting its potential to revolutionize data analysis in these fields. Finally, we address the current limitations and open research questions associated with Graph Mamba. By acknowledging these challenges, we aim to stimulate further research and development in this promising area. This survey serves as a valuable resource for both newcomers and experienced researchers seeking to understand and leverage the power of Graph Mamba.
Inferencing Gene Regulatory Networks (GRNs) from gene expression data is a pivotal challenge in systems biology, and several innovative computational methods have been introduced. However, most of these studies have not considered the skewed degree distribution of genes. Specifically, some genes may regulate multiple target genes while some genes may be regulated by multiple regulator genes. Such a skewed degree distribution issue significantly complicates the application of directed graph embedding methods. To tackle this issue, we propose the Cross-Attention Complex Dual Graph Embedding Model (XATGRN). Our XATGRN employs a cross-attention mechanism to effectively capture intricate gene interactions from gene expression profiles. Additionally, it uses a Dual Complex Graph Embedding approach to manage the skewed degree distribution, thereby ensuring precise prediction of regulatory relationships and their directionality. Our model consistently outperforms existing state-of-the-art methods across various datasets, underscoring its efficacy in elucidating complex gene regulatory mechanisms. Our codes used in this paper are publicly available at: https://github.com/kikixiong/XATGRN.
Community structures are critical for understanding the mesoscopic organization of networks, bridging local and global patterns. While methods such as DeepWalk and node2vec capture local positional information through random walks, they fail to preserve community structures. Other approaches like modularized nonnegative matrix factorization and evolutionary algorithms address this gap but are computationally expensive and unsuitable for large-scale networks. To overcome these limitations, we propose Two Layer Walk (TLWalk), a novel graph embedding algorithm that incorporates hierarchical community structures. TLWalk balances intra- and inter-community relationships through a community-aware random walk mechanism without requiring additional parameters. Theoretical analysis demonstrates that TLWalk effectively mitigates locality bias. Experiments on benchmark datasets show that TLWalk outperforms state-of-the-art methods, achieving up to 3.2% accuracy gains for link prediction tasks. By encoding dense local and sparse global structures, TLWalk proves robust and scalable across diverse networks, offering an efficient solution for network analysis.
Dynamic graph embedding has emerged as an important technique for modeling complex time-evolving networks across diverse domains. While transformer-based models have shown promise in capturing long-range dependencies in temporal graph data, they face scalability challenges due to quadratic computational complexity. This study presents a comparative analysis of dynamic graph embedding approaches using transformers and the recently proposed Mamba architecture, a state-space model with linear complexity. We introduce three novel models: TransformerG2G augment with graph convolutional networks, \mathcal{DG}-Mamba, and \mathcal{GDG}-Mamba with graph isomorphism network edge convolutions. Our experiments on multiple benchmark datasets demonstrate that Mamba-based models achieve comparable or superior performance to transformer-based approaches in link prediction tasks while offering significant computational efficiency gains on longer sequences. Notably, \mathcal{DG}-Mamba variants consistently outperform transformer-based models on datasets with high temporal variability, such as UCI, Bitcoin, and Reality Mining, while maintaining competitive performance on more stable graphs like SBM. We provide insights into the learned temporal dependencies through analysis of attention weights and state matrices, revealing the models' ability to capture complex temporal patterns. By effectively combining state-space models with graph neural networks, our work addresses key limitations of previous approaches and contributes to the growing body of research on efficient temporal graph representation learning. These findings offer promising directions for scaling dynamic graph embedding to larger, more complex real-world networks, potentially enabling new applications in areas such as social network analysis, financial modeling, and biological system dynamics.
Knowledge Graphs (KGs) and their machine learning counterpart, Knowledge Graph Embedding Models (KGEMs), have seen ever-increasing use in a wide variety of academic and applied settings. In particular, KGEMs are typically applied to KGs to solve the link prediction task; i.e. to predict new facts in the domain of a KG based on existing, observed facts. While this approach has been shown substantial power in many end-use cases, it remains incompletely characterised in terms of how KGEMs react differently to KG structure. This is of particular concern in light of recent studies showing that KG structure can be a significant source of bias as well as partially determinant of overall KGEM performance. This paper seeks to address this gap in the state-of-the-art. This paper provides, to the authors' knowledge, the first comprehensive survey exploring established relationships of Knowledge Graph Embedding Models and Graph structure in the literature. It is the hope of the authors that this work will inspire further studies in this area, and contribute to a more holistic understanding of KGs, KGEMs, and the link prediction task.
