Related papers: Column and row subset selection using nuclear scor…
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 CUR approximation of a matrix $A$ is a particular type of low-rank approximation $A \approx C U R$, where $C$ and $R$ consist of columns and rows of $A$, respectively. One way to obtain such an approximation is to apply column subset…
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…
The CUR matrix decomposition and the Nystr\"{o}m approximation are two important low-rank matrix approximation techniques. The Nystr\"{o}m method approximates a symmetric positive semidefinite matrix in terms of a small number of its…
A common problem in large-scale data analysis is to approximate a matrix using a combination of specifically sampled rows and columns, known as CUR decomposition. Unfortunately, in many real-world environments, the ability to sample…
In this work, we analyze a sublinear-time algorithm for selecting a few rows and columns of a matrix for low-rank approximation purposes. The algorithm is based on an initial uniformly random selection of rows and columns, followed by a…
We consider the problem of matrix column subset selection, which selects a subset of columns from an input matrix such that the input can be well approximated by the span of the selected columns. Column subset selection has been applied to…
We propose a continuous optimization algorithm for the Column Subset Selection Problem (CSSP) and Nystr\"om approximation. The CSSP and Nystr\"om method construct low-rank approximations of matrices based on a predetermined subset of…
The problem of column subset selection asks for a subset of columns from an input matrix such that the matrix can be reconstructed as accurately as possible within the span of the selected columns. A natural extension is to consider a…
This article studies how to form CUR decompositions of low-rank matrices via primarily random sampling, though deterministic methods due to previous works are illustrated as well. The primary problem is to determine when a column submatrix…
We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nystr\"om approximation, where one approximates two positive semi-definite kernel matrices using "landmark" points from the…
Given a fixed matrix, the problem of column subset selection requests a column submatrix that has favorable spectral properties. Most research from the algorithms and numerical linear algebra communities focuses on a variant called…
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…
Prior optimal CUR decomposition and near optimal column reconstruction methods have been established by combining BSS sampling and adaptive sampling. In this paper, we propose a new approach to the optimal CUR decomposition and near optimal…
The singular value decomposition (SVD) is commonly used in applications requiring a low rank matrix approximation. However, the singular vectors cannot be interpreted in terms of the original data. For applications requiring this type of…
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…
We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…
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…
Dimensionality reduction is a first step of many machine learning pipelines. Two popular approaches are principal component analysis, which projects onto a small number of well chosen but non-interpretable directions, and feature selection,…
CUR and low-rank approximations are among most fundamental subjects of numerical linear algebra, with a wide range of applications to a variety of highly important areas of modern computing, which range from the machine learning theory and…