Real-world systems often involve multiple interaction types and complex higher order relationships that go beyond simple pairwise connections, making multilayer hypergraphs a powerful framework for modeling such intricate structures. Community detection, a fundamental problem in network science, is particularly significant in the context of multilayer hypergraphs. However, existing research in this area remains limited. Current approaches often rely on heuristic techniques, such as clustering and random walks, which lack robust theoretical foundations and flexibility, or on layer fusion methods that compress all layers into a single-layer network, thereby discarding valuable cross-layer information and yielding hard partitioning results. In this article, we propose a statistically grounded generative model—the stochastic block model for multilayer hypergraphs—that employs the expectation–maximization algorithm to infer community structures and community interaction strength matrix for each layer. Our framework enables soft partitioning, allowing nodes to belong to multiple communities with probabilistic assignments, while simultaneously leveraging cross-layer information to enhance hyperlink prediction within specific layers. Experiments on synthetic and real-world networks demonstrate the model’s superior performance in community detection and hyperlink prediction, showcasing its ability to capture the complexity of multilayer higher order interactions effectively.

Cognitive modeling, as an emerging technology in the field of computer-aided education, aims to explore students’ knowledge levels and learning abilities to achieve various intelligent educational applications. Although some existing work focuses on addressing the problem of student forgetting, it is still a less explored area how to naturally integrate the forgetting effect caused by the time interval between answering exercises into student knowledge state modeling. Additionally, traditional cognitive modeling methods mostly assume that students answer exercises one by one, which often does not align with real answering behavior and cannot be directly extended to diverse learning scenarios. Therefore, in this article, we propose a Continuous Time-based Neural Cognitive (CT-NC) framework and several implemented models (CT-NCM and two extensions) to effectively integrate the dynamic and continuous characteristics of knowledge forgetting into student learning process modeling, making it more natural. Specifically, we adopt a specially designed learning event encoding method to adjust the neural Hawkes process to capture the relationship between knowledge learning and forgetting over continuous time. Furthermore, we propose a customizable learning function to jointly model the changes in different knowledge states and their interaction with each practice moment. In the end, we demonstrate an extension CT-NCM+ that can adapt well to diverse learning scenarios, indicating that CT-NCM can solve real-world problems by flexibly adjusting its structure. Extensive experimental results on real datasets clearly demonstrate that CT-NCM and CT-NCM+ outperform the current state-of-the-art KT methods in student performance prediction, while our work points out a realistic research direction for KT and demonstrates its interpretability in knowledge learning visualization.

Federated learning (FL)-based fault diagnosis is being widely developed. However, most of the existing FL methods may suffer from two drawbacks: 1) they are limited to a single diagnosis task, and this may be insufficient when comprehensive health status information is needed and 2) most of them work offline, thus neglecting the useful information contained in newly collected operation data. For this end, this article proposes a multitask federated incremental learning (multitask-FIL) framework. First of all, a multitask feature sharing network is established by assigning the extracted general features to different downstream tasks, so that the joint loss function is obtained for subsequent collaborative training. Then, Q-learning algorithm is used to select the incremental sequences for all the parties from real-time running data, which can facilitate the model performance by involving additional data information and preferred parties. After that, the incremental weight of each party is dynamically adjusted according to the loss depth and sample size in each round of communication, so that the effects of different parties can be quantified throughout the model iteration and aggregation process. Finally, experiments on three challenging cases are performed to show that the proposed method has strong multitask collaboration capability.

Network reconstruction, which involves inferring a network’s topology from observational data, is a critical challenge in network science. Because observational data are often limited, prior knowledge is often employed to enhance the accuracy of network reconstruction, including constraints related to sparsity, symmetry, or network dynamics. In many cases, we may possess prior knowledge regarding the number of types of edges within networks, yet the specific solutions of these types of edges remain unknown. For instance, while it is evident that two types of edges (i.e., positive and negative) exist in signed networks, the possible solution for each edge type is frequently unclear, rendering existing methods, such as the signal Lasso approach, ineffective. In this work, to effectively leverage this readily available prior knowledge, we propose a novel network reconstruction framework based on the Gaussian mixture model (GMM), which integrates Bayesian models and employs the GMM to model the distribution of unknown edges as prior probabilities. The method is effective for both unsigned and signed networks and achieves high accuracy even with limited prior information, without requiring specific solutions for each edge type, particularly in cases of network sparsity or noisy data.

