To underscore the significance of the interactive frequency among diverse vertices in each snapshot, prior research has extended the$k$-core of general graphs to the$(k,h)$-core of temporal graphs, in which each vertex has at least$k$neighbors and is connected by at least$h$edges to each of these neighbors. Due to the numerous combinations of$k$and$h$, the quantity of$(k,h)$-cores is substantial, which necessitates considerable time and space for querying and decomposition. As a temporal graph evolves, for instance, with edges being inserted or removed from the previous snapshot, the affected$(k,h)$-cores must also be updated to reflect the latest structure. To address these challenges, we initially develop a novel$(k,h)$-core storage index that exhibits excellent query performance while consuming linear space regarding the graph size. Subsequently, we design an efficient decomposition algorithm to extract$(k,h)$-cores from a snapshot. Following this, we offer two maintenance algorithms to manage temporal graph evolution. Finally, we validate the effectiveness of our proposed methods on actual temporal graphs. Experimental results indicate that our methods surpass existing techniques by two orders of magnitude.

How to simultaneously locate multiple global peaks and achieve certain accuracy on the found peaks are two key challenges in solving multimodal optimization problems (MMOPs). In this article, a landscape-aware differential evolution (LADE) algorithm is proposed for MMOPs, which utilizes landscape knowledge to maintain sufficient diversity and provide efficient search guidance. In detail, the landscape knowledge is efficiently utilized in the following three aspects. First, a landscape-aware peak exploration helps each individual evolve adaptively to locate a peak and simulates the regions of the found peaks according to search history to avoid an individual re-locating an already found peak. Second, a landscape-aware peak distinction distinguishes whether an individual locates a new global peak, a new local peak, or an already found peak. Accuracy refinement can thus only be conducted on the global peaks to enhance the search efficiency. Third, a landscape-aware reinitialization specifies the initial position of an individual adaptively according to the distribution and distinction of the found peaks, which helps explore more peaks. The experiments are conducted on the widely-used benchmark MMOPs and multimodal nonlinear equation system problems. Experimental results show that LADE obtains generally better or competitive performance compared with seven well-performing recent algorithms and four winner algorithms in the IEEE CEC competitions for multimodal optimization.

As a pivotal variant of multi-label classification, hierarchical text classification (HTC) faces unique challenges due to its intricate taxonomic hierarchy. Recent state-of-the-art approaches improve performance by considering both global hierarchy covering all labels and local hierarchy indicating substructure of sample-specific ground-truth labels. However, they often over-condense hierarchical information into one or several tokens, which may cause the loss of useful knowledge. Accordingly, we propose a dual classifier model with global and local hierarchies (DCGL). It adopts prompt tuning-based BERT as the backbone, where global hierarchy is integrated into the soft prompt template. And this resulting classifier branch is termed global pipeline. To mitigate information loss caused by hierarchy condensation, we introduce a parallel local hierarchy-aware classifier pipeline. This local pipeline acquires label-level classification features through text propagation on the label hierarchy and aligns these features with oracle label representations of local hierarchy via graph contrastive learning, which serve as a novel strategy for local hierarchy incorporation. Thereby, DCGL obtains more granular and targeted features and captures local hierarchy information such as label co-occurrence and local structure. Moreover, since global and local pipelines capture distinct yet complementary information, we further apply mutual knowledge distillation to bridge the gap between their output logits and facilitate mutual learning. And to better control the distillation degree, we design a dynamic temperature negatively correlated with label confidence. Comprehensive experiments demonstrate that our DCGL outperforms several representative HTC methods.

Feature selection can increase the classification accuracy and reduce the scale of feature subset, which is important in various machine learning tasks. However, there are various preferences and limitations for the usage of features in different application scenes, and thus different scenes may require different feature subsets. To this end, multimodal feature selection, which aims to simultaneously find multiple feature subsets with low overlap and promising classification accuracy, is also important but does not attract enough attention yet. Therefore, a new multimodal feature selection model is formulated and two grouping-based crowding differential evolution approaches are proposed in this paper. Mutual information is utilized to cluster features with high correlation and the two proposed grouping-based crowding differential evolution approaches incorporate a shuffle-based grouping strategy and a threshold-based grouping strategy, respectively, so as to simultaneously search for multiple low-overlap feature subsets with promising classification accuracy. Experimental results on eight widely used datasets validate the effectiveness of the proposed approaches.

