Minimum Description Length Principle Based Atomic Norm for Synthetic Low-Rank Matrix Recovery

Abstract

Recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers has been attracting increasing interest. However, in many low-rank problems, neither the exact rank of estimated matrix nor the particular locations as well as the values of outliers is known. The conventional methods fail to separate the low-rank and sparse component, especially gross outliers. So we exploit the advantage of minimum description length principle and atomic norm to overcome the above limitations. In this paper, we first apply atomic norm to find all the candidate atoms of low-rank and sparse term respectively, and then minimize the description length of model as well as residual, in order to select the appropriate atoms of low-rank and the sparse matrix. The experimental results based on synthetic data sets demonstrate the effectiveness of the proposed method.