SRF: Matrix completion based on smoothed rank function

In this paper, we address the matrix completion problem and propose a novel algorithm based on a smoothed rank func-tion (SRF) approximation. Among available algorithms like FPCA and OptSpace, there is no solution that can simulta-neously cover wide range of easy and hard problems. This new algorithm provides accurate results in almost all scena-rios with a reasonable run time. It especially has low execu-tion time in hard problems where other methods need long time to converge. Furthermore, when the rank is known in advance and is high, our method is very faster than previous methods for the same accuracy. The main idea of the algo-rithm is based on a continuous and differentiable approxi-mation of the rank function and then, using gradient projec-tion approach to minimize it. Index Terms — Matrix completion, nuclear norm