Optimal column-based low-rank matrix reconstruction

نویسندگان

  • Venkatesan Guruswami
  • Ali Kemal Sinop
چکیده

We prove that for any real-valued matrix X ∈ R, and positive integers r > k, there is a subset of r columns of X such that projecting X onto their span gives a

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

Local reconstruction of low-rank matrices and subspaces

We study the problem of reconstructing a low-rank matrix, where the input is an n × m matrix M over a field F and the goal is to reconstruct a (near-optimal) matrix M ′ that is lowrank and close to M under some distance function ∆. Furthermore, the reconstruction must be local, i.e., provides access to any desired entry of M ′ by reading only a few entries of the input M (ideally, independent o...

متن کامل

Low-Rank Matrix Recovery from Row-and-Column Affine Measurements

We propose and study a row-and-column affine measurement scheme for low-rank matrix recovery. Each measurement is a linear combination of elements in one row or one column of a matrix X . This setting arises naturally in applications from different domains. However, current algorithms developed for standard matrix recovery problems do not perform well in our case, hence the need for developing ...

متن کامل

A Scalable Approach to Column-Based Low-Rank Matrix Approximation

In this paper, we address the column-based low-rank matrix approximation problem using a novel parallel approach. Our approach is based on the divide-andcombine idea. We first perform column selection on submatrices of an original data matrix in parallel, and then combine the selected columns into the final output. Our approach enjoys a theoretical relative-error upper bound. In addition, our c...

متن کامل

Rank-One Matrix Completion with Automatic Rank Estimation via L1-Norm Regularization

Completing a matrix from a small subset of its entries, i.e., matrix completion, is a challenging problem arising from many real-world applications, such as machine learning and computer vision. One popular approach to solving the matrix completion problem is based on low-rank decomposition/factorization. Low-rank matrix decomposition-based methods often require a pre-specified rank, which is d...

متن کامل

Concentration-Based Guarantees for Low-Rank Matrix Reconstruction

We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank matrix reconstruction using both the trace-norm, as well as the less-studied max-norm, and present reconstruction guarantees based on existing analysis on the R...

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:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012