Accelerated Matrix Factorisation Method for Fuzzy Clustering

Factorised fuzzy c-means (F-FCM) based on semi nonnegative matrix factorization is a new approach for fuzzy clustering. It does not need the weighting exponent parameter compared with traditional fuzzy c-means, and not sensitive to initial conditions. However, F-FCM does not propose an efficient method to solve the constrained problem, and just suggests to use a lsqlin() function in MATLAB which lead to slow convergence rate and nonconvergence. In this paper, we propose a method to accelerate the convergence rate of F-FCM combining with a non-monotone accelerate proximal gradient (nmAPG) method. We also propose an efficient method to solve the proximal mapping problem when implementing nmAPG. Finally, the experiment results on synthetic and real-world datasets show the performances and feasibility of our method.