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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…

Machine Learning · Computer Science 2012-10-05 Shusen Wang , Zhihua Zhang , Jian Li

Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized…

Numerical Analysis · Mathematics 2019-05-20 Rachel Minster , Arvind K. Saibaba , Misha E. Kilmer

In this paper, we present a Rank Revealing Randomized Singular Value Decomposition (R3SVD) algorithm to incrementally construct a low-rank approximation of a potentially large matrix while adaptively estimating the appropriate rank that can…

Numerical Analysis · Computer Science 2016-05-27 Hao Ji , Wenjian Yu , Yaohang Li

We define the reduced biquaternion tensor ring (RBTR) decomposition and provide a detailed exposition of the corresponding algorithm RBTR-SVD. Leveraging RBTR decomposition, we propose a novel low-rank tensor completion algorithm RBTR-TV…

Commutative Algebra · Mathematics 2025-01-10 Hui Luo , Xin Liu , Wei Liu , Yang Zhang

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…

Numerical Analysis · Mathematics 2026-02-26 Taejun Park , Yuji Nakatsukasa

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…

Data Structures and Algorithms · Computer Science 2007-08-29 Petros Drineas , Michael W. Mahoney , S. Muthukrishnan

The low-rank quaternion matrix approximation has been successfully applied in many applications involving signal processing and color image processing. However, the cost of quaternion models for generating low-rank quaternion matrix…

Numerical Analysis · Mathematics 2024-03-01 Peng-Ling Wu , Kit Ian Kou , Hongmin Cai , Zhaoyuan Yu

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…

Numerical Analysis · Mathematics 2025-07-01 Weiwei Xu , Weijie Shen , Chang Liu , Zhigang Jia

The recently introduced algorithm randUTV provides a highly efficient technique for computing accurate approximations to all the singular values of a given matrix $A$. The original version of randUTV was designed to compute a full…

Numerical Analysis · Mathematics 2019-03-28 Nathan Heavner , Per-Gunnar Martinsson

Many applications in scientific computing and data science require the computation of a rank-revealing factorization of a large matrix. In many of these instances the classical algorithms for computing the singular value decomposition are…

Numerical Analysis · Mathematics 2018-12-17 Abinand Gopal , Per-Gunnar Martinsson

This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…

Numerical Analysis · Mathematics 2023-03-22 Maolin Che , Yimin Wei , Hong Yan

In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given tensor by a tensor that is sparsely representable. For matrices, i.e. 2-tensors, such a representation can be obtained…

Numerical Analysis · Mathematics 2014-12-12 Shmuel Friedland , Venu Tammali

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…

Numerical Analysis · Computer Science 2016-08-24 Linxiao Yang , Jun Fang , Hongbin Li , Bing Zeng

A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…

Numerical Analysis · Mathematics 2014-08-12 Ming Gu

This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…

Numerical Analysis · Mathematics 2019-11-28 N. Benjamin Erichson , Lionel Mathelin , Steven L. Brunton , J. Nathan Kutz

A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with the…

Numerical Analysis · Computer Science 2015-10-28 Yiguang Liu

Deep Click-Through Rate (CTR) prediction models play an important role in modern industrial recommendation scenarios. However, high memory overhead and computational costs limit their deployment in resource-constrained environments.…

Information Retrieval · Computer Science 2024-06-12 Hao Yu , Minghao Fu , Jiandong Ding , Yusheng Zhou , Jianxin Wu

The performance of Deep Neural Networks (DNNs) keeps elevating in recent years with increasing network depth and width. To enable DNNs on edge devices like mobile phones, researchers proposed several network compression methods including…

Computer Vision and Pattern Recognition · Computer Science 2020-01-27 Yuhui Xu , Yuxi Li , Shuai Zhang , Wei Wen , Botao Wang , Yingyong Qi , Yiran Chen , Weiyao Lin , Hongkai Xiong

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…

Numerical Analysis · Mathematics 2025-05-23 Kathryn Linehan , Radu Balan

Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation…

Machine Learning · Computer Science 2019-05-27 Dongsoo Lee , Se Jung Kwon , Byeongwook Kim , Gu-Yeon Wei