Related papers: Matrix completion with deterministic pattern - a g…
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…
This paper considers the problem of completing a matrix with many missing entries under the assumption that the columns of the matrix belong to a union of multiple low-rank subspaces. This generalizes the standard low-rank matrix completion…
In this article we prove a necessary and a sufficient condition for a finite subset of the special linear group to be dominated. These conditions are purely geometric in nature, as they only involve the trace and the eigenvectors of the…
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.
In this lecture note, we discuss a fundamental concept, referred to as the {\it characteristic rank}, which suggests a general framework for characterizing the basic properties of various low-dimensional models used in signal processing.…
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in 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.,…
We give the first algorithm for Matrix Completion whose running time and sample complexity is polynomial in the rank of the unknown target matrix, linear in the dimension of the matrix, and logarithmic in the condition number of the matrix.…
This paper studies decision-making and statistical inference for two-sided matching markets via matrix completion. In contrast to the independent sampling assumed in classical matrix completion literature, the observed entries, which arise…
A very simple interpretation of matrix completion problem is introduced based on statistical models. Combined with the well-known results from missing data analysis, such interpretation indicates that matrix completion is still a valid and…
A fundamental component of modern trackers is an online learned tracking model, which is typically modeled either globally or locally. The two kinds of models perform differently in terms of effectiveness and robustness under different…
Although a unique solution is guaranteed in the Linear complementarity problem (LCP) when the matrix $\mathbf{M}$ is positive definite, practical applications often involve cases where $\mathbf{M}$ is only positive semi-definite, leading to…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…
We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters,…
The need to predict or fill-in missing data, often referred to as matrix completion, is a common challenge in today's data-driven world. Previous strategies typically assume that no structural difference between observed and missing entries…
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…
In the low-rank matrix completion (LRMC) problem, the low-rank assumption means that the columns (or rows) of the matrix to be completed are points on a low-dimensional linear algebraic variety. This paper extends this thinking to cases…
Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…
Given only a few observed entries from a low-rank matrix $X$, matrix completion is the problem of imputing the missing entries, and it formalizes a wide range of real-world settings that involve estimating missing data. However, when there…
Low-rank matrix completion is the task of recovering unknown entries of a matrix by assuming that the true matrix admits a good low-rank approximation. Sometimes additional information about the variables is known, and incorporating this…