The field of knowledge graph representation learning (KGRL) has been rapidly expanding. To effectively apply KGRL models to large real-world knowledge graphs (KGs), anchor-based methods have been proposed. These methods aim to reduce computational costs and parameter requirements by encoding entities using a small set of entity anchors. However, existing anchor selection approaches are often rudimentary and sometimes yield suboptimal results. In this article, we propose a scalable anchor-based KGRL method called SKIP. By leveraging prototype information, our method selects representative entities as anchors. The SKIP method consists of two main steps. First, pretraining models are employed to encode entities by utilizing the topological structure and textual information in KGs. Second, the prototype learning module (PLM) extracts entity prototypes, which are then used to sample entity anchors that contain valuable prototype information. These settings enable SKIP to identify representative and reasonable entity anchors, leading to improved performance while requiring fewer computational resources. Extensive experiments conducted on various downstream tasks using KGs of different scales demonstrate the superiority and effectiveness of SKIP. Particularly, on the large OGB WikiKG 2 dataset, our method achieves comparable performance while reducing running time by approximately 21.28% and requiring 21.43% fewer model parameters compared to the baseline. This indicates the superior scalability of SKIP.

Zero-shot anomaly detection (ZSAD) aims to detect anomalies and localize defective regions in unseen target domains without target training data. Recent ZSAD methods build on pretrained vision models, particularly CLIP, and construct normal and anomaly references from textual prompts or learnable visual representations. These methods perform anomaly discrimination primarily in spatial feature spaces, where subtle changes in texture, boundaries, and local structures can be confused with normal appearance variations. Although inconspicuous spatially, such defects can disrupt local texture regularity or boundary continuity, inducing response deviations across frequency bands. However, existing ZSAD methods do not explicitly model these frequency-dependent characteristics. Our image-domain analysis reveals that local defects exhibit spatial-frequency deviations from normal references across low-, middle-, and high-frequency bands, indicating that anomaly evidence is not universally dominated by high-frequency responses. Motivated by this observation, we propose FreqAnchorAD, a frequency-aware framework that organizes frequency-enhanced responses for anchor-relative anomaly discrimination. Specifically, the Local Frequency Compensation Module (LFCM) enhances intermediate patch tokens with local spatial-frequency cues. The Frequency-Deviation Anchor Projector (FDAP), our core discrimination module, organizes enhanced responses along a source-derived channel coordinate and measures anomaly evidence through relative similarity to normal and anomaly anchors. Finally, Asymmetric Anchor Supervision (AAS) stabilizes normal-anchor alignment while preserving diverse anomaly patterns. Experiments on thirteen industrial and medical benchmarks show that FreqAnchorAD achieves state-of-the-art mean performance in image-level anomaly recognition and pixel-level defect localization.

Graph clustering, which aims to divide nodes in the graph into several distinct clusters, is a fundamental yet challenging task. Benefiting from the powerful representation capability of deep learning, deep graph clustering (DGC) methods have achieved great success in recent years. However, the corresponding survey paper is relatively scarce, and it is imminent to make a summary of this field. From this motivation, we conduct a comprehensive survey of DGC. Firstly, we introduce formulaic definition, evaluation, and development in this field. Secondly, the taxonomy of DGC methods is presented based on four different criteria, including graph type, network architecture, learning paradigm, and clustering method. Thirdly, we carefully analyze the existing methods via extensive experiments and summarize the challenges and opportunities from five perspectives, including graph data quality, stability, scalability, discriminative capability, and unknown cluster number. Besides, the applications of DGC methods in six domains, including computer vision, natural language processing, recommendation systems, social network analysis, bioinformatics, and medical science, are presented. Last but not least, this paper provides open resource supports, including 1) a collection of state-of-the-art DGC methods (papers, codes, and datasets) and 2) a flexible and extensible Python library for DGC. We hope this work can serve as a quick guide and help researchers overcome challenges in this vibrant field.

