Most existing studies on knowledge graph representation learning simply characterize knowledge as entities and relations, and ignore complex relation learning and multi-associative knowledge chains. It is difficult to accurately build a subject knowledge system, which affects the generation of learning paths. Thus, we propose a structural Bidirectional Encoding-Based Representation Learning model (SBE) for disciplinary knowledge graphs. Graph data augmentation is used to characterize entities and relations as initialized vector sequences. Additionally, the model combines structured bidirectional encoding and decoding to accurately represent positional information in context and complex relationship chains. Moreover, an inference strategy is proposed based on counterfactual link generation. Experimental results demonstrate that the proposed model can enhance the accuracy of both link prediction and knowledge recommendation. Furthermore, a case study on middle school mathematics reveals that the SBE model can generate learning paths tailored to student needs and effectively improve the precision, comprehensiveness, and interpretability. 

mathematical knowledge graph representation learning, structural bidirectional encoding, counter-factual link generation, learning paths 

现有知识图谱表示学习方法大多仅将知识简单地表征为实体和关系, 忽略复杂关系学习和多关联知识链, 导致无法准确地搭建学科知识体系, 并影响学习路径的生成。针对这一问题, 提出一种基于BERT的结构化双向编码的数学知识图谱表示学习模型(SBE), 通过图数据增强, 将实体和关系表征为初始化向量序列, 结合结构化双向编码和解码, 精准地表示知识在上下文的位置信息和复杂关系链, 并提出基于反事实链路生成的推理策略。实验结果表明, 模型可提升链路预测和知识推荐的准确度。以中学数学知识为案例的分析结果表明, SBE模型可以根据学生需求生成对应的学习路径, 并能够提升数学知识学习路径的精度、完备性和可解释性。

数学知识图谱表示学习, 结构化双向编码, 反事实链路, 学习路径