Paper #5

Graph Clustering Research Based on Adaptive and Optimal Probabilistic Graph Learning

Lingguo Zou and Meihua Zhang

Abstract: With the continuous development of mobile internet, related data has experienced explosive growth. However, existing graph clustering methods suffer from issues such as high sensitivity to the quality of initial graph structures, the disconnect between graph construction and representation learning, and difficulty in handling graph structural noise. This research proposes a graph clustering model based on adaptive graph learning and optimal probabilistic graph learning. First, to address the limitation of static graph structures that cannot dynamically optimize based on node representations, the Adaptive Graph Clustering (AGC) model is proposed. Through a learnable adjacency matrix update mechanism, the graph structure adapts to serve the clustering objective during training. Second, to address the limitation of existing deterministic graph learning ignoring edge uncertainty, the Optimal Probabilistic Graph Clustering (OPGC) model is proposed. It models the graph structure as a Bernoulli distribution, learning edge existence probabilities through probability-weighted graph convolutions and entropy regularization, thereby explicitly quantifying structural noise. Additionally, a dual self-supervised clustering strategy is designed to simultaneously generate soft assignments from both attribute and graph spaces while minimizing Kullback-Leibler divergence from the target distribution. This unifies attribute feature learning and probabilistic graph structure learning within an end-to-end framework. The adaptive graph clustering model demonstrates outstanding performance on both structural and textual data. It achieves a maximum clustering accuracy of 80.2%, surpassing the second-best deep adaptive graph clustering by 7.8%. After removing 15% of original edges, the model's normalized mutual information decreases by only 0.044. The optimal probabilistic graph clustering model achieves a clustering accuracy of 0.852. Ablation experiments demonstrate that the adaptive graph learning module is most critical for enhancing model performance. The model converges 26.9% faster than graph attention networks and consumes 23.6% less memory. Consequently, the proposed model effectively improves graph clustering accuracy and robustness, significantly boosts computational efficiency, and simplifies complex networks.

Keywords: Adaptive graph learning; Graph clustering; Graph convolutional neural network; Optimal probability; Self-supervised learning.