Graph Neural Networks (GNNs) have received increasing attention due to their ability to handle graph-structured data, yet their explainability remains a significant challenge. An effective solution is to provide the GNN models with counterfactual explanations, which aim to answer “How should the input instance be perturbed to change the model's prediction?". However, existing works mainly focus on generating explanations that can effectively alter model predictions, while neglecting whether the explanations remain aligned with the original data distribution, leading to the distribution shift problem. To address this problem, we propose a novel method called ICExplainer for generating explanations within the original distribution. Specifically, we introduce graph diffusion-based generative model into the counterfactual reasoning, treating it as an optimization objective for graph distribution learning. Taking insights from variational inference, we use it to estimate the true distribution of the input graphs to retain essential structural and semantic information. The inferred distribution is then utilized as prior knowledge to guide the reverse process, ensuring that generated explanations are both counterfactual and distributionally coherent. Extensive experiments conducted on both synthetic and real-world datasets demonstrate the superior performance of ICExplainer over existing methods.

Learning path recommendation seeks to provide students with a structured sequence of learning items (e.g., knowledge concepts or exercises) to optimize their learning efficiency. Despite significant efforts in this area, most existing methods primarily rely on prerequisite relations, which present two major limitations: (1) Prerequisite relations between knowledge concepts are difficult to obtain due to the cost of expert annotation, hindering the application of current learning path recommendation methods. (2) Relying on a single sequentially dependent knowledge structure based on prerequisite relations implies that a confusing knowledge concept can disrupt subsequent learning processes, which is referred to as blocked learning. To address these two challenges, we propose a novel approach, GraphRAG-Induced Dual Knowledge Structure Graphs for Personalized Learning Path Recommendation (KnowLP), which enhances learning path recommendations by incorporating both prerequisite and similarity relations between knowledge concepts. Specifically, we introduce a knowledge structure graph generation module EDU-GraphRAG that constructs knowledge structure graphs for different educational datasets, significantly improving the applicability of learning path recommendation methods. We then propose a Discrimination Learning-driven Reinforcement Learning (DLRL) module that utilizes similarity relations as fallback relations when prerequisite relations become ineffective, thereby alleviating the blocked learning. Finally, we conduct extensive experiments on three benchmark datasets, demonstrating that our method not only achieves state-of-the-art performance but also generates more effective and longer learning paths.

Large Vision--Language Models (LVLMs) frequently fail on knowledge-intensive educational video QA despite the presence of requisite visual evidence. Through region-level analysis, we identify a systematic evidence-suppression pattern: task-critical tokens (e.g., diagrams) exhibit lower representational energy than distractors at the encoder output, rendering them prone to persistent attention neglect during decoding. While a controlled study shows that performance is sensitive to the strength and amount of injected candidate evidence signals, we find that rigid heuristics are insufficient due to sensitivity to token quality. To address this, we propose Bi-level Active Evidence Injection (BAEI), a decoding-time intervention that keeps the LVLM backbone frozen. BAEI employs a lightweight Injection Policy Network (IPN), optimized via GRPO, to dynamically select candidate evidence tokens and predict their token-wise injection strengths. The framework operates on two levels: increasing the contribution of candidate evidence-related signals in shallow layers and performing adaptive correction in deep layers triggered by predictive entropy. Experiments on educational benchmarks demonstrate consistent gains, validating decoding-time evidence intervention as an effective solution for factual alignment. The code is available at https://github.com/diojojolc-cell/BAEI.

