Abstract To monitor clients potentially bypassing position limits, business units employ the disjoint sets principle to identify potential client correlations based on account profiles. The key challenge lies in computing disjoint sets for large-scale topological graphs (with millions of nodes and billions of edges) in a short response time. In this article, we propose a multi-DAG indexing algorithm, namely the Hierarchical Isomerism Distributed Equivalent (HIDE) union find. First, in large-scale topological graphs, we utilize two new topological structures: the equivalent sub-Directed Acyclic Graph (sub-DAG) and the hierarchical isomerism topological graph, to reduce the number of edges and nodes in the multi-DAG indexing merging process. Then, our HIDE union find is proposed to achieve computable splitting across temporal and spatial spans. HIDE union find is theoretically proven to ensure correctness and universality. Experimental validation demonstrates that HIDE union find outperforms previous methods in large-scale topological graphs. The results indicate that HIDE union find achieves response times 100 to 200 times faster than those of the current leading methods.

Recommendation systems have become an indispensable part of daily life. Social recommendation systems, which utilize social relationships and past behaviors to infer users’ preferences, have gained popularity in recent years. Exploring the inherent characteristics implied by higher-order relationships offers a new approach to social recommendation. However, it is challenging due to sparse social networks, influence heterogeneity, and noisy feedback. In this article, we propose a Heterogeneous Meta-path Graph Learning model for Higher-order Social Recommendation (HEAL). Within HEAL, we introduce a heterogeneous graph in social recommendation and utilize a meta-path-guided random walk to generate higher-order relationships. By encoding higher-order structures and semantics along different meta-graphs, HEAL can mitigate the limitation of data sparsity. Moreover, HEAL exploits aspect-aware and semantic-aware attentions to adaptively propagate and aggregate useful features from different meta-neighbors and higher-order relations. These attention-based aggregation layers allow HEAL to suppress the heterogeneity of social influences. Furthermore, HEAL adopts contrastive learning as a supplemental task to the recommendation task by maximizing the consistency between the self-discriminating objectives. This auxiliary task enables the model to learn more differentiated representations, further reducing its sensitivity to noisy feedback. We evaluate the performance of HEAL through extensive experiments on public datasets. The results demonstrate that leveraging higher-order relations can enhance the quality of social recommendations by better capturing the complexity and diversity of users’ preferences and interactions.

Temporal link prediction (TLP) is among the most important graph learning tasks, capable of predicting dynamic, time-varying links within networks. The key problem of TLP is how to explore potential link-evolving tendency from the increasing number of links over time. There exist three major challenges toward solving this problem: temporal nonlinear sparsity, weak serial correlation, and discontinuous structural dynamics. In this article, we propose a novel transfer learning model, called DNformer, to predict temporal link sequence in dynamic networks. The structural dynamic evolution is sequenced into consecutive links one by one over time to inhibit temporal nonlinear sparsity. The self-attention of the model is used to capture the serial correlation between the input and output link sequences. Moreover, our structural encoding is designed to obtain changing structures from the consecutive links and to learn the mapping between link sequences. This structural encoding consists of two parts: the node clustering encoding of each link and the link similarity encoding between links. These encodings enable the model to perceive the importance and correlation of links. Furthermore, we introduce a measurement of structural similarity in the loss function for the structural differences of link sequences. The experimental results demonstrate that our model outperforms other state-of-the-art TLP methods such as Transformer, TGAT, and EvolveGCN. It achieves the three highest AUC and four highest precision scores in five different representative dynamic networks problems.

Detecting self-organized coalitions from functional networks is one of the most important ways to uncover functional mechanisms in the brain. Determining these raises well-known technical challenges in terms of scale imbalance, outliers and hard-examples. In this article, we propose a novel self-adaptive skeleton approach to detect coalitions through an approximation method based on probabilistic mixture models. The nodes in the networks are characterized in terms of robust k -order complete subgraphs ( k -clique ) as essential substructures. The k -clique enumeration algorithm quickly enumerates all k -cliques in a parallel manner for a given network. Then, the cliques, from max -clique down to min -clique, of each order k , are hierarchically embedded into a probabilistic mixture model. They are self-adapted to the corresponding structure density of coalitions in the brain functional networks through different order k . All the cliques are merged and evolved into robust skeletons to sustain each unbalanced coalition by eliminating outliers and separating overlaps. We call this the k -CLIque Merging Evolution (CLIME) algorithm. The experimental results illustrate that the proposed approaches are robust to density variation and coalition mixture and can enable the effective detection of coalitions from real brain functional networks. There exist potential cognitive functional relations between the regions of interest in the coalitions revealed by our methods, which suggests the approach can be usefully applied in neuroscientific studies.

Missing value (MV) imputation is a critical preprocessing means for data mining. Nevertheless, existing MV imputation methods are mostly designed for batch processing, and thus are not applicable to streaming data, especially those with poor quality. In this article, we propose a framework, called Real-time and Error-tolerant Missing vAlue ImputatioN (REMAIN), to impute MVs in poor-quality streaming data. Instead of imputing MVs based on all the observed data, REMAIN first initializes the MV imputation model based on a-RANSAC which is capable of detecting and rejecting anomalies in an efficient manner, and then incrementally updates the model parameters upon the arrival of new data to support real-time MV imputation. As the correlations among attributes of the data may change over time in unforseenable ways, we devise a deterioration detection mechanism to capture the deterioration of the imputation model to further improve the imputation accuracy. Finally, we conduct an extensive evaluation on the proposed algorithms using real-world and synthetic datasets. Experimental results demonstrate that REMAIN achieves significantly higher imputation accuracy over existing solutions. Meanwhile, REMAIN improves up to one order of magnitude in time cost compared with existing approaches.