Online completion of Ill-conditioned low-rank matrices

We consider the problem of online completion of ill-conditioned low-rank matrices. While many matrix completion algorithms have been proposed recently, they often struggle with ill-conditioned matrices and take a long time to converge. In this paper, we present a new algorithm called Polar Incremental Matrix Completion (PIMC) to address this problem. Our method is based on the GROUSE algorithm, and we show how a polar decomposition can be used to maintain an estimate of the singular value matrix to better deal with ill-conditioned problems. The method is also online, allowing it to be applied to streaming data. We evaluate our algorithm on both synthetic data and a real "structure from motion" dataset from the computer vision community, and show that PIMC outperforms similar methods.