Variational autoencoders (VAEs) have been widely used for node clustering, with existing methods mainly focusing on enhancing the expressiveness of their latent space. Recently, the integration of diffusion models with VAEs has provided new opportunities to achieve this objective. However, the mechanism by which the diffusion model improves performance remains unclear. To bridge this gap, we conduct an empirical analysis from the perspective of graph spectral theory, revealing that the signal modulation induced by diffusion models closely aligns with the low-frequency spectral characteristics of VAEs, which in turn explains their effectiveness. Nevertheless, further experiments highlight that diffusion models exhibit limitations in modulating high-frequency signals, which diverge from the spectral characteristics of VAEs. Moreover, existing diffusion methods fail to enable the latent space to adequately capture and reflect cluster-specific characteristics. To address these challenges, we propose a novel plug-and-play method, FVD, to improve the performance of VAE-based methods in node clustering tasks. Specifically, we incorporate the graph wavelet transform as a secondary signal modulator, enabling independent adjustments of specific frequency bands to better align with the spectral characteristics of VAEs. Additionally, we introduce the Student's t-distribution as a conditional constraint in the reverse process of FVD, deriving a more compact variational lower bound. This enhancement preserves fine-grained node information while focusing on clustering details, effectively mitigating the cluster collapse phenomenon. Comprehensive experimental results demonstrate that integrating FVD with existing methods achieves competitive performance improvements in most cases.

Variational autoencoder performs well in community detection on static networks, but it is difficult to directly extend to continuous dynamic networks. The main reason is that traditional methods mainly rely on adjacency structures to complete the inference and generation processes. However, continuous dynamic networks cannot be described by this structure because the inherent timeliness and causality information of the network would be lost. To address this issue, we propose a novel variational autoencoder, CT-VAE, for community detection in continuous dynamic networks, along with its scalable variant, CT-CAVAE. By conceptualizing node interactions as event streams and adopting the Hawkes process to capture temporal dynamics and causality, and incorporating them into the inference process, CT-VAE can effectively extend the traditional inference approach to continuous dynamic networks. Additionally, in the generation phase, CT-VAE combines pseudo-labeling and compact constraint strategies to facilitate the reconstruction process of non-adjacent structures. For the scalable variant, CT-CAVAE, end-to-end community detection is achieved by cleverly combining Gaussian mixture distribution. Extensive experimental results demonstrate that the proposed CT-VAE and CT-CAVAE achieve more favorable performance compared with the state-of-the-art baselines.

Signed networks are commonly used to represent positive and negative relationships in the real world. Link sign prediction in signed networks is a significant research topic. In the past decades, various link sign prediction methods have been proposed. However, most of them following the message-passing paradigm encounter two challenges: i) capture the relationship between nodes and their high-order neighborhoods, and ii) alleviate the over-smoothing problem. To address these challenges, we propose a method called Signed Graph Transformer (SGTrans), which uses a node sequence encoding approach based on Transformer. For the first challenge, we introduce three types of positional encoding, guided by path-level balance theory, while adding more network layers to capture the relationships between nodes and their high-order neighborhoods effectively. For the second challenge, SGTrans utilizes self-attention to handle a sampled relevant node sequence rather than message passing. This approach not only minimizes the introduction of excessive irrelevant node information but also alleviates the over-smoothing problem. Extensive experiments are conducted on four real-world datasets, and the results illustrate the effectiveness of SGTrans.

With the widespread adoption of online education platforms, an increasing number of students are gaining new knowledge through Massive Open Online Courses (MOOCs). Exercise recommendation have made strides toward improving student learning outcomes. However, existing methods not only struggle with high dropout rates but also fail to match the diverse learning pace of students. They frequently face difficulties in adjusting to inactive students' learning patterns and in accommodating individualized learning paces, resulting in limited accuracy and diversity in recommendations. To tackle these challenges, we propose Neural Re-ranking for Diversified Exercise Recommendation (in short, NR4DER). NR4DER first leverages the mLSTM model to improve the effectiveness of the exercise filter module. It then employs a sequence enhancement method to enhance the representation of inactive students, accurately matches students with exercises of appropriate difficulty. Finally, it utilizes neural re-ranking to generate diverse recommendation lists based on individual students' learning histories. Extensive experimental results indicate that NR4DER significantly outperforms existing methods across multiple real-world datasets and effectively caters to the diverse learning pace of students.