Graphs face challenges when dealing with massive datasets. They are essential tools for modeling interconnected data and often become computationally expensive. Graph embedding techniques, on the other hand, provide an efficient approach. By projecting complex graphs into a lower-dimensional space, these techniques simplify the analysis and processing of large-scale graphs. By transforming graphs into vectors, it simplifies the analysis and processing of large-scale datasets. Several approaches, such as GraphSAGE, Node2Vec, and FastRP, offer efficient methods for generating graph embeddings. By storing embeddings as node properties, it is possible to compare different embedding techniques and evaluate their effectiveness for specific tasks. This flexibilityallows for dynamic updates to embeddings and facilitates experimentation with different approaches. By analyzing these embeddings, one can extract valuable insights into the relationships between nodes and their similarities within the embedding space
Modelling information from complex systems such as humans social interaction or words co-occurrences in our languages can help to understand how these systems are organized and function. Such systems can be modelled by networks, and network theory provides a useful set of methods to analyze them. Among these methods, graph embedding is a powerful tool to summarize the interactions and topology of a network in a vectorized feature space. When used in input of machine learning algorithms, embedding vectors help with common graph problems such as link prediction, graph matching, etc. Word embedding has the goal of representing the sense of words, extracting it from large text corpora. Despite differences in the structure of information in input of embedding algorithms, many graph embedding approaches are adapted and inspired from methods in NLP. Limits of these methods are observed in both domains. Most of these methods require long and resource greedy training. Another downside to most methods is that they are black-box, from which understanding how the information is structured is rather complex. Interpretability of a model allows understanding how the vector space is structured without the need for external information, and thus can be audited more easily. With both these limitations in mind, we propose a novel framework to efficiently embed network vertices in an interpretable vector space. Our Lower Dimension Bipartite Framework (LDBGF) leverages the bipartite projection of a network using cliques to reduce dimensionality. Along with LDBGF, we introduce two implementations of this framework that rely on communities instead of cliques: SINr-NR and SINr-MF. We show that SINr-MF can perform well on classical graphs and SINr-NR can produce high-quality graph and word embeddings that are interpretable and stable across runs.
The influence maximization (IM) problem involves identifying a set of key individuals in a social network who can maximize the spread of influence through their network connections. With the advent of geometric deep learning on graphs, great progress has been made towards better solutions for the IM problem. In this paper, we focus on the dynamic non-progressive IM problem, which considers the dynamic nature of real-world social networks and the special case where the influence diffusion is non-progressive, i.e., nodes can be activated multiple times. We first extend an existing diffusion model to capture the non-progressive influence propagation in dynamic social networks. We then propose the method, DNIMRL, which employs deep reinforcement learning and dynamic graph embedding to solve the dynamic non-progressive IM problem. In particular, we propose a novel algorithm that effectively leverages graph embedding to capture the temporal changes of dynamic networks and seamlessly integrates with deep reinforcement learning. The experiments, on different types of real-world social network datasets, demonstrate that our method outperforms state-of-the-art baselines.
In this essay we discuss the recent trends in visual analysis and exploration of Knowledge Graphs, particularly in conjunction with Knowledge Graph Embedding techniques. We present an overview of the current state of visualization techniques and frameworks for KGs, in relation to four identified challenges. The challenges in visualizing Knowledge Graphs include the need for intuitive and modular interfaces, performance in handling big data, and difficulties for users in understanding and using query languages. We find frameworks that generally satisfy the intuitive UI, performance, and query support requirements, but few satisfying the modularity requirement. In the context of Knowledge Graph Embeddings, we divide the approaches that use embeddings to facilitate exploration of Knowledge Graphs from those that aim at the explanation of the embeddings themselves. We find significant differences between the two perspectives. Finally, we highlight some possible directions for future work, including diffusion of the unmet requirements, implementation of new visual features, and experimentation with relation visualization as a peculiar element of Knowledge Graphs.
