Related papers: A Note on Alternating Minimization Algorithm for t…

In this paper, a general algorithm is proposed for rate analysis and code design of linear index coding problems. Specifically a solution for minimum rank matrix completion problem over finite fields representing the linear index coding…

In this paper we consider a general matrix factorization model which covers a large class of existing models with many applications in areas such as machine learning and imaging sciences. To solve this possibly nonconvex, nonsmooth and…

In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…

We propose an iterative algorithm for low-rank matrix completion that can be interpreted as an iteratively reweighted least squares (IRLS) algorithm, a saddle-escaping smoothing Newton method or a variable metric proximal gradient method…

Matrix decomposition is ubiquitous and has applications in various fields like speech processing, data mining and image processing to name a few. Under matrix decomposition, nonnegative matrix factorization is used to decompose a…

Matrix sensing is the problem of reconstructing a low-rank matrix from a few linear measurements. In many applications such as collaborative filtering, the famous Netflix prize problem, and seismic data interpolation, there exists some…

The matrix-completion problem has attracted a lot of attention, largely as a result of the celebrated Netflix competition. Two popular approaches for solving the problem are nuclear-norm-regularized matrix approximation (Candes and Tao,…

In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint. We first establish that a class of special rank minimization problems has closed-form solutions. Using this result,…

We study the completion of approximately low rank matrices with entries missing not at random (MNAR). In the context of typical large-dimensional statistical settings, we establish a framework for the performance analysis of the nuclear…

The problem of low-rank matrix reconstruction arises in various applications in communications and signal processing. The state of the art research largely focuses on the recovery techniques that utilize affine maps satisfying the…

Mixed linear regression involves the recovery of two (or more) unknown vectors from unlabeled linear measurements; that is, where each sample comes from exactly one of the vectors, but we do not know which one. It is a classic problem, and…

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

Recent work in the matrix completion literature has shown that prior knowledge of a matrix's row and column spaces can be successfully incorporated into reconstruction programs to substantially benefit matrix recovery. This paper proposes a…

For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…

Recently, there is a revival of interest in low-rank matrix completion-based unsupervised learning through the lens of dual-graph regularization, which has significantly improved the performance of multidisciplinary machine learning tasks…

We present a random-subspace variant of cubic regularization algorithm that chooses the size of the subspace adaptively, based on the rank of the projected second derivative matrix. Iteratively, our variant only requires access to…

We analyze alternating minimization for column space recovery of a partially observed, approximately low rank matrix with a growing number of columns and a fixed budget of observations per column. In this work, we prove that if the budget…

In this paper, the problem of matrix rank minimization under affine constraints is addressed. The state-of-the-art algorithms can recover matrices with a rank much less than what is sufficient for the uniqueness of the solution of this…

This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other…

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system…