Dynamic link prediction (DLP) is a crucial task in graph learning, aiming to predict future links between nodes at subsequent time in dynamic graphs. Recently, graph masked autoencoders (GMAEs) have shown promising performance in self-supervised learning. However, their application to DLP is under-explored. Existing GMAEs struggle to capture temporal dependencies, and their random masking causes crucial information loss for DLP. Moreover, most existing DLP methods rely on local information, ignoring global information and failing to capture complex features in real-world dynamic graphs. To address these issues, we propose DyGMAE, a novel dynamic GMAE method specifically designed for DLP. DyGMAE introduces a Multi-Scale Masking Strategy (MSMS), which generates multiple graph views by masking parts of the edges and tries to reconstruct them. Additionally, a multi-scale masking representation alignment module with a contrastive learning objective is employed to align representations which are encoded by unmasked edges across these views. Through this design, different masked views can provide diverse information to alleviate the drawbacks of random masking, and contrastive learning can align different views to mitigate the problem of exploiting local and global information simultaneously. Experiments on benchmark datasets show DyGMAE achieves superior performance in the DLP task.

Recommending suitable exercises and providing the reasons for these recommendations is a highly valuable task, as it can significantly improve students' learning efficiency. Nevertheless, the extensive range of exercise resources and the diverse learning capacities of students present a notable difficulty in recommending exercises. Collaborative filtering approaches frequently have difficulties in recommending suitable exercises, whereas deep learning methods lack explanation, which restricts their practical use. To address these issue, this paper proposes KG4EER, an explainable exercise recommendation with a knowledge graph. KG4EER facilitates the matching of various students with suitable exercises and offers explanations for its recommendations. More precisely, a feature extraction module is introduced to represent students' learning features, and a knowledge graph is constructed to recommend exercises. This knowledge graph, which includes three primary entities - knowledge concepts, students, and exercises - and their interrelationships, serves to recommend suitable exercises. Extensive experiments conducted on three real-world datasets, coupled with expert interviews, establish the superiority of KG4EER over existing baseline methods and underscore its robust explainability.

Multi-view clustering (MVC) is essential for integrating heterogeneous data from multiple sources. However, many existing approaches are hindered by high computational complexity and the separate optimization of similarity and cluster structures. In light of these challenges, this paper presents a novel anchor-based MVC method termed simple one-step multi-view clustering with fast similarity and cluster structure learning (SONIC), which models adaptive anchor learning, multi-view similarity structure learning, and discrete cluster structure learning in a joint framework. In particular, we employ the anchor-based multi-view similarity learning to capture the consensus manifold structure latent in multiple views, thereby constructing a unified bipartite graph with adaptive anchor learning and view weighting. Then we impose a low-rank constraint on the bipartite graph structure to directly reveal the desired number of clusters without additional post-processing. An efficient alternating minimization algorithm is developed to optimize the model, resulting in a computational complexity that scales linearly with the number of samples. Extensive experiments on eight benchmark datasets demonstrate the superior performance of SONIC in both clustering quality and computational efficiency. Code available:https://github.com/huangdonghere/SONIC.

Methods based on variational bayes theorytare widely used to detect community structures in networks. In recent years, many related methods have emerged that provide valuable insights into variational bayes theory. Remarkably, a fundamental assumption remains incomprehensible. Variational bayes-based methods typically employ a posterior distribution that follows a gaussian distribution to approximate the unknown prior distribution. However, the complexity and irregularity of node distributions in real-world networks prompt us to consider what characteristics of network information are suitable for the posterior distribution. Mathematically, inappropriate low- and high-frequency signals in expectation inference and variance inference can intensify the adverse effects of community distortion and ambiguity. To analysis these two phenomena and propose reasonable countermeasures, we conduct an empirical study. It is found that appropriately compressing low-frequency signals during expectation inference and amplifying high-frequency signals during variance inference are effective strategies. Based on these two strategies, this paper proposes a novel variational bayes plug-in, namely VBPG, to boost the performance of existing variational bayes-based community detection methods. Specifically, we modulate the frequency signals during expectation and variance inference to generate a new gaussian distribution. This strategy improves the fitting accuracy between the posterior distribution and the unknown true distribution without altering the modules of existing methods. The comprehensive experimental results validate that methods using VBPG achieve competitive performance improvements in most cases.