Graph neural networks (GNNs) are efficient techniques for learning graph representations and have shown remarkable success in tackling diverse graph-related tasks. However, in the context of the neighborhood aggregation paradigm, conventional GNNs have limited capabilities in capturing the higher order structures and topological semantics of graphs. Researchers have attempted to overcome this limitation by designing new GNNs that explore the impacts of motifs to capture potentially higher order graph information. However, existing motif-based GNNs often ignore lower order connectivity patterns such as nodes and edges, which leads to poor representation of sparse networks. To address these limitations, we propose an innovative approach. First, we design convolution kernels on both motif-based and simple graphs. Second, we introduce a multilevel graph convolution framework for extracting higher order topological semantics of graphs. Our approach overcomes the limitations of prior methods, demonstrating state-of-the-art performance in downstream tasks with excellent scalability. Extensive experiments on real-world datasets validate the effectiveness of our proposed method.

Recently, the problem of user identification across multiple social networks (UIAMSNs) has attracted considerable attention since it is a prerequisite for many downstream tasks and applications. Although substantial network feature-based approaches have been proposed to solve the UIAMSNs' problem, the matching degree in most of the current works is given by experience, which lacks a solid theoretical basis. To alleviate the above predicament, we propose a user identification algorithm based on naive Bayes model (UI-NBM) within the network feature-based framework. First, a matching degree index is designed based on the naive Bayes model, which can accurately measure the contributions of different common matched node pairs (MNPs) to the connection probability of unmatched node pairs (UMNPs). Second, the matching degrees of all UMNPs are formulated as the product of matrices, giving rise to the great reduction of the time complexity and the compact expression; Finally, with the idea of recursion process, more UMNPs can be iteratively predicted even when only a small amount of prior information (i.e., a few number of MNPs) is known. The experimental results on the synthetic and real cross platforms demonstrate that the method outperforms the baseline methods within the feature-based framework.

In many cases, a network may be dispersedly recorded by different participants and each participant is one part of the original network, and no one is willing to share its data due to commercial competition. Therefore, each participant forms an independent private network, and they form a “ multiple private networks” regarding the original network. Existing methods only use the structure of private network itself to predict missing links, leading to underutilized information and deteriorated prediction accuracy. One natural question arises: how to integrate the information of multiple private networks by formulating a security protocol, so as to help each private network to better predict missing links in its own network without disclosing its structure to others. To this end, we propose an SMPC-LP method based on secure multiparty computation (SMPC) to solve this problem. The method fuses the information of each private network without disclosing their inputs, and then, the similarity score of each node pair is jointly calculated, achieving enhanced link prediction performance in each private network. The experimental results show that the SMPC-LP method can better predict the missing links than the methods only using the information of the one private network, without violating data privacy agreement.

Existing methods regarding the influential nodes identification in complex networks usually assume that the structures of the networks are fully known. However, in many cases, knowing the full structure of one network is hard or impossible, and each participant can only obtain the partial structure of the networks. Therefore, each participant can be viewed as a private network (PN) of the original network, and they form multiple PNs. Then, one question arises: how to collaboratively identify influential nodes in multiple PNs while protecting the privacy of each PN. To this end, a secure multiparty computation ranking (SMPC-ranking) method is proposed to solve such an all-new problem based on the secure multiparty computation (SMPC) protocol, in which the SMPC protocol jointly computes a centrality function to measure the comprehensive importance of nodes or their ranking results by integrating each PN’s inputs without disclosing their inputs (i.e., the nodes’ importance). Experimental results in different networks demonstrate that, no matter what type of the centrality index is, the SMPC-ranking method can better identify the influential nodes in networks than that of the baseline method only using the structural information of one PN. What is more, our SMPC-ranking method does not violate the privacy of each PN. Therefore, the proposed method provides new insights on collaboratively identifying influential nodes in multiple PNs and has potential applications in many fields.