Pedestrian detection is a critical task in autonomous driving, aimed at enhancing safety and reducing risks on the road. Over recent years, significant advancements have been made in improving detection performance. However, these achievements still fall short of human perception, particularly in cases involving occluded pedestrians, especially entirely invisible ones. In this work, we present the Occlusion-Rich Road Scenes with Pedestrians (OccluRoads) dataset, which features a diverse collection of road scenes with partially and fully occluded pedestrians in both real and virtual environments. All scenes are meticulously labeled and enriched with contextual information that encapsulates human perception in such scenarios. Using this dataset, we developed a pipeline to predict the presence of occluded pedestrians, leveraging Knowledge Graph (KG), Knowledge Graph Embedding (KGE), and a Bayesian inference process. Our approach achieves a F1 score of 0.91, representing an improvement of up to 42% compared to traditional machine learning models.
Quaternion contains one real part and three imaginary parts, which provided a more expressive hypercomplex space for learning knowledge graph. Existing quaternion embedding models measure the plausibility of a triplet either through semantic matching or geometric distance scoring functions. However, it appears that semantic matching diminishes the separability of entities, while the distance scoring function weakens the semantics of entities. To address this issue, we propose a novel quaternion knowledge graph embedding model. Our model combines semantic matching with entity's geometric distance to better measure the plausibility of triplets. Specifically, in the quaternion space, we perform a right rotation on head entity and a reverse rotation on tail entity to learn rich semantic features. Then, we utilize distance adaptive translations to learn geometric distance between entities. Furthermore, we provide mathematical proofs to demonstrate our model can handle complex logical relationships. Extensive experimental results and analyses show our model significantly outperforms previous models on well-known knowledge graph completion benchmark datasets. Our code is available at https://github.com/llqy123/DaBR.
Gene Ontology (GO) and its Annotations (GOA) provide a controlled and evolving vocabulary for gene products and gene functions widely used in molecular biology. GO \& GOA are updated and maintained both automatically from biological publications and manually by curators. These knowledge bases however are often incomplete for two reasons: 1) Research in biological domain itself is still ongoing; 2) The amount of experimental evidence might not be yet sufficient to validate annotations. In this paper, we address the gap in evidence between gene products and their annotations by making link predictions using Knowledge Graph Embedding (KGE) methods. Through the application of the True Path Rule (TPR) in the training stage of KGE, we were able to improve the performance of traditional KGE methods. We report two experimental scenarios with GO and GO Chicken Annotation datasets to show the contribution of embedding TPR to prediction accuracy.
Knowledge graph (KG) embedding methods map entities and relations into continuous vector spaces, improving performance in tasks like link prediction and question answering. With rising privacy concerns, machine unlearning (MU) has emerged as a critical AI technology, enabling models to eliminate the influence of specific data. Existing MU approaches often rely on data obfuscation and adjustments to training loss but lack generalization across unlearning tasks. This paper introduces MetaEU, a Meta-Learning-Based Knowledge Graph Embedding Unlearning framework. MetaEU leverages meta-learning to unlearn specific embeddings, mitigating their impact while preserving model performance on remaining data. Experiments on benchmark datasets demonstrate its effectiveness in KG embedding unlearning.
The notion of local intrinsic dimensionality (LID) has important theoretical implications and practical applications in the fields of data mining and machine learning. Recent research efforts indicate that LID measures defined for graphs can improve graph representational learning methods based on random walks. In this paper, we discuss how NC-LID, a LID measure designed for static graphs, can be adapted for dynamic networks. Focusing on dynnode2vec as the most representative dynamic graph embedding method based on random walks, we examine correlations between NC-LID and the intrinsic quality of 10 real-world dynamic network embeddings. The obtained results show that NC-LID can be used as a good indicator of nodes whose embedding vectors do not tend to preserve temporal graph structure well. Thus, our empirical findings constitute the first step towards LID-aware dynamic graph embedding methods.
Knowledge Graph Embedding models, representing entities and edges in a low-dimensional space, have been extremely successful at solving tasks related to completing and exploring Knowledge Graphs (KGs). One of the key aspects of training most of these models is teaching to discriminate between true statements positives and false ones (negatives). However, the way in which negatives can be defined is not trivial, as facts missing from the KG are not necessarily false and a set of ground truth negatives is hardly ever given. This makes synthetic negative generation a necessity. Different generation strategies can heavily affect the quality of the embeddings, making it a primary aspect to consider. We revamp a strategy that generates corruptions during training respecting the domain and range of relations, we extend its capabilities and we show our methods bring substantial improvement (+10% MRR) for standard benchmark datasets and over +150% MRR for a larger ontology-backed dataset.