Multi-Modal Large Language Models (MM-LLMs) have demonstrated powerful reasoning abilities in various visual question-answering tasks. However, they face the challenge of lacking rigorous reasoning and precise arithmetic, when solving geometry questions. To address this challenge, we propose a novel prompting method, namely Reason-and-Execute (R&E), to enhance the accuracy of solving geometry questions by MM-LLMs. Specifically, the R&E method includes two templates: reasoning template and execution template. We first adopt a reverse-thinking approach to construct a rigorous reasoning template so that it guides MM-LLMs to start reasoning from the most relevant domain knowledge of the question and ultimately identify the arithmetic requirements. We then make use of program-assisted thought to construct execution template in order to guide MM-LLMs to understand the arithmetic requirements from reasoning template and generate executable code block. The answer is finally obtained by executing the code block. We evaluate our prompting method on 9 models in answering questions on 6 datasets (including four geometry datasets and two science datasets) compared to Chain-of-Thought (CoT) and Program-Aided Language (PAL) prompting methods. R&E method shows up to 12.8% improvement compared to CoT and PAL, proving strong reasoning and arithmetic abilities for solving geometry questions of our method. Moreover, we further analyze the answering accuracy from the different perspectives on solving geometric questions, including domain knowledge, geometry shapes, question length, and language. Through multiple analysis, our method is able to enhance the ability of MM-LLMs to solve geometry questions.

Although previous graph-based multi-view clustering (MVC) algorithms have gained significant progress, most of them are still faced with three limitations. First, they often suffer from high computational complexity, which restricts their applications in large-scale scenarios. Second, they usually perform graph learning either at the single-view level or at the view-consensus level, but often neglect the possibility of the joint learning of single-view and consensus graphs. Third, many of them rely on the k -means for discretization of the spectral embeddings, which lack the ability to directly learn the graph with discrete cluster structure. In light of this, this article presents an efficient MVC approach via u nified and d iscrete b ipartite g raph l earning (UDBGL). Specifically, the anchor-based subspace learning is incorporated to learn the view-specific bipartite graphs from multiple views, upon which the bipartite graph fusion is leveraged to learn a view-consensus bipartite graph with adaptive weight learning. Furthermore, the Laplacian rank constraint is imposed to ensure that the fused bipartite graph has discrete cluster structures (with a specific number of connected components). By simultaneously formulating the view-specific bipartite graph learning, the view-consensus bipartite graph learning, and the discrete cluster structure learning into a unified objective function, an efficient minimization algorithm is then designed to tackle this optimization problem and directly achieve a discrete clustering solution without requiring additional partitioning, which notably has linear time complexity in data size. Experiments on a variety of multi-view datasets demonstrate the robustness and efficiency of our UDBGL approach. The code is available at https://github.com/huangdonghere/UDBGL.

Link prediction is a hot research topic in graph data analytics, which aims to identify the likelihood of a future connection between two nodes in a network. Among the approaches to link prediction, network embedding has gained tremendous popularity in tackling link prediction tasks. Basically, there are several network embedding methods, such as matrix factorization, random walk, and deep learning. However, most of the existing methods for network embedding solely rely on structure information or fail to effectively combine network structure and feature data. To this end, this paper proposes a novel method that learns network embedding with enhanced feature representations for link prediction (EFRLP). Specifically, structure graphs, bipartite graphs, and co-feature graphs are generated from the attributed network, weighted bipartite graphs are then built over bipartite graphs and correlation weights between features. We further adopt a biased random walk to obtain more representative node sequences. With the help of enriched feature representations, not only can the higher-order semantic relationships be effectively captured but also network sparsity can be alleviated. Then, node sequences are selected into the Skip-Gram model for learning low-dimensional embeddings. Finally, the probability of the existence of edges between nodes is predicted by deep fusion. The effectiveness of the EFRLP method is demonstrated by extensive comparison experiments with several baselines on two real-world datasets.