Knowledge tracing (KT) refers to predicting learners’ performance in the future according to their historical learning interactions, which has become an essential task for the computer-aided education (CAE) system. Recent studies alleviate the data sparsity problem by mining higher-order information between questions and skills. However, the effect of multiple skills in the question is not distinguished, and various learning behaviors need to be better modeled. In this article, we propose a knowledge-associated embedding for the memory-aware KT (KMKT) framework. Specifically, we first construct a question-skill bipartite graph with attribute features. A knowledge-associated embedding (KAE) module is proposed to capture the distinctiveness of multiskills via the process of knowledge propagation and knowledge aggregation based on predefined knowledge-paths. Then, to simulate the memory recall phenomenon of the learners in KT, we design a memory-aware module for long short-term memory (MA-LSTM) networks. A temporal attention layer in MA-LSTM is proposed to learn the forgetting mechanism of the human brain. Finally, we introduce a learning-gain (LG) layer to obtain learners’ benefits after each exercise. Extensive experiments on four real-world datasets illustrate that our KMKT model performs better than the other baseline models, which verifies the effectiveness of our work.

Trip planning service can save the time and energy of tourists for preparing a trip and provide a more comfortable and satisfying travel experience. This paper particularly considers the planning of transportation mode between point of interests (POI) and formulates a multiobjective trip planning model to simultaneously maximize the visit time in POIs, minimize the travel time between POIs, and minimize the travel fare needed for the trip. To simulate the real-world environment, the formulated model incorporates the real-world POI and transportation data crawled from Tripadvisor and Baidu Map API, respectively. To obtain efficient trip planning schemes, a multipopulation ant colony system algorithm for trip planning, abbreviated as MACS-TP, is proposed. First, MACS-TP uses two colonies to optimize the time-related objective and fare-related objective respectively, which enhances the search efficiency. Second, an archive is employed to store the nondominated solutions found by both colonies and a new pheromone global update rule is designed based on the archive to help colonies optimize their corresponding objective sufficiently. Third, an elite learning strategy is proposed to further enhance the quality of solutions in the archive. Experimental results on a real-world dataset of Guangzhou, China illustrate the effectiveness of MACS-TP.

A$k$-core is the special cohesive subgraph where each vertex has at least$k$degree. It is widely used in graph mining applications such as community detection, visualization, and clique discovery. Because dynamic graphs frequently evolve, obtaining their$k$-cores via decomposition is inefficient. Instead, previous studies proposed various methods for updating$k$-cores based on inserted (removed) edges. Unfortunately, the parallelism of existing approaches is limited due to their theoretical constraints. To further improve the parallelism of maintenance algorithms, we refine the$k$-core maintenance theorem and propose two effective parallel methods to update$k$-cores for insertion and removal cases. Experimental results show that our methods outperform the state-of-the-art algorithms on real-world graphs by one order of magnitude.

Many recent studies of Entity Alignment (EA) use Graph Neural Networks (GNNs) to aggregate the neighborhood features of entities and achieve better performance. However, aligned entities in real Knowledge Graphs (KGs) usually have non-isomorphic neighborhood structures due to the different data sources of KGs. Therefore, it is insufficient to simply compare the global direct neighborhood of aligned entities, which may also become a variable for the EA judgment. In this paper, we propose a Relation-based Adaptive Neighborhood Matching method (RANM), which matches larger range and higher confidence neighborhoods for aligned entities based on relation matching instead of alignment seeds.RANMfirst uses alignment seeds to construct the best relation matching set, and then performs local direct neighborhood matching and feature aggregation on the candidate alignments. To obtain high-quality entity embeddings, we design a variant attention mechanism based on heterogeneous graphs, which considers the heterogeneity of relations in KGs. We also adopt a bi-directional iterative co-training to further improve the performance. Extensive experiments on three well-known datasets show our method significantly outperforms 14 state-of-the-art methods, and is 3.01-11.5% higher than the best-performing baselines in [email protected] shows high performance on the long-tailed entities and the dataset with less alignment seeds.

Summary Traditional feature‐based semantic similarity (SS) approaches exploit the Wikipedia features in term of sets. They evaluate the similarity of concepts based on the commonalities among their feature sets. However, these feature‐based approaches treat all the features equally in similarity evaluation. Therefore, they ignore the underlying statistics of the features and consequently lose the essential semantic details about them. One solution is that each feature can be assigned a specific weight using its statistics. This weight will reflect the relative importance of a feature in similarity evaluation. Therefore, in this paper, based on two statistical models, ie, information content and TFIDF, we propose some hybrid semantic similarity measurement methods. Firstly, we propose some new methods called weighting functions to compute the weights of the features and feature sets in Wikipedia. Secondly, based on the weighting functions, we propose some new weighted feature‐based SS approaches for Wikipedia concepts. Thirdly, we evaluate the proposed methods on well‐known benchmarks for English, German, French, and Spanish languages. Finally, we compare the performance of our methods with the traditional feature‐based and some state‐of‐the‐art SS approaches. The experimental evaluation shows that our weighted methods perform better than the traditional feature‐based and some state‐of‐the‐art approaches in similarity evaluation.