Attribute-missing deep graph clustering (DGC), which groups graph data containing samples with missing attributes, holds great potential to address the challenges of label scarcity and data absence in real-world scenarios. Among existing efforts, imputation-driven solutions (e.g., AMGC) employ the idea of classical imputation to tolerate missing attributes with the aid of prior clustering knowledge and show promising results. However, their abilities to conduct accurate imputation for clustering are impeded by the lack of ground truth of missing attributes, particularly in cases with high ratios of missing data. To tackle this issue, we propose a novel attribute-missing DGC framework called AMGC2, which leverages the prediction of intra-cluster feature distribution to enhance robustness in clustering and data completion at a high attribute-missing ratio. Specifically, we first encode observed attributes and structures separately and then entangle them into a common latent space. With the structure-attribute entangled embedding, we estimate the missing data by predicting the feature distribution within each cluster via Gaussian approximation rather than simply conducting feature similarity-based imputation using available attributes, such that the model can preserve intra-class compact signals for attribute-missing samples as well as boost the tolerance to a large proportion of data absence. Moreover, we perform cost-efficient prototype-level non-contrastive learning over completed samples, which in turn acquires more reliable sample partition prompts for distribution prediction in subsequent iterations. Extensive experiments verify the superior performance of AMGC2 against state-of-the-art competitors on seven datasets.

The ubiquity of Graph Neural Networks (GNNs) emphasizes the imperative to assess their resilience against node injection attacks, a type of evasion attacks that impact victim models by injecting nodes with fabricated attributes and structures. However, prevailing attacks face two primary limitations: (1) Sequential construction of attributes and structures results in suboptimal outcomes as structure information is overlooked during attribute construction and vice versa. (2) In black-box scenarios, where attackers lack access to victim model architecture and parameters, reliance on surrogate models degrades performance due to architectural discrepancies. To overcome these limitations, we introduce GZOO, a black-box node injection attack that leverages an adversarial graph generator, compromising both attribute and structure sub-generators. This integration crafts optimal attributes and structures by considering their mutual information, enhancing their influence when aggregating information from injected nodes. Furthermore, GZOO proposes a zeroth-order optimization algorithm leveraging prediction results from victim models to estimate gradients for updating generator parameters, eliminating the necessity to train surrogate models. Across sixteen datasets, GZOO significantly outperforms state-of-the-art attacks, achieving remarkable effectiveness and robustness. Notably, on the Cora dataset with the GCN model, GZOO achieves an impressive 95.69% success rate, surpassing the maximum 66.01% achieved by baselines.

Program induction is a key paradigm for addressing complex knowledge base question answering. Recent studies have utilized large language models (LLMs) to decompose semantically complex queries into several sub-questions to assist semantic parsing of program induction. However, existing prompting methods often apply decomposition indiscriminately to all queries and lack mechanisms for modeling sub-question interrelations and evaluating decomposition results, easily leading to unreasonable decompositions that impair program generation and answer accuracy. To tackle these issues, we propose PDC-ACQA, a novel adaptive complex question answering framework that introduces a program decomposition chain to represent progressive decomposition process of complex queries while handling decomposable ones separately. PDC-ACQA consists of five modules. Specifically, the question decomposition discriminator (QDD) generates program decomposition chain that determines the decomposability of queries. The program induction model (PIM) parses non-decomposable queries directly. The prompt constructor based on program decomposition chain (PC-PDC) builds progressive decomposition prompts for decomposable queries. Additionally, the expert models (EMs) and self-correction strategy collaboratively evaluate and refine each step's decomposition result. Finally, the training-free program aggregator (PA) assembles all unit sub-programs corresponding to decomposition results into a complete executable program for answer query. Experimental results demonstrate that PDC-ACQA consistently outperforms baselines, validating the effectiveness of our adaptive framework in enhancing decomposition quality and improving overall performance of program induction-based question answering.

