Fast optimization of spectral embedding and improved spectral rotation

Abstract

Spectral clustering is a vital clustering method and has been widely applied for data analysis and pattern reorganization. A routine of solving spectral clustering problem consists of two successive stages: (1) solving a relaxed continuous optimization problem to obtain a real-valued indicator solution (2) transform the real-valued indicator into a 0-1 discrete one as the final clustering result. However, we may lose the optimal solution with such a two-stage process. Besides, the spectral clustering has a high time complexity which limits the analysis of large-scale data. To alleviate these problems, this paper proposes an efficient spectral clustering framework that computes spectral embedding and improved spectral rotation simultaneously (SE-ISR). In addition, we also provide a parameter-free method (SE-ISR-PF) to automatically choose the trade-off parameter. Furthermore, with an anchor-based similarity matrix construction, it is scalable to large-scale data. An effective algorithm with a strict convergence proof is provided to solve the corresponding optimization problem. Experimental results on several benchmark datasets demonstrate that the proposed algorithm outperforms the state-of-art methods.