Cognitive diagnosis is a fundamental issue of intelligent education platforms, whose goal is to reveal the mastery of students on knowledge concepts. Recently, certain efforts have been made to improve the diagnosis precision, by designing deep neural networks-based diagnostic functions or incorporating more rich context features to enhance the representation of students and exercises. However, how to interpretably infer the student's mastery over non-interactive knowledge concepts (i.e., knowledge concepts not related to his/her exercising records) still remains challenging, especially when not giving relations between knowledge concepts. To this end, we propose a Knowledge-Sensed Cognitive Diagnosis (KSCD) framework, aiming at learning intrinsic relations among knowledge concepts from student response logs and incorporating them for inferring students' mastery over all knowledge concepts in an end-to-end manner. Specifically, we firstly project students, exercises and knowledge concepts into embedding representation matrices, where the intrinsic relations among knowledge concepts are reflected in the knowledge embedding representation matrix. Then, the knowledge-sensed student knowledge mastery vector and exercise factor vectors are obtained by the multiply product of their embedding representations and the knowledge embedding representation matrix, which make the student's mastery of non-interactive knowledge concepts be interpretably inferred. Finally, we can utilize classical student-exercise interaction functions to predict student's exercising performance and jointly train the model. In additional, we also design a new function to better model the student-exercise interactions. Extensive experimental results on two real-world datasets clearly show the significant performance gain of our KSCD framework, especially in predicting students' mastery over non-interactive knowledge concepts, by comparing to state-of-the-art cognitive diagnosis models (CDMs).

With the rapid development of intelligent education platforms, how to enhance the performance of diagnosing students' knowledge proficiency has become an important issue, e.g., by incorporating the prerequisite relation of knowledge concepts. Unfortunately, the differentiated influence from different predecessor concepts to successor concepts is still underexplored in existing approaches. To this end, we propose a Prerequisite Attention model for Knowledge Proficiency diagnosis of students (PAKP) to learn the attentive weights of precursor concepts on successor concepts and model it for inferring the knowledge proficiency. Specifically, given the student response records and knowledge prerequisite graph, we design an embedding layer to output the representations of students, exercises, and concepts. Influence coefficient among concepts is calculated via an efficient attention mechanism in a fusion layer. Finally, the performance of each student is predicted based on the mined student and exercise factors. Extensive experiments on real-data sets demonstrate that PAKP exhibits great efficiency and interpretability advantages without accuracy loss.

As an emerging technology of computer-aided education, cognitive modeling aims at discovering the knowledge proficiency or learning ability of students, which can enable a wide range of intelligent educational applications. While considerable efforts have been made in this direction, a long-standing research challenge is how to naturally integrate the forgetting mechanism into the learning process of knowledge concepts. To this end, in this paper, we propose a novel Continuous Time based Neural Cognitive Modeling(CT-NCM) approach to integrate the dynamism and continuity of knowledge forgetting into students' learning process modeling in a realistic manner. To be specific, we first adapt the neural Hawkes process with a specially-designed learning event encoding method to model the relationship between knowledge learning and forgetting with continuous time. Then, we propose a learning function with extendable settings to jointly model the change of different knowledge states and their interactions with the exercises at each moment. In this way, CT-NCM can simultaneously predict the future knowledge state and exercise performance of students. Finally, we conduct extensive experiments on five real-world datasets with various benchmark methods. The experimental results clearly validate the effectiveness of CT-NCM and show its interpretability in terms of knowledge learning visualization.

