Robust Matrix Completion with Corrupted Columns

This paper considers the problem of matrix completion, when some number of the columns are arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return arbitrarily poor results, if even a single column is corrupted. What can be done if a large number, or even a constant fraction of columns are corrupted? In this paper, we study this very problem, and develop an efficient algorithm for its solution. Our results show that with a vanishing fraction of observed entries, it is nevertheless possible to succeed in performing matrix completion, even when the number of corrupted columns grows. When the number of corruptions is as high as a constant fraction of the total number of columns, we show that again exact matrix completion is possible, but in this case our algorithm requires many more – a constant fraction – of observations. One direct application comes from robust collaborative filtering. Here, some numbe...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Yudong Chen, Huan Xu, Constantine Caramanis, Sujay Sanghavi
• Keywords: Columns, Constant Fraction, CORR 2011, Education, Matrix Completion