Fast and efficient algorithm for matrix completion via closed-form 2/3-thresholding operator - Wang, Zhi; Wang, Wendong; Wang, Jianjun; Chen, Siqi (Neurocomputing (Amsterdam), 2019)
Matrix completion is arguably one of the most studied problems in machine learning and data analysis. Inspired by the closed-form formulas for L2/3 regularization, we employ the Schatten 2/3 quasi-norm to approximate the rank of a matrix, which can provide a better approximation than traditional ways. We also establish a necessary optimal condition and propose a fixed point iterative scheme for solving L2/3 regularization problem. Through analysing the monotonicity and the accumulation point of L2/3 regularization problem, the convergence of this iteration is analysed. By discussing the optimal selection of the regularization parameter together with a fast Monte Carlo algorithm and an approximate singular value decomposition (SVD) procedure, we build a fast and efficient algorithm that solves the induced optimization problem well. Extensive experiments have been conducted and the results show that the proposed algorithm is fast, efficient and robust. Specifically, we compare the proposed algorithm with state-of-the-art matrix completion algorithms on many synthetic data and large recommendation datasets. Our proposed algorithm is able to achieve similar or better prediction performance, while being faster and more efficient than alternatives. Furthermore, we demonstrate the effectiveness of our proposed algorithm by solving image inpainting problems.