Many link prediction algorithms regarding single-layer social networks have been proposed, and however, how to predict interlayer links in multiplex social networks is still in the initial stage. In fact, the prediction of interlayer links in multiplex networks is of great significance, which is closely related to network security, product recommendation, social network mining, and so forth. Given that many social networks are sparse and the number of the first-order common matched neighbors (CMNs) is very few, it is not sufficient to implement link prediction only based on the first-order CMNs. Moreover, many social networks have scale-free property, leading to the roles of CMNs in link prediction which are significantly different. In doing so, we propose a second-order iterative degree penalty (SOIDP) algorithm to predict interlayer links in multiplex networks, in which the information of the first- and second-order CMNs is integrally considered, as well as a degree penalty mechanism is introduced to give larger weight to the CMNs with fewer connections. In particular, to solve the problem of cumulative error in the iterative process, we demonstrate that the interlayer links can be predicted by directly calculating the matching degree matrix without iteration. Experiments on real-world networks show that the performance of SOIDP algorithm in predicting interlayer links is always better than the baseline algorithms, and the accuracy is increased 10% at least. For synthetic networks, the improvement is also very surprising when networks are rather sparse.

Compared with traditional models, semi-random epidemic network models may be more reasonable to describe the real dynamics of many epidemics. In this paper, we first investigate the optimal control problem (OCP) of semi-random epidemic networks. By using the Pontryagin's minimum principle, we obtain the optimal control strategy aimed to minimize the total epidemic incidence and control cost. We then define a centrality index which can measure average control strength of the optimal control. Based on this index, the OCP is converted into a static OCP (SOCP), whose solution is utilized to design a nonidentical constant control (NCC). NCC is suboptimal as it is optimal on a subset of the whole control set, and is determined by only the network's clustering coefficient and initial condition. We finally propose an effective targeted constant quarantine control by using this centrality index. The results uncover the relationship between the optimal control and the network's topological structure, provide a convenient method to determine suboptimal control, and present a strategy for targeted constant control. This paper can help to design effective control strategies for more general epidemic networks in the real world.

Inferring the structures and the dynamics of the complex networked systems based on time series data is a challenging problem. The existing reconstruction methods often rely on the knowledge of the dynamics on networks. In many cases, a prior knowledge of the dynamics is unknown, so it is natural to ask: is it possible to reconstruct network and estimate the dynamical processes on complex networks only rely on the observed data? In this article, we develop a framework to reconstruct the structures of networks with binary-state dynamics, in which the knowledge of the original dynamical processes is unknown. Within the reconstruction framework, the transition probabilities of binary dynamical processes are described by the Sigmoid function in logistic regression, we then apply the mean-field approximation to enable maximum likelihood estimation (MLE), which gives rise to that the network structure can be inferred by solving the linear system of equations. Meanwhile, the original dynamical processes can be simulated by estimating the parameters in the Sigmoid function. Our framework has been validated by a variety of binary dynamical processes on synthetic and empirical networks, indicating that our method can not only reveal the network structures but also estimate the dynamical processes. Moreover, the high accuracy of our method is highlighted by comparing it with the existing methods.

Community detection is an important tool to analyze hidden information such as functional module and topology structure in complex networks. Compared with traditional community detection, it is more challenging to find overlapping communities in complex networks, especially when the networks are of large scales. Among various overlapping community detection techniques, the well-known clique percolation method (CPM) has shown promising performance in terms of quality of found communities, but suffers from serious curse of dimensionality due to its high computational complexity, which makes it very unlikely to be applied to large-scale networks. To address this issue, in this paper, we propose a weak-CPM for overlapping community detection in large-scale networks. A new measure for characterizing the similarity between weak cliques is also suggested to check whether the weak cliques can be merged into a community. Experimental results on synthetic and realworld networks demonstrate the competitive performance of the proposed method over six popular overlapping community detection algorithms in terms of both computational efficiency and quality of found communities. In addition, the proposed method is also suitable for detecting large-scale networks with an unclear community structure under different levels of overlapping density and overlapping diversity, which is an important property of many real-world complex networks.