Related papers: A random algorithm for low-rank decomposition of l…
We study the problem of estimating a low-rank positive semidefinite (PSD) matrix from a set of rank-one measurements using sensing vectors composed of i.i.d. standard Gaussian entries, which are possibly corrupted by arbitrary outliers.…
The Singular Value Decomposition is a matrix decomposition technique widely used in the analysis of multivariate data, such as complex space-time images obtained in both physical and biological systems. In this paper, we examine the…
Digital image inpainting is an interpolation problem, inferring the content in the missing (unknown) region to agree with the known region data such that the interpolated result fulfills some prior knowledge. Low-rank and nonlocal…
We present a novel method for matrix completion, specifically designed for matrices where one dimension is significantly larger than the other. Our Columns Selected Matrix Completion (CSMC) method combines Column Subset Selection with…
Low-rank representation~(LRR) has been a significant method for segmenting data that are generated from a union of subspaces. It is, however, known that solving the LRR program is challenging in terms of time complexity and memory…
In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional first-order methods depend on the eigenvalue decomposition at…
On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…
Let $A$ be an $m \times n$ matrix with rank $r$ and spectral decomposition $A = \sum_{i=1}^r \sigma_i u_i v_i^\top,$ where $\sigma_i$ are its singular values, ordered decreasingly, and $u_i, v_i$ are the corresponding left and right…
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…
Extracting a small subset of representative tuples from a large database is an important task in multi-criteria decision making. The regret-minimizing set (RMS) problem is recently proposed for representative discovery from databases.…
The advancements of hardware technology in recent years has brought many possibilities for low-precision applications. However, the use of low precision can introduce significant computational errors, posing a considerable challenge to…
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…
This paper introduces a new framework of fast and efficient sensing matrices for practical compressive sensing, called Structurally Random Matrix (SRM). In the proposed framework, we pre-randomize a sensing signal by scrambling its samples…
This tutorial provides an introduction to the development of fast matrix algorithms based on the notions of displacement and various low-rank structures.
We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…
A Gaussian elimination algorithm is presented that reveals the numerical rank of a matrix by yielding small entries in the Schur complement. The algorithm uses the maximum volume concept to find a square nonsingular submatrix of maximum…
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…
Subspace segmentation assumes that data comes from the union of different subspaces and the purpose of segmentation is to partition the data into the corresponding subspace. Low-rank representation (LRR) is a classic spectral-type method…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…