We consider the problem of constructing embeddings of large attributed graphs and supporting multiple downstream learning tasks. We develop a graph embedding method, which is based on extending deep metric and unbiased contrastive learning techniques to 1) work with attributed graphs, 2) enabling a mini-batch based approach, and 3) achieving scalability. Based on a multi-class tuplet loss function, we present two algorithms -- DMT for semi-supervised learning and DMAT-i for the unsupervised case. Analyzing our methods, we provide a generalization bound for the downstream node classification task and for the first time relate tuplet loss to contrastive learning. Through extensive experiments, we show high scalability of representation construction, and in applying the method for three downstream tasks (node clustering, node classification, and link prediction) better consistency over any single existing method.
To leverage the complex structures within heterogeneous graphs, recent studies on heterogeneous graph embedding use a hyperbolic space, characterized by a constant negative curvature and exponentially increasing space, which aligns with the structural properties of heterogeneous graphs. However, despite heterogeneous graphs inherently possessing diverse power-law structures, most hyperbolic heterogeneous graph embedding models use a single hyperbolic space for the entire heterogeneous graph, which may not effectively capture the diverse power-law structures within the heterogeneous graph. To address this limitation, we propose Multi-hyperbolic Space-based heterogeneous Graph Attention Network (MSGAT), which uses multiple hyperbolic spaces to effectively capture diverse power-law structures within heterogeneous graphs. We conduct comprehensive experiments to evaluate the effectiveness of MSGAT. The experimental results demonstrate that MSGAT outperforms state-of-the-art baselines in various graph machine learning tasks, effectively capturing the complex structures of heterogeneous graphs.
To effectively manage and utilize knowledge graphs, it is crucial to have metrics that can assess the quality of knowledge graphs from various perspectives. While there have been studies on knowledge graph quality metrics, there has been a lack of research on metrics that measure how richly ontologies, which form the backbone of knowledge graphs, are defined or the impact of richly defined ontologies. In this study, we propose a new metric called Class Granularity, which measures how well a knowledge graph is structured in terms of how finely classes with unique characteristics are defined. Furthermore, this research presents potential impact of Class Granularity in knowledge graph's on downstream tasks. In particular, we explore its influence on graph embedding and provide experimental results. Additionally, this research goes beyond traditional Linked Open Data comparison studies, which mainly focus on factors like scale and class distribution, by using Class Granularity to compare four different LOD sources.
Hyperbolic rotation is commonly used to effectively model knowledge graphs and their inherent hierarchies. However, existing hyperbolic rotation models rely on logarithmic and exponential mappings for feature transformation. These models only project data features into hyperbolic space for rotation, limiting their ability to fully exploit the hyperbolic space. To address this problem, we propose a novel fully hyperbolic model designed for knowledge graph embedding. Instead of feature mappings, we define the model directly in hyperbolic space with the Lorentz model. Our model considers each relation in knowledge graphs as a Lorentz rotation from the head entity to the tail entity. We adopt the Lorentzian version distance as the scoring function for measuring the plausibility of triplets. Extensive results on standard knowledge graph completion benchmarks demonstrated that our model achieves competitive results with fewer parameters. In addition, our model get the state-of-the-art performance on datasets of CoDEx-s and CoDEx-m, which are more diverse and challenging than before. Our code is available at https://github.com/llqy123/FHRE.
Knowledge graphs have gained popularity for their ability to organize and analyze complex data effectively. When combined with graph embedding techniques, such as graph neural networks (GNNs), knowledge graphs become a potent tool in providing valuable insights. This study explores the application of graph embedding in identifying competitors from a financial knowledge graph. Existing state-of-the-art(SOTA) models face challenges due to the unique attributes of our knowledge graph, including directed and undirected relationships, attributed nodes, and minimal annotated competitor connections. To address these challenges, we propose a novel graph embedding model, JPEC(JPMorgan Proximity Embedding for Competitor Detection), which utilizes graph neural network to learn from both first-order and second-order node proximity together with vital features for competitor retrieval. JPEC had outperformed most existing models in extensive experiments, showcasing its effectiveness in competitor retrieval.