Related papers: Optimal Weighted Low-rank Matrix Recovery with Sub…
We propose a new algorithm for the problem of recovering data that adheres to multiple, heterogeneous low-dimensional structures from linear observations. Focusing on data matrices that are simultaneously row-sparse and low-rank, we propose…
In many computer vision tasks, for example saliency prediction or semantic segmentation, the desired output is a foreground map that predicts pixels where some criteria is satisfied. Despite the inherently spatial nature of this task…
This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the…
The problem of recovering a matrix of low rank from an incomplete and possibly noisy set of linear measurements arises in a number of areas. In order to derive rigorous recovery results, the measurement map is usually modeled…
We propose a new iteratively reweighted least squares (IRLS) algorithm for the recovery of a matrix $X \in \mathbb{C}^{d_1\times d_2}$ of rank $r \ll\min(d_1,d_2)$ from incomplete linear observations, solving a sequence of low complexity…
Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations…
We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past. We establish that when the…
We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
Matrix factorization is a widely used approach for top-N recommendation and collaborative filtering. When implemented on implicit feedback data (such as clicks), a common heuristic is to upweight the observed interactions. This strategy has…
We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a…
Subspace identification is a classical and very well studied problem in system identification. The problem was recently posed as a convex optimization problem via the nuclear norm relaxation. Inspired by robust PCA, we extend this framework…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
Many real world datasets subsume a linear or non-linear low-rank structure in a very low-dimensional space. Unfortunately, one often has very little or no information about the geometry of the space, resulting in a highly under-determined…
This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly…
The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works…
A novel framework to construct an efficient sensing (measurement) matrix, called mixed adaptive-random (MAR) matrix, is introduced for directly acquiring a compressed image representation. The mixed sampling (sensing) procedure hybridizes…
Previous work regarding low-rank matrix recovery has concentrated on the scenarios in which the matrix is noise-free and the measurements are corrupted by noise. However, in practical application, the matrix itself is usually perturbed by…
In compressed sensing problems, $\ell_1$ minimization or Basis Pursuit was known to have the best provable phase transition performance of recoverable sparsity among polynomial-time algorithms. It is of great theoretical and practical…
The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…