Related papers: Robust Rotation Synchronization via Low-rank and S…
Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…
We consider the problem of recovering an unknown low-rank matrix X with (possibly) non-orthogonal, effectively sparse rank-1 decomposition from measurements y gathered in a linear measurement process A. We propose a variational formulation…
In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used…
We consider the classic problem of establishing a statistical ranking of a set of n items given a set of inconsistent and incomplete pairwise comparisons between such items. Instantiations of this problem occur in numerous applications in…
This work presents ReSync, a Riemannian subgradient-based algorithm for solving the robust rotation synchronization problem, which arises in various engineering applications. ReSync solves a least-unsquared minimization formulation over the…
The goal of this paper is to find a low-rank approximation for a given tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP-hard problem. In this paper,…
Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…
Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to…
In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…
This paper proposes a framework for simultaneous dimensionality reduction and regression in the presence of outliers in data by applying low-rank and sparse matrix decomposition. For multivariate data corrupted with outliers, it is…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
The problem of joint direction-of-arrival estimation and distorted sensor detection has received a lot of attention in recent decades. Most state-of-the-art work formulated such a problem via low-rank and row-sparse decomposition, where the…
We present a fast randomized algorithm that computes a low rank LU decomposition. Our algorithm uses random projections type techniques to efficiently compute a low rank approximation of large matrices. The randomized LU algorithm can be…
Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable…
Clock synchronization has become a key design objective in wireless networks for its essential importance in many applications. However, as the wireless link is prone to random network delays due to unreliable channel conditions, it is in…
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…
Recently, low-rank matrix recovery theory has been emerging as a significant progress for various image processing problems. Meanwhile, the group sparse coding (GSC) theory has led to great successes in image restoration (IR) problem with…
This paper addresses the Kidnapped Robot Problem (KRP), a core localization challenge of relocalizing a robot in a known map without prior pose estimate upon localization loss or at SLAM initialization. For this purpose, a passive 2-D…
Motivated by graphical models, we consider the "Sparse Plus Low-rank" decomposition of a positive definite concentration matrix -- the inverse of the covariance matrix. This is a classical problem for which a rich theory and numerical…
Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…