Few-shot relation reasoning on knowledge graphs (FS-KGR) is an important and practical problem that aims to infer long-tail relations and has drawn increasing attention these years. Among all the proposed methods, self-supervised learning (SSL) methods, which effectively extract the hidden essential inductive patterns relying only on the support sets, have achieved promising performance. However, the existing SSL methods simply cut down connections between high-frequency and long-tail relations, which ignores the fact, i.e., the two kinds of information could be highly related to each other. Specifically, we observe that relations with similar contextual meanings, called aliasing relations (ARs), may have similar attributes. In other words, the ARs of the target long-tail relation could be in high-frequency, and leveraging such attributes can largely improve the reasoning performance. Based on the interesting observation above, we proposed a novel Self-supervised learning model by leveraging Aliasing Relations to assist FS-KGR, termed . Specifically, we propose a graph neural network (GNN)-based AR-assist module to encode the ARs. Besides, we further provide two fusion strategies, i.e., simple summation and learnable fusion, to fuse the generated representations, which contain extra abundant information underlying the ARs, into the self-supervised reasoning backbone for performance enhancement. Extensive experiments on three few-shot benchmarks demonstrate that achieves state-of-the-art (SOTA) performance compared with other methods in most cases.

Chain-of-thought (CoT) distillation allows a large language model (LLM) to guide a small language model (SLM) in reasoning tasks. Existing methods train the SLM to learn the long rationale in one iteration, resulting in two issues: 1) Long rationales lead to a large token-level batch size during training, making gradients of core reasoning tokens (i.e., the token will directly affect the correctness of subsequent reasoning) over-smoothed as they contribute a tiny fraction of the rationale. As a result, the SLM converges to sharp minima where it fails to grasp the reasoning logic. 2) The response is slow, as the SLM must generate a long rationale before reaching the answer. Therefore, we propose chunk-wise training (CWT), which uses a heuristic search to divide the rationale into internal semantically coherent chunks and focuses SLM on learning from only one chunk per iteration. In this way, CWT naturally isolates non-reasoning chunks that do not involve the core reasoning token (e.g., summary and transitional chunks) from the SLM learning for reasoning chunks, making the fraction of the core reasoning token increase in the corresponding iteration. Based on CWT, skip-thinking training (STT) is proposed. STT makes the SLM automatically skip non-reasoning medium chunks to reach the answer, improving reasoning speed while maintaining accuracy. We validate our approach on a variety of SLMs and multiple reasoning tasks.

Recent advancements in knowledge graph enhanced RAG methods have shown promise in delivering efficient and accurate responses to complex multi-hop QA tasks by leveraging both graph-based and text-based knowledge. However, existing methods suffer from the problem of insufficient extraction, utilization, and fusion of graph information. To address these limitations, this paper presents RDMSFR-RAG, a novel methodology that enhances RAG's performance in multi-hop QA task through three key improvements in indexing, retrieval, and generation in RAG pipeline. Specifically, the triplet extraction method based on relation disambiguation accurately captures entity-relation triplets, yielding precise and concise graph data; The multi-scale score fusion approach effectively combines retrieval results from graph and text databases; The CoT reasoning based on classification method utilizes the idea chain of thought to guide targeted reasoning in LLMs for different multi-hop question types. Extensive experiments demonstrate that RDMSFR-RAG significantly outperforms the HippoRAG baseline, achieving 6-9 percentage point improvements in both retrieval and QA accuracy. Comprehensive experiments and ablation studies demonstrate that each of the three proposed enhancements significantly contributes to the improvement of retrieval and generation within the graph-based RAG method for complex multi-hop QA tasks.

Temporal Graph Clustering (TGC) is a new task with little attention, focusing on node clustering in temporal graphs. Compared with existing static graph clustering, it can find the balance between time requirement and space requirement (Time-Space Balance) through the interaction sequence-based batch-processing pattern. However, there are two major challenges that hinder the development of TGC, i.e., inapplicable clustering techniques and inapplicable datasets. To address these challenges, we propose a comprehensive benchmark, called BenchTGC. Specially, we design a BenchTGC Framework to illustrate the paradigm of temporal graph clustering and improve existing clustering techniques to fit temporal graphs. In addition, we also discuss problems with public temporal graph datasets and develop multiple datasets suitable for TGC task, called BenchTGC Datasets. According to extensive experiments, we not only verify the advantages of BenchTGC, but also demonstrate the necessity and importance of TGC task. We wish to point out that the dynamically changing and complex scenarios in real world are the foundation of temporal graph clustering.

