Sequential recommendation is one of the important branches of recommender system, aiming to achieve personalized recommended items for the future through the analysis and prediction of users’ ordered historical interactive behaviors. However, along with the growth of the user volume and the increasingly rich behavioral information, how to understand and disentangle the user’s interactive multi-intention effectively also poses challenges to behavior prediction and sequential recommendation. In light of these challenges, we propose a Contrastive Learning sequential recommendation method based on Multi-Intention Disentanglement (MIDCL). In our work, intentions are recognized as dynamic and diverse, and user behaviors are often driven by current multi-intentions, which means that the model needs to not only mine the most relevant implicit intention for each user, but also impair the influence from irrelevant intentions. Therefore, we choose Variational Auto-Encoder (VAE) to realize the disentanglement of users’ multi-intentions. We propose two types of contrastive learning paradigms for finding the most relevant user’s interactive intention, and maximizing the mutual information of positive sample pairs, respectively. Experimental results show that MIDCL not only has significant superiority over most existing baseline methods, but also brings a more interpretable case to the research about intention-based prediction and recommendation.

Multivariate anomaly causes interpretation provides insight into the root cause of information system anomalies, identifying the direct factors that trigger anomalies and revealing potential systemic flaws. However, current research generally focuses on two directions: on the one hand, anomaly diagnosis research for nodes with high anomaly degree; on the other hand, single‐layer anomaly causes interpretation graph construction based on explicit features capturing anomaly locations and their neighborhood structures. These approaches pay insufficient attention to the attack defense of anomaly causes interpretation graph, thereby weakening the credibility and reliability of anomaly causation interpretation. Therefore, we systematically explore the attack strategy and defense mechanism of the multivariate anomaly causes interpretation graph. Firstly, we propose an adaptive learning method for constructing a dual‐layer anomaly causes interpretation graph. The method reduces the dependence on artificial a priori assumptions by introducing an adaptive mechanism and realizes the dynamic decoupling of the spatiotemporal coupling relationships of multivariate data, thus providing a diversified perspective for the multivariate anomaly causes interpretation. Second, considering the vulnerability of the multivariate spatiotemporal correlation after decoupling and the structural characteristics of the dual‐layer anomaly causes interpretation graph, we further propose a structural protection mechanism based on dual‐layer complex networks to improve the structural robustness and resistance to the interference of anomaly causes interpretation graph. Finally, we verify the effectiveness of the proposed model by testing various attack defense scenarios such as noise attack, gradient attack, and structure attack. The experimental results show that the model in this paper can effectively defend against multiple attack methods and ensure the integrity and reliability of the anomaly causes interpretation graph.

Connectivity is one of important parameters for the fault tolerant of an interconnection network. In 1996, Fàbrega and Fiol proposed the concept of g-extra connectivity. A subset of vertices S is said to be a cutset if G−S is not connected. A cutset S is called an Rg-cutset, where g is a non-negative integer, if every component of G−S has at least g+1 vertices. If G has at least one Rg-cutset, the g-extra connectivity of G, denoted by κg(G), is then defined as the minimum cardinality over all Rg-cutsets of G. In this paper, we first obtain the exact value of g-extra connectivity for the lexicographic product of two general graphs. Next, the upper and lower sharp bounds of g-extra connectivity for the Cartesian product of two general graphs are given. In the end, we apply our results on grid graphs and 2-dimensional generalized hypercubes.

In recent years, heterogeneous graph neural networks have become the mainstream approach for handling heterogeneous graph data. However, due to the sparsity of labels, most existing methods for heterogeneous graph neural networks typically employ a semi-supervised learning approach, which has certain limitations in practical applications. To address this issue, we propose a self-supervised heterogeneous graph representation learning method, namely Multi-scale Heterogeneous Graph Contrastive Learning (MHGCL). This approach decodes encoded information from two perspectives: meta-paths and network patterns, in a multi-scale fashion. It uses a loss function that maximizes the similarity between positive pairs at different scales and minimizes the similarity between negative pairs. This encourages related nodes and edges to be close to each other in the embedding space, while unrelated nodes and edges are pushed farther apart. Experimental results demonstrate that MHGCL comprehensively captures semantic information at different scales between nodes. It exhibits excellent performance in node classification tasks, validating its effectiveness in heterogeneous graph node embedding learning.

Currently, most existing link prediction algorithms simply study the interrelationships between node pairs without considering the interaction force and the higher order relationships between node pairs. In order to find a solution to this problem, the concept of the gravitational field is introduced in this article, and then, a novel algorithmic framework is proposed from the perspective of physics. The framework is applied to the classic link prediction algorithms to effectively enhance their prediction performance. First, the node contraction method is applied to measure the node importance, and a similarity-based link prediction algorithm is used to calculate the similarity values between node pairs. Second, the importance of nodes is introduced into the gravitational field model as the mass attribute, and the similarity values between node pairs are used as a distance metric between node pairs. Thereby, a gravitational field model of the complex network from the perspective of physics is established. Finally, the edges of the undirected complex network are assigned the weights, and a weighted local random walking-based link prediction algorithm is proposed. The link prediction method is adopted to evaluate the reasonableness and practical value of the gravitational field model. Experimental results show that most link prediction algorithms using the proposed algorithmic framework have got improvement with a minimum improvement of 2% and a maximum improvement of 33%; thus, the effectiveness and feasibility of the algorithm are verified.