Hongle Du

Whether learners can correctly complete exercises is influenced by multiple factors, including their mastery of relevant knowledge concepts and the interdependencies among these concepts. To investigate how the structure of the knowledge space—particularly the complex relationships among learners, exercises, and knowledge points—affects learning outcomes, this study proposes the Hierarchical Heterogeneous Graph Knowledge Tracing model (HHGKT). A hierarchical heterogeneous graph was constructed to capture two types of interactions—“learner–knowledge concept” and “exercise–knowledge concept”—and incorporate the interdependencies among knowledge concepts into the graph structure. By leveraging this hierarchical representation, the model’s ability to characterize learners and exercises was enhanced. A hierarchical heterogeneous graph encompassing users, exercises, and knowledge concepts was built based on the ASSISTments dataset, and simulation experiments were conducted. The results indicate that the proposed structure effectively represents the complexity of the knowledge space. Incorporating knowledge concept interdependencies improves prediction accuracy by 1.79%, while the hierarchical heterogeneous graph outperforms traditional bipartite graphs by approximately 1.5 percentage points in accuracy. These findings demonstrate that the model better integrates node and relational information, offering valuable insights for knowledge space modeling and its application in educational contexts.

The knowledge space theory can better understand the knowledge concept and its internal connection by analyzing and understanding the connection and combination of knowledge concepts. A personalized learning resource recommendation framework based on knowledge space theory is designed to help students better understand and master subject knowledge in this paper. The framework mainly includes the following three steps: firstly, analyze the students' learning behavior, and establish the student knowledge space model; secondly, establish the subject knowledge space model by analyzing the structure and relationship of subject knowledge; finally, according to the student's The knowledge space model and subject knowledge space model design personalized learning resource recommendation algorithms to provide students with the most suitable learning resources. Experiments are conducted to verify the validity and feasibility of the framework, as well as its impact on student learning outcomes.

Under the imbalanced dataset, the performance of the base-classifier, the computingmethod of weight of base-classifier and the selection method of the base-classifier have a great impact on the performance of the ensemble classifier. In order to solve above problem toimprove the generalization performance of ensemble classifier, a selective ensemble learning algorithm based on cluster under-sampling for imbalanced dataset is proposed. First, the proposed algorithm calculates the number K of under-sampling samples according to the relationship between class sample density. Then, we use the improved K-means clustering algorithm to under-sample the majority class samples and obtain K cluster centers. Then, all cluster centers (or the sample of the nearest cluster center) are regarded as new majority samples to construct a new balanced training subset combine with the minority class’s samples. Repeat those processes to generate multiple training subsets and get multiple base-classifiers. However, with the increasing of iterations, the number of base-classifiers increase, and the similarity among the base-classifiers will also increase. Therefore, it is necessary to select some base-classifier with good classification performance and large difference for ensemble. In the stage of selecting base-classifiers, according to the difference and performance of base-classifiers, we use the idea of maximum correlation and minimum redundancy to select base-classifiers. In the ensemble stage, G-mean or F-mean, which is selected to evaluate the classification performance of base-classifier forimbalanced dataset, is selected to compute the weight of each base-classifier, and then the weighted voting method is used for ensemble. Finally, the simulation results on the artificial dataset, UCI dataset and KDDCUP dataset show that the algorithm has good generalization performance on imbalanced dataset, especially on the dataset with high imbalance degree.

Online education has become an important part of education services. Faced with the vast online learning resources, how to provide students with personalized learning resources and achieve the goal of precise teaching is an important part of the intelligent teaching system. The premise of personalized recommendation is accurate personalized cognitive diagnosis and accurate analysis of each student's mastery of knowledge. Since cognitive diagnosis can diagnose and evaluate individual knowledge structure or cognitive process, combined with knowledge space theory, this paper designs a personalized exercise recommendation method based on cognitive diagnosis. The sequential dependency between course knowledge points has an impact on personalized exercise recommendation. Therefore, firstly, according to the knowledge space theory, the relationship graph between the knowledge concepts of the course is constructed, that is, the course knowledge topology map; Students conduct cognitive diagnosis and analyze the knowledge mastery status of each student; finally, the knowledge structure of each student is visualized on the knowledge map, and personalized test questions are recommended based on students' knowledge structure, question difficulty and course knowledge map. While improving the accuracy and reliability of the recommended test items, the interpretability of test item recommendation is guaranteed. The experimental comparison proves the accuracy and interpretability of the method in test item recommendation.