相关论文: New Results on CGR/CUR Approximation of a Matrix

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

Low Rank Approximation is among most fundamental subjects of numerical linear algebra having important applications to various areas of modern computing and %they range from machine learning theory and %neural networks to data mining and…

We study superfast algorithms that computes low rank approximation of a matrix (hereafter referred to as LRA) that use much fewer memory cells and arithmetic operations than the input matrix has entries. We first specify a family of 2mn…

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…

CUR matrix decomposition is a randomized algorithm that can efficiently compute the low rank approximation for a given rectangle matrix. One limitation with the existing CUR algorithms is that they require an access to the full matrix A for…

Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…

Many data analysis applications deal with large matrices and involve approximating the matrix using a small number of ``components.'' Typically, these components are linear combinations of the rows and columns of the matrix, and are thus…

CUR matrix decomposition computes the low rank approximation of a given matrix by using the actual rows and columns of the matrix. It has been a very useful tool for handling large matrices. One limitation with the existing algorithms for…

The CUR decomposition is a technique for low-rank approximation that selects small subsets of the columns and rows of a given matrix to use as bases for its column and rowspaces. It has recently attracted much interest, as it has several…

A low-rank approximation of a parameter-dependent matrix $A(t)$ is an important task in the computational sciences appearing for example in dynamical systems and compression of a series of images. In this work, we introduce AdaCUR, an…

This paper proposes a scalable binary CUR low-rank approximation algorithm that leverages parallel selection of representative rows and columns within a deterministic framework. By employing a blockwise adaptive cross approximation…

The computation of accurate low-rank matrix approximations is central to improving the scalability of various techniques in machine learning, uncertainty quantification, and control. Traditionally, low-rank approximations are constructed…

Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…

The CUR matrix decomposition is an important extension of Nystr\"{o}m approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR…

Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…

Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…

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

A matrix algorithm runs superfast (aka at sublinear cost) if it involves much fewer flops and memory cells than an input matrix has entries. Big Data are frequently represented by matrices of immense sizes that cannot be handled directly…

Certain classes of CUR algorithms, also referred to as cross or pseudoskeleton algorithms, are widely used for low-rank matrix approximation when direct access to all matrix entries is costly. Their key advantage lies in constructing a…

This article discusses a useful tool in dimensionality reduction and low-rank matrix approximation called the CUR decomposition. Various viewpoints of this method in the literature are synergized and are compared and contrasted; included in…