相关论文: Low Rank Pure Quaternion Approximation for Pure Qu…

For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by rank-1 matrices, the matrices can be obtained…

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often…

Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and related low-rank approximation techniques. QR with Column Pivoting (QRCP) is usually…

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…

Low rank approximation of a matrix (hereafter LRA) is a highly important area of Numerical Linear and Multilinear Algebra and Data Mining and Analysis. One can operate with an LRA at sublinear cost -- by using much fewer memory cells and…

Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g.,…

X-ray phase-contrast imaging has the potential to improve image contrast with lower dose by probing an object's refractive properties as well as its absorptive properties. To reconstruct a phase-contrast image from a raw dataset, a phase…

By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…

Matrix completion, i.e., the exact and provable recovery of a low-rank matrix from a small subset of its elements, is currently only known to be possible if the matrix satisfies a restrictive structural constraint---known as {\em…

Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In…

This paper describes a new algorithm for computing Nonnegative Low Rank Matrix (NLRM) approximation for nonnegative matrices. Our approach is completely different from classical nonnegative matrix factorization (NMF) which has been studied…

Low-rank approximation is a technique to approximate a tensor or a matrix with a reduced rank to reduce the memory required and computational cost for simulation. Its broad applications include dimension reduction, signal processing,…

Low-rank matrix approximations play a fundamental role in numerical linear algebra and signal processing applications. This paper introduces a novel rank-revealing matrix decomposition algorithm termed Compressed Randomized UTV (CoR-UTV)…

For the antisymmetric tensors the paper examines a low-rank approximation which is represented via only three vectors. We describe a suitable low-rank format and propose an alternating least squares structure-preserving algorithm for…

We consider the problem of approximating an affinely structured matrix, for example a Hankel matrix, by a low-rank matrix with the same structure. This problem occurs in system identification, signal processing and computer algebra, among…

We introduce a structured low rank matrix completion algorithm to recover a series of images from their under-sampled measurements, where the signal along the parameter dimension at every pixel is described by a linear combination of…

This paper describes the passage of light through a system of waveplates mathematically in terms of quaternions, an extension of the complex numbers, instead of the more usual Jones vectors and Jones matrices. Both the light beam and the…

Low-Rank Representation (LRR) is arguably one of the most powerful paradigms for Multi-view spectral clustering, which elegantly encodes the multi-view local graph/manifold structures into an intrinsic low-rank self-expressive data…

Low-rank matrix approximation plays an important role in various applications such as image processing, signal processing and data analysis. The existing methods require a guess of the ranks of matrices that represent images or involve…