FGC_SS: Fast Graph Clustering Method by Joint Spectral Embedding and Improved Spectral Rotation

Spectral clustering, one of the most popular clustering methods, has attracted considerable attention in many fields owing to its excellent empirical properties. However, previously developed solutions to spectral clustering problems consist of two successive steps: (1) performing spectral embedding and eigendecomposition to obtain relaxed partition matrix; (2) performing k-means or spectral rotation to obtain the final binary indicator matrix. However, these two steps may miss a co-optimal solution, leading to unreasonable results. Furthermore, the implementation of eigendecomposition is significantly time-consuming and requires a computational complexity of 0(n³). To address these issues, in this study, we propose a new framework for jointly performing spectral embedding and improving spectral rotation using an anchor-based acceleration strategy. In addition, we replace the spectral rotation term with a more mathematically rigorous form. To effectively solve the proposed model, we iteratively use the generalized power iteration method and the improved version of the coordinate descent method to solve our unified framework directly. Extensive experimental results on real benchmark datasets validate the effectiveness of the proposed algorithm compared with other state-of-the-art spectral-based methods. The proposed algorithm achieves the best performance on six-eighths of small-scale datasets, five-sixths of large-scale datasets, and three-fourths of high-dimensional datasets, while maintaining superior implementation efficiency.