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In this paper we propose an approach to approximate a truncated singular value decomposition of a large structured matrix. By first decomposing the matrix into a sum of Kronecker products, our approach can be used to approximate a large…

Numerical Analysis · Mathematics 2018-04-03 Clarissa Garvey , Chang Meng , James G. Nagy

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

Distributions measured in high energy physics experiments are usually distorted and/or transformed by various detector effects. A regularization method for unfolding these distributions is re-formulated in terms of the Singular Value…

High Energy Physics - Phenomenology · Physics 2008-11-26 Andreas Hoecker , Vakhtang Kartvelishvili

Singular Value Decomposition (SVD) is a powerful tool in linear algebra.We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The paper illustrates nonlinear SVD…

Chaotic Dynamics · Physics 2009-02-11 Prabhakar G. Vaidya , Sajini Anand P. S , Nithin Nagaraj

The signal resulting from magnetic resonance spectroscopy is occupied by noises and irregularities so in the further analysis preprocessing techniques have to be introduced. The main idea of the paper is to develop a model of a signal as a…

Signal Processing · Electrical Eng. & Systems 2021-03-30 Michał Staniszewski , Andrzej Polański

Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness…

Machine Learning · Computer Science 2017-04-20 Miaoyan Wang , Yun S. Song

In this paper, we present a class of high order methods to approximate the singular value decomposition of a given complex matrix (SVD). To the best of our knowledge, only methods up to order three appear in the the literature. A first part…

Numerical Analysis · Mathematics 2023-09-13 Diego Armentano , Jean-Claude Yakoubsohn

We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…

Numerical Analysis · Mathematics 2024-07-25 Mengyu Wang , Jingchun