Fast smooth rank function approximation based on matrix tri-factorization

Recently, Smooth Rank Function (SRF) is proposed for matrix completion problem. The main idea of this algorithm is based on a continuous and differentiable approximation of the rank function. However, it need to deal with singular value decomposition of matrix in each iteration, which consumes much time for large matrix. In this paper, by utilizing the tri-factorization of matrix, a fast matrix completion method based on SRF is proposed. Then, based on our fast matrix completion method, a rank adaptive smooth rank function approximation is presented with appropriate rank estimation. We mathematically prove the convergence of the proposed method. Experimental results show that our proposed method improves the running time significantly. Furthermore, our proposed method outperforms other existing matrix completion approaches in most cases.