Robust Matrix Completion with Corrupted Columns

نویسندگان

  • Yudong Chen
  • Huan Xu
  • Constantine Caramanis
  • Sujay Sanghavi
چکیده

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 number of users are so-called manipulators, and try to skew the predictions of the algorithm. Significantly, our results hold without any assumptions on the number, locations or values of the observed entries of the manipulated columns. In particular, this means that manipulators can act in a completely adversarial manner.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Robust Matrix Completion and Corrupted Columns

This paper considers the problem of matrix completion, when some number of the columns are arbitrarily corrupted. 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...

متن کامل

Nearly Optimal Robust Matrix Completion

In this paper, we consider the problem of Robust Matrix Completion (RMC) where the goal is to recover a low-rank matrix by observing a small number of its entries out of which a few can be arbitrarily corrupted. We propose a simple projected gradient descent-based method to estimate the low-rank matrix that alternately performs a projected gradient descent step and cleans up a few of the corrup...

متن کامل

Graph Matrix Completion in Presence of Outliers

Matrix completion problem has gathered a lot of attention in recent years. In the matrix completion problem, the goal is to recover a low-rank matrix from a subset of its entries. The graph matrix completion was introduced based on the fact that the relation between rows (or columns) of a matrix can be modeled as a graph structure. The graph matrix completion problem is formulated by adding the...

متن کامل

The Augmented Lagrange Multipliers Method for Matrix Completion from Corrupted Samplings with Application to Mixed Gaussian-Impulse Noise Removal

This paper studies the problem of the restoration of images corrupted by mixed Gaussian-impulse noise. In recent years, low-rank matrix reconstruction has become a research hotspot in many scientific and engineering domains such as machine learning, image processing, computer vision and bioinformatics, which mainly involves the problem of matrix completion and robust principal component analysi...

متن کامل

Pixel-level multisensor image fusion based on matrix completion and robust principal component analysis

Acquired digital images are often corrupted by a lack of camera focus, faulty illumination, or missing data. An algorithm is presented for fusion of multiple corrupted images of a scene using the lifting wavelet transform. The method employs adaptive fusion arithmetic based on matrix completion and self-adaptive regional variance estimation. Characteristics of the wavelet coefficients are used ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • CoRR

دوره abs/1102.2254  شماره 

صفحات  -

تاریخ انتشار 2011