Community detection in multiplex networks has received considerable attention in recent years. However, existing methods that combine graph embedding and downstream tasks still face two challenges. The first is how to fully explore the correlation among the layers in the multiplex networks, and the second is how to make the learned node representation more applicable to the community detection tasks. Aiming at these challenges, we propose a novel self-supervised multiplex community detection model called MGCAE which is based on graph neural networks. To solve the first challenge, we compute the mutual information maximization loss in the self-supervision module. The mutual information includes global representation and common representation of nodes in different layers, and node representation in each layer. For the second challenge, we combine a Bernoulli-Poisson loss and a modularity maximization loss to jointly optimize the reconstruction of the original adjacency matrix, which is in line with the rigorous theory of modularity. We treat graph convolutional autoencoder (GCAE) as the backbone framework and train it by using the unified loss mentioned above. In addition, the model obtains the community detection results in an end-to-end manner, which makes the model independent of downstream tasks and more stable. Experiments on real-world attributed multiplex network datasets demonstrate the effectiveness of our model.

Existing community detection methods for attributed multiplex networks focus on exploiting the complementary information from different topologies, while they are paying little attention to the role of attributes. However, we observe that real attributed multiplex networks exhibit two unique features, namely, consistency and homogeneity of node attributes. Therefore, in this paper, we propose a novel method, called ACDM, which is based on these two characteristics of attributes, to detect communities on attributed multiplex networks. Specifically, we extract commonality representation of nodes through the consistency of attributes. The collaboration between the homogeneity of attributes and topology information reveals the particularity representation of nodes. The comprehensive experimental results on real attributed multiplex networks well validate that our method outperforms state-of-the-art methods in most networks.

Since existing methods are often not effective to detect communities with multiple topics in attributed networks, we propose a method named SSAGCN via Autoencoder-style self-supervised learning. SSAGCN firstly designs an adaptive graph convolutional network (AGCN), which is treated as the encoder for fusing topology information and attribute information automatically, and then utilizes a dual decoder to simultaneously reconstruct network topology and attributes. By further introducing the modularity maximization and the joint optimization strategies, SSAGCN can detect communities with multiple topics in an end-to-end manner. Experimental results show that SSAGCN outperforms state-of-the-art approaches, and also can be used to conduct topic analysis well.

Community detection is one of the hottest research topics in attributed networks analysis. Nonnegative matrix factorization (NMF) is widely used in community detection of attributed networks because of its high interpretability and extensibility. However, the existing NMF based methods still encounter some obstacles which affect the performance of community detection. Firstly, it is impossible to solve the problem of sparse semantic description. Besides, these methods cannot integrate the heterogeneity of topology structure and nodes attributes. Obviously, these methods cannot accurately identify community structure and assign specific semantic descriptions to each community. To overcome the aforementioned problems, we propose a novel method which combines graph neural networks with weighted-traction regularization. Moreover, we use graph neural networks to discover the semantic characteristics between adjacent nodes which can alleviate the problem of sparse semantic description. Furthermore, the regularizer we proposed can improve the performance of community detection in attributed networks. Experiments on some real attributed networks show that the method we proposed not only is better than some representative related methods but also can assign specific semantic descriptions to each community at the same time.