Deep graph clustering, which aims to reveal the underlying graph structure and divide the nodes into different clusters without human annotations, is a fundamental yet challenging task. However, we observe that the existing methods suffer from the representation collapse problem and tend to encode samples with different classes into the same latent embedding. Consequently, the discriminative capability of nodes is limited, resulting in suboptimal clustering performance. To address this problem, we propose a novel deep graph clustering algorithm termed improved dual correlation reduction network (IDCRN) through improving the discriminative capability of samples. Specifically, by approximating the cross-view feature correlation matrix to an identity matrix, we reduce the redundancy between different dimensions of features, thus improving the discriminative capability of the latent space explicitly. Meanwhile, the cross-view sample correlation matrix is forced to approximate the designed clustering-refined adjacency matrix to guide the learned latent representation to recover the affinity matrix even across views, thus enhancing the discriminative capability of features implicitly. Moreover, we avoid the collapsed representation caused by the oversmoothing issue in graph convolutional networks (GCNs) through an introduced propagation regularization term, enabling IDCRN to capture the long-range information with the shallow network structure. Extensive experimental results on six benchmarks have demonstrated the effectiveness and efficiency of IDCRN compared with the existing state-of-the-art deep graph clustering algorithms. The code of IDCRN is released at https://github.com/yueliu1999/IDCRN. Besides, we share a collection of deep graph clustering, including papers, codes, and datasets at https://github.com/yueliu1999/Awesome-Deep-Graph-Clustering.

As an emerging task, temporal graph clustering (TGC) is committed to clustering nodes on temporal graphs through interaction sequence-based batch-processing patterns. These patterns allow for more flexibility in finding a balance between time and space requirements than adjacency matrix-based static graph clustering. However, as a new task, TGC still has important unresolved challenges, such as insufficient information. This challenge manifests itself in a variety of problems in real-world datasets, including missing features (eigenvalues are missing or even nonexistent), long-tail nodes (most inactive nodes have little interaction), and noisy data (data is subject to anomalies, errors, and sparsity). These problems occur before training, making it difficult for the model to train well with insufficient information. To solve the challenge, we propose a method that introduces multiview clustering (MVC) into TGC, called MVTGC. Our method aims to perform data augmentation on the temporal graph by constructing multiple views to increase the information richness. In particular, we utilize different techniques to model a certain part of the temporal graph to generate enhanced views focusing on different angles. These views are combined into training through early fusion and late fusion and ultimately enhance the model’s receptive field and information richness. Comparative experiments and a case study on real-world datasets demonstrate the significance and effectiveness of MVTGC, which achieves at most 10.48% performance improvement. The code and data are available at https://github.com/MGitHubL/MVTGC

Reasoning paths are reliable information in knowledge graph completion (KGC) in which algorithms can find strong clues of the actual relation between entities. However, in real-world applications, it is difficult to guarantee that computationally affordable paths exist toward all candidate entities. According to our observation, the prediction accuracy drops significantly when paths are absent. To make the proposed algorithm more stable against the missing path circumstances, we introduce soft reasoning paths. Concretely, a specific learnable latent path embedding is concatenated to each relation to help better model the characteristics of the corresponding paths. The combination of the relation and the corresponding learnable embedding is termed a soft path in our paper. By aligning the soft paths with the reasoning paths, a learnable embedding is guided to learn a generalized path representation of the corresponding relation. In addition, we introduce a hierarchical ranking strategy to make full use of information about the entity, relation, path, and soft path to help improve both the efficiency and accuracy of the model. Extensive experimental results illustrate that our algorithm outperforms the compared state-of-the-art algorithms by a notable margin. Our code will be released at https://github.com/7HHHHH/SRP-KGC.

