Graph Clustering With Harmonic-Maxmin Cut Guidance

Graph clustering has become a crucial technique for uncovering community structures in complex network data. However, existing approaches often introduce cumbersome regularization or constraints (hyperparameter tuning burden) to obtain balanced clustering results, thereby increasing hyperparameter tuning requirements and intermediate variables. These limitations can lead to suboptimal performance, particularly in scenarios involving imbalanced clusters or large-scale datasets. Besides, most graph cut clustering methods solve two separate discrete problems, resulting in information loss and relying on time-consuming eigen-decomposition. To address these challenges, this paper propose an effective graph cut framework, termed Harmonic MaxMin Cut (HMMC), inspired by worst-case objective optimization and the harmonic mean. Unlike traditional spectral clustering, HMMC produces all cluster assignments in a single step, eliminating the need for additional discretization and notably enhancing robustness to "worst-case cluster"boundaries. this paper further devise a fast coordinate descent (CD) solver that scales linearly complexity with the graph size, offering a computationally efficient alternative to eigen decomposition. Extensive experiments on real-world datasets demonstrate that HMMC is comparable to, or even surpasses, state-of-the-art methods, while also finding more favorable local solutions than non-negative matrix factorization techniques.