ROUTE: Robust Outlier Estimation for Low Rank Matrix Recovery

Abstract

In practice, even very high-dimensional data are typically sampled from low-dimensional subspaces but with intrusion of outliers and/or noises. Recovering the underlying structure and the pollution from the observations is key to understanding and processing such data. Besides properly modeling the low-rank structure of subspace, how to handle the pollution is core regarding the performance of recovery. Often, the observed data is posed as a superimposition of the clean data and residual, while the residual can be roughly divided into two groups, including small dense noises and gross sparse outliers. Compared with small noises, outliers more likely ruin the recovery, as they can be arbitrarily large. By considering the above, this paper designs a method for recovering the low rank matrix with robust outlier estimation, termed as ROUTE, in a unified manner. Theoretical analysis on convergence and optimality, and experimental results on both synthetic and real data are provided to demonstrate the efficacy of our proposed method and show its superiority over other state-of-the-arts.