QGKM: A Quantum Fidelity-Based Graph Clustering Framework for Robust Data Pattern Recognition in Education Social Networks

In the era of data-driven education, educational social networks generate large volumes of high-dimensional and complex-structured data through learner interactions, collaborative activities, and resource-sharing behaviors, posing significant challenges to traditional unsupervised learning methods. Such data often exhibit non-convex distributions, heterogeneity, and noise sensitivity, making conventional clustering approaches insufficient for capturing their intrinsic structural relationships. To address this issue, this paper proposes Quantum Fidelity-Based Graph K-Means (QGKM), a clustering framework for robust pattern recognition in educational social networks. Specifically, QGKM employs quantum state encoding to map complex educational data into a quantum state space and utilizes quantum fidelity as a similarity metric to uncover latent correlations that Euclidean distance cannot effectively capture. In addition, the incorporation of k-nearest neighbor graphs preserves the local geometric structure of learner interaction networks, while a deterministic greedy hierarchical merging strategy eliminates the instability caused by random initialization. Experimental results on seven real-world datasets demonstrate that QGKM consistently outperforms classical K-Means in clustering accuracy. The proposed framework provides an effective solution for learning pattern discovery, learner profiling, and intelligent recommendation in digital education environments.