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Related papers: Matrix Compression using the Nystro\"om Method

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In this paper, we present methods for image compression on the basis of eigenvalue decomposition of normal matrices. The proposed methods are convenient and self-explanatory, requiring fewer and easier computations as compared to some…

Multimedia · Computer Science 2015-06-30 E. Kokabifar , G. B. Loghmani , A. Latif

Randomized methods, such as the randomized SVD (singular value decomposition) and Nystr\"om approximation, are an effective way to compute low-rank approximations of large matrices. Motivated by applications to operator learning, Boull\'e…

Numerical Analysis · Mathematics 2026-02-09 Daniel Kressner , David Persson , André Uschmajew

The Nystr\"{o}m method is an effective tool to generate low-rank approximations of large matrices, and it is particularly useful for kernel-based learning. To improve the standard Nystr\"{o}m approximation, ensemble Nystr\"{o}m algorithms…

Machine Learning · Statistics 2023-02-23 Keaton Hamm , Zhaoying Lu , Wenbo Ouyang , Hao Helen Zhang

We propose new algorithms for singular value decomposition (SVD) of very large-scale matrices based on a low-rank tensor approximation technique called the tensor train (TT) format. The proposed algorithms can compute several dominant…

Numerical Analysis · Mathematics 2016-02-11 Namgil Lee , Andrzej Cichocki

Inverse Vandermonde matrix calculation is a long-standing problem to solve nonsingular linear system $Vc=b$ where the rows of a square matrix $V$ are constructed by progression of the power polynomials. It has many applications in…

Numerical Analysis · Mathematics 2019-09-19 Mahdi S. Hosseini , Alfred Chen , Konstantinos N. Plataniotis

The Nystr\"om method offers an effective way to obtain low-rank approximation of SPD matrices, and has been recently extended and analyzed to nonsymmetric matrices (leading to the generalized Nystr\"om method). It is a randomized,…

Numerical Analysis · Mathematics 2024-04-24 Alberto Bucci , Leonardo Robol

We propose a new algorithm for the computation of a singular value decomposition (SVD) low-rank approximation of a matrix in the Matrix Product Operator (MPO) format, also called the Tensor Train Matrix format. Our tensor network randomized…

Numerical Analysis · Mathematics 2017-07-26 Kim Batselier , Wenjian Yu , Luca Daniel , Ngai Wong

The higher-order generalized singular value decomposition (HO-GSVD) is a matrix factorization technique that extends the GSVD to $N \ge 2$ data matrices, and can be used to identify shared subspaces in multiple large-scale datasets with…

Numerical Analysis · Mathematics 2022-06-22 Idris Kempf , Paul J. Goulart , Stephen R. Duncan

Memristor crossbars enable vector-matrix multiplication (VMM), and are promising for low-power applications. However, it can be difficult to write the memristor conductance values exactly. To improve the accuracy of VMM, we propose a scheme…

Signal Processing · Electrical Eng. & Systems 2025-10-07 Binyu Lu , Matthias Frey , Stark Draper , Jingge Zhu

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…

Machine Learning · Computer Science 2013-10-02 Shusen Wang , Zhihua Zhang

Matrix rank minimization (RM) problems recently gained extensive attention due to numerous applications in machine learning, system identification and graphical models. In RM problem, one aims to find the matrix with the lowest rank that…

Information Theory · Computer Science 2011-02-22 Amin Khajehnejad , Samet Oymak , Babak Hassibi

Singular value decomposition (SVD) is one of the most popular compression methods that approximate a target matrix with smaller matrices. However, standard SVD treats the parameters within the matrix with equal importance, which is a simple…

Computation and Language · Computer Science 2022-12-19 Ting Hua , Yen-Chang Hsu , Felicity Wang , Qian Lou , Yilin Shen , Hongxia Jin

Symmetric positive semi-definite (SPSD) matrix approximation methods have been extensively used to speed up large-scale eigenvalue computation and kernel learning methods. The standard sketch based method, which we call the prototype model,…

Machine Learning · Computer Science 2016-12-13 Shusen Wang , Zhihua Zhang , Tong Zhang

The singular value decomposition (SVD) of a matrix is a powerful tool for many matrix computation problems. In this paper, we consider generalizing the standard SVD to analyze and compute the regularized solution of linear ill-posed…

Numerical Analysis · Mathematics 2023-12-19 Haibo Li

In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for…

Information Theory · Computer Science 2013-11-01 Zemin Zhang , Gregory Ely , Shuchin Aeron , Ning Hao , Misha Kilmer

There are two problems need to be dealt with for Non-negative Matrix Factorization (NMF): choose a suitable rank of the factorization and provide a good initialization method for NMF algorithms. This paper aims to solve these two problems…

Machine Learning · Computer Science 2014-10-13 Hanli Qiao

Singular value decomposition (SVD) is a standard matrix factorization technique that produces optimal low-rank approximations of matrices. It has diverse applications, including machine learning, data science and signal processing. However,…

Mathematical Software · Computer Science 2019-07-16 Vadim Demchik , Miroslav Bačák , Stefan Bordag

We extend the randomized singular value decomposition (SVD) algorithm \citep{Halko2011finding} to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory. With no loss in the accuracy of the…

Machine Learning · Statistics 2019-12-02 Ali Basirat

The Nystr\"om method is a popular choice for finding a low-rank approximation to a symmetric positive semi-definite matrix. The method can fail when applied to symmetric indefinite matrices, for which the error can be unboundedly large. In…

Numerical Analysis · Mathematics 2023-10-10 Taejun Park , Yuji Nakatsukasa

In deep learning inference, model parameters are pruned and quantized to reduce the model size. Compression methods and common subexpression (CSE) elimination algorithms are applied on sparse constant matrices to deploy the models on…

Machine Learning · Computer Science 2023-03-29 Emre Bilgili , Arda Yurdakul