Community detection is of great help to understand the structures and functions of complex networks. It has become one of popular research topics in the field of complex networks analysis. Due to the simplicity, flexibility, effectiveness and better interpretability, Nonnegative Matrix Factorization (NMF)-based methods have been widely employed for community detection. However, most existing NMF-based community detection methods are linear and their performance is limited when facing networks with diversified structure information. In view of this, we propose a nonlinear NMF-based method named NMFGAAE, which is composed of two main modules: NMF and Graph Attention Auto-Encoder (GAAE). This approach can boost the performance of NMF-based community detection methods by the aid of graph neural networks and deep clustering. More specifically, GAAE introduces an attention mechanism directed by NMF-based community detection to learn the node representations, while NMF can simultaneously factor these representations to uncover the community structure. We design a unified framework to jointly optimize GAAE and NMF modules, which is very beneficial to obtain better community detection results. We conduct extensive experiments on synthetic and real-world networks. The results show that our NMFGAAE not only performs better than state-of-the-art NMF-based community detection methods, but also outperforms some network representation based baselines. More importantly, NMFGAAE indeed can boost the performance of NMF-based community detection methods.

Community detection is one of the popular research topics in the field of complex networks analysis. It aims to identify communities, represented as cohesive subgroups or clusters, where nodes in the same community link to each other more densely than others outside. Due to the interpretability, simplicity, flexibility, and generality, nonnegative matrix factorization (NMF) has become a very ideal model for community detection and lots of related methods have been presented. To facilitate research on NMF-based community detection, in this article, we make a comprehensive review on NMF-based methods for community detection, especially the state-of-the-art methods presented in high prestige journals or conferences. First, we introduce the basic principles of NMF and explain why NMF can detect communities and design a general framework of NMF-based community detection. Second, according to the applicable network types, we propose a taxonomy to divide the existing NMF-based methods for community detection into six categories, namely, topology networks, signed networks, attributed networks, multilayer networks, dynamic networks, and large-scale networks. We deeply analyze representative methods in every category. Finally, we summarize the common problems faced by all methods and potential solutions and propose four promising research directions. We believe that this survey can fully demonstrate the versatility of NMF-based community detection and serve as a useful guideline for researchers in related fields.

In today's society, social networking has been integrated into everyone's life. The detection of network community has been a hotspot in recent years, and it has been widely used in fraud prevention, personalized recommendation, risk control and other fields. In this paper, we present an improved community detection algorithm for fusing topology and attribute information (FTAI) based on Non-Negative Matrix Factorization (NMF). Firstly, we use the attribute similarity matrix instead of a binary matrix based on string matching to cope with the sparsity of the attribute matrix. Next, we introduce the transfer matrix and the attribute feedback adjustment method to fuse the topological matrix and the attribute matrix. Then, we deduce the iteration formula of each matrix with a rigorous mathematical method, which shows the reliability of the algorithm. Finally, we evaluate our method with extensive experiments by using the data set from a real academic social network (SCHOLAT). Experimental results show that FTAI is superior to other baseline algorithms. The results also indicate that FTAI is more flexible, robust and suitable for community detection in social networks with complex attribute information.

Summary Online social networks (OSNs) have become more and more popular and have attracted a great many users. Friend recommendation, which is one of the important services in OSN, can help users discover their interested friends and alleviate the problem of information overload. However, most of existing recommendation methods only consider either user link or content information and hence are not effective enough to provide high quality recommendations. In this paper, we propose a topic community‐based method via Nonnegative Matrix Factorization (NMF). This method first applies joint NMF model to mine topic communities existing in OSN by combing link and content information. Then it computes user pairwise similarities and makes friends recommendation based on topic communities. Furthermore, this method can be implemented using the MapReduce distributed computing framework. Extensive experiments show that our proposed method not only has better recommendation performance than state‐of‐the‐art methods but also has good scalability to deal with the problem of friend recommendation in large‐sale OSNs. Moreover, the application case demonstrates that it can significantly improve friend recommendation service in the real world OSN. Copyright © 2016 John Wiley & Sons, Ltd.