Incomplete multi-view deep clustering is an emerging research hot-pot to incorporate data information of multiple sources or modalities when parts of them are missing. Most of existing approaches encode the available data observations into multiple view-specific latent representations and subsequently integrate them for the next clustering task. However, they ignore that the latent representations are unique to a fixed set of data samples in all views. Meanwhile, the pair-wise similarities of missing data observations are also failed to utilize in latent representation learning sufficiently, leading to unsatisfactory clustering performance. To address these issues, we propose an incomplete multi-view deep clustering method with data imputation and alignment. Assuming that each data sample corresponds to a same latent representation among all views, it projects the latent representations into feature spaces with neural networks. As a result, not only the available data observations are reconstructed, but also the missing ones can be imputed accordingly. Moreover, a linear alignment measurement of linear complexity is defined to compute the pair-wise similarities of all data observations, especially including those of the missing. By executing the above two procedures iteratively, the discriminative latent representations can be learned and used to group the data into categories with off-the-shelf clustering algorithms. In experiment, the proposed method is validated on a set of benchmark datasets and achieves state-of-the-art performances.

Knowledge graphs (KGs) represent known entities and their relationships using triplets, but this method cannot represent relationships between facts, limiting their expressiveness. Recently, the Bi-level Knowledge Graph (Bi-level KG) has addressed this issue by modeling facts as nodes and establishing relationships between these facts, introducing two new tasks: triplet prediction and conditional link prediction. Existing methods enhance triplets through data augmentation method and represent facts using entity representations. However, these methods do not address the isolated nodes at the structure level, nor do they effectively capture the information of facts at the feature level. To address these two issues, we design a data augmentation method that identifies islanded node by detecting anomalous structures and features in the graph. Subsequently, we perform similar subgraph matching for each isolated node to construct potential facts. To enrich the features of facts, we design a weighted combination initialization method for facts and introduce a new relation R, to connect facts with related entities. This approach allows for the co-training of fact and entity representations during the training process. Extensive experiments validate the effectiveness of our data augmentation and co-training methods. Our model achieves optimal performance in triplet prediction and conditional link prediction tasks.

Text-based knowledge graph completion methods take advantage of pre-trained language models (PLM) to enhance intrinsic semantic connections of raw triplets with detailed text descriptions. Typical methods in this branch map an input query (textual descriptions associated with an entity and a relation) and its candidate entities into feature vectors, respectively, and then maximize the probability of valid triples. These methods are gaining promising performance and increasing attention for the rapid development of large language models. According to the property of the language models, the more related and specific context information the input query provides, the more discriminative the resultant embedding will be. In this paper, through observation and validation, we find a neglected fact that the relation-aware neighbors of the head entities in queries could act as effective contexts for more precise link prediction. Driven by this finding, we propose a relation-aware anchor enhanced knowledge graph completion method (RAA-KGC). Specifically, in our method, to provide a reference of what might the target entity be like, we first generate anchor entities within the relation-aware neighborhood of the head entity. Then, by pulling the query embedding towards the neighborhoods of the anchors, it is tuned to be more discriminative for target entity matching. The results of our extensive experiments not only validate the efficacy of RAA-KGC but also reveal that by integrating our relation-aware anchor enhancement strategy, the performance of current leading methods can be notably enhanced without substantial modifications.

Site selection aims to select optimal locations for new stores, which is crucial in business management and urban computing. The early data-driven models heavily relied on feature engineering, which could not effectively model the complex relationships and diverse influences among different data. To alleviate such issues, the knowledge-driven paradigm is proposed based on urban knowledge graphs (KGs). However, the research on them is at an early stage. They omit extra multi-modal information corresponding to brands and stores due to two main challenges, i.e., (1) building available datasets, and (2) designing effective models. It constrains the expressive ability and practical value of previous models. To this end, we first construct new multi-modal urban KGs for site selection with three extra modal ( i.e., visual, textual, and acoustic) attributes. Then, we propose a novel multi-modal knowledge-driven model (MGKsite). Concretely, a graph neural network (GNN) based fusion network is designed to fuse the features based on the attribute K-Nearest Neighbor (KNN) graph, which models both intra and inter-modal correlations among the features. The fused embeddings are further injected into the knowledge-driven backbones for learning and inference. Experiments prove promising capacities of MGKsite from five aspects, i.e., superiority, effectiveness, sensitivity, transferability and complexity.

