Related papers: Consistent Collective Matrix Completion under Join…

This paper concerns the problem of matrix completion, which is to estimate a matrix from observations in a small subset of indices. We propose a calibrated spectrum elastic net method with a sum of the nuclear and Frobenius penalties and…

Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor…

Matrix completion has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. Current literature on matrix completion focuses primarily on independent sampling models under…

This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions,…

High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…

We propose a theory for matrix completion that goes beyond the low-rank structure commonly considered in the literature and applies to general matrices of low description complexity. Specifically, complexity of the sets of matrices…

This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and…

It was recently shown that low rank matrix completion theory can be employed for designing new sampling schemes in the context of MIMO radars, which can lead to the reduction of the high volume of data typically required for accurate target…

The matrix completion problem consists in reconstructing a matrix from a sample of entries, possibly observed with noise. A popular class of estimator, known as nuclear norm penalized estimators, are based on minimizing the sum of a data…

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…

Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…

We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and…

Recent theory of mapping an image into a structured low-rank Toeplitz or Hankel matrix has become an effective method to restore images. In this paper, we introduce a generalized structured low-rank algorithm to recover images from their…

In this paper, we show that the low rank matrix completion problem can be reduced to the problem of finding the rank of a certain tensor.

We present a novel method for matrix completion, specifically designed for matrices where one dimension is significantly larger than the other. Our Columns Selected Matrix Completion (CSMC) method combines Column Subset Selection with…

We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…

Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…

In this paper, we study the problem of decomposing a superposition of a low-rank matrix and a sparse matrix when a relatively few linear measurements are available. This problem arises in many data processing tasks such as aligning multiple…

In this paper, we propose a novel method for matrix completion under general non-uniform missing structures. By controlling an upper bound of a novel balancing error, we construct weights that can actively adjust for the non-uniformity in…