Related papers: Computational Limits for Matrix Completion
Low-rank Matrix Completion (LRMC) describes the problem where we wish to recover missing entries of partially observed low-rank matrix. Most existing matrix completion work deals with sampling procedures that are independent of the…
A symmetric matrix $C$ is completely positive (CP) if there exists an entrywise nonnegative matrix $B$ such that $C=BB^T$. The CP-completion problem is to study whether we can assign values to the missing entries of a partial matrix (i.e.,…
In this paper, we study the popularly dubbed matrix completion problem, where the task is to "fill in" the unobserved entries of a matrix from a small subset of observed entries, under the assumption that the underlying matrix is of…
Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…
A matrix network is a family of matrices, with relatedness modeled by a weighted graph. We consider the task of completing a partially observed matrix network. We assume a novel sampling scheme where a fraction of matrices might be…
This paper studies the low-rank matrix completion problem from an information theoretic perspective. The completion problem is rephrased as a communication problem of an (uncoded) low-rank matrix source over an erasure channel. The paper…
We consider the related tasks of matrix completion and matrix approximation from missing data and propose adaptive sampling procedures for both problems. We show that adaptive sampling allows one to eliminate standard incoherence…
Matrix completion (MC) is a promising technique which is able to recover an intact matrix with low-rank property from sub-sampled/incomplete data. Its application varies from computer vision, signal processing to wireless network, and…
Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we…
Many applications require recovering a matrix of minimal rank within an affine constraint set, with matrix completion a notable special case. Because the problem is NP-hard in general, it is common to replace the matrix rank with the…
Matrix rank minimization problems are gaining a plenty of recent attention in both mathematical and engineering fields. This class of problems, arising in various and across-discipline applications, is known to be NP-hard in general. In…
We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…
Most of the existing works on provable guarantees for low-rank matrix completion algorithms rely on some unrealistic assumptions such that matrix entries are sampled randomly or the sampling pattern has a specific structure. In this work,…
Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…
The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in collaborative filtering, computer vision and…
Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse…
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…
The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…
As a paradigm to recover unknown entries of a matrix from partial observations, low-rank matrix completion (LRMC) has generated a great deal of interest. Over the years, there have been lots of works on this topic but it might not be easy…
The matrix recovery (completion) problem, a central problem in data science and theoretical computer science, is to recover a matrix $A$ from a relatively small sample of entries. While such a task is impossible in general, it has been…