With the development of various applications, such as recommendation systems and social network analysis, graph data have been ubiquitous in the real world. However, graphs usually suffer from being absent during data collection due to copyright restrictions or privacy-protecting policies. The graph absence could be roughly grouped into attribute-incomplete and attribute-missing cases. Specifically, attribute-incomplete indicates that a portion of the attribute vectors of all nodes are incomplete, while attribute-missing indicates that all attribute vectors of partial nodes are missing. Although various graph imputation methods have been proposed, none of them is custom-designed for a common situation where both types of graph absence exist simultaneously. To fill this gap, we develop a novel graph imputation network termed revisiting initializing then refining (RITR), where both attribute-incomplete and attribute-missing samples are completed under the guidance of a novel initializing-then-refining imputation criterion. Specifically, to complete attribute-incomplete samples, we first initialize the incomplete attributes using Gaussian noise before network learning, and then introduce a structure-attribute consistency constraint to refine incomplete values by approximating a structure-attribute correlation matrix to a high-order structure matrix. To complete attribute-missing samples, we first adopt structure embeddings of attribute-missing samples as the embedding initialization, and then refine these initial values by adaptively aggregating the reliable information of attribute-incomplete samples according to a dynamic affinity structure. To the best of our knowledge, this newly designed method is the first end-to-end unsupervised framework dedicated to handling hybrid-absent graphs. Extensive experiments on six datasets have verified that our methods consistently outperform the existing state-of-the-art competitors. Our source code is available at https://github.com/WxTu/RITR.

Attribute-missing graph learning, a common yet challenging problem, has recently attracted considerable attention. Existing efforts have at least one of the following limitations: 1) lack a noise filtering and information enhancing scheme, resulting in less comprehensive data completion; 2) isolate the node attribute and graph structure encoding processes, introducing more parameters and failing to take full advantage of the two types of information; and 3) impose overly strict distribution assumptions on the latent variables, leading to biased or less discriminative node representations. To tackle the issues, based on the idea of introducing intimate information interaction between the two information sources, we propose Weight-sharing Attribute-missing Graph autoEncoder (WAGE) to boost the expressive capacity of node representations for high-quality missing attribute reconstruction. Specifically, three strategies have been conducted. Firstly, we entangle the attribute embedding and structure embedding by introducing a weight-sharing architecture to share the parameters learned by both processes, which allows the network training to benefit from more abundant and diverse information. Secondly, we introduce a $K$-nearest neighbor-based dual non-local learning mechanism to improve the quality of data imputation by revealing unobserved high-confidence connections while filtering unreliable ones. Thirdly, we manually mask the connections on multiple adjacency matrices and force the structure-oriented embedding sub-network to recover the actual adjacency matrix, thus enforcing the resulting network to be able to selectively exploit more high-order discriminative features for data completion. Extensive experiments on six benchmark datasets demonstrate the effectiveness and superiority of WAGE against state-of-the-art competitors.

Late fusion multi-view clustering (LFMVC) has become a rapidly growing class of methods in the multi-view clustering (MVC) field, owing to its excellent computational speed and clustering performance. One bottleneck faced by existing late fusion methods is that they are usually aligned to the average kernel function, which makes the clustering performance highly dependent on the quality of datasets. Another problem is that they require subsequent k-means clustering after obtaining the consensus partition matrix to get the final discrete labels, and the resulting separation of the label learning and cluster structure optimization processes limits the integrity of these models. To address the above issues, we propose an integrated framework named One-Step Late Fusion Multi-view Clustering with Compressed Subspace (OS-LFMVC-CS). Specifically, we use the consensus subspace to align the partition matrix while optimizing the partition fusion, and utilize the fused partition matrix to guide the learning of discrete labels. A six-step iterative optimization approach with verified convergence is proposed. Sufficient experiments on multiple datasets validate the effectiveness and efficiency of our proposed method.