Utilizing big data and artificial intelligence technologies, we developed the Collaborative Structure Search Framework (CSSF) algorithm to analyze students’ learning paths from real-world data to determine the optimal sequence of learning knowledge components. This study enhances sustainability and balance in education by identifying students’ learning paths. This allows teachers and intelligent systems to understand students’ strengths and weaknesses, thereby providing personalized teaching plans and improving educational outcomes. Identifying causal relationships within knowledge structures helps teachers pinpoint and address learning issues, forming the basis for adaptive learning systems. Using real educational datasets, the research introduces a multi-sub-population collaborative search mechanism to enhance search efficiency by maintaining individual-level superiority, population-level diversity, and solution-set simplicity across sub-populations. A bidirectional feedback mechanism is implemented to discern high-quality and low-quality edges within the knowledge graph. Oversampling high-quality edges and undersampling low-quality edges address optimization challenges in Learning Path Recognition (LPR) due to edge sparsity. The proposed Collaborative Structural Search Framework (CSSF) effectively uncovers relationships within knowledge structures. Experimental validations on real-world datasets show CSSF’s effectiveness, with a 14.41% improvement in F1-score over benchmark algorithms on a dataset of 116 knowledge structures. The algorithm helps teachers identify the root causes of students’ errors, enabling more effective educational strategies, thus enhancing educational quality and learning outcomes. Intelligent education systems can better adapt to individual student needs, providing personalized learning resources, facilitating a positive learning cycle, and promoting sustainable education development.

Graph Convolutional Networks (GCNs) demonstrate an excellent performance in node classification tasks by updating node representation via aggregating information from the neighbor nodes. Note that the complex interactions among all the nodes can produce challenges for GCNs. Independent subgraph sampling effectively limits the neighbor aggregation in convolutional computations, and it has become a popular method to improve the efficiency of training GCNs. However, there are still some improvements in the existing subgraph sampling strategies: 1) a loss of the model performance caused by ignoring the connection information among different subgraphs; and 2) a lack of representation power caused by an incomplete topology. Therefore, we propose a novel model called Dual-channel Progressive Graph Convolutional Network (DPGCN) via sub-graph sampling. We construct subgraphs via clustering and maintain the connection information among the different subgraphs. To enhance the representation power, we construct a dual channel fusion module by using both the geometric information of the node feature and the original topology. Specifically, we evaluate the complementary information of the dual channels based on the joint entropy between the feature information and the adjacency matrix, and effectively reduce the information redundancy by reasonably selecting the feature information. Then, the model convergence is accelerated through parameter sharing and weight updating in progressive training. We select 4 real datasets and 8 characteristic models for comparison on the semi-supervised node classification task. The results verify that the DPGCN possesses superior classification accuracy and robustness. In addition, the proposed architecture performs excellently in the low labeling rate, which is of practical value to label scarcity problems in real cases.

In recent years, Graph Convolutional Networks (GCNs) have emerged as a crucial methodology for handling graph-structured data, exhibiting superior performance in semi-supervised classification tasks. However, most existing GCNs encounter two main issues in real-world scenarios: 1) graph-structured data may be incomplete, for example, containing outlier nodes and noisy edges, which poses a great challenge for GCNs to extract the relation information for classification tasks; 2) the scarcity of labeled data, often limited to a few-shot scenario, hampers the ability of GCNs to learn comprehensive embedding representations. To cope with these issues, we propose a novel framework called pseudo labeling collaborative multi-channel graph convolutional networks (PCM-GCN). First, considering incomplete graph-structured data, we develop two modules: graph generation module and multi-channel fusion module. The graph generation module is designed to extend the raw data to multiple graphs, which avoids being constrained by the effective expression ability of the raw data. Meanwhile, the multi-channel fusion module integrates embeddings from multiple graphs, capturing the complementarity among multiple channels. Second, to address the problem of sparse labels, we develop a confidence-based pseudo labeling module, appending confident data with pseudo label to the labeled set to enlarge the training set. PCM-GCN leverages pseudo labeling to enhance multi-channel embedding fusion, resulting in rich and comprehensive node embedding representation. Extensive experiments on five benchmark datasets have shown that PCM-GCN surpasses other state-of-the-art methods in semi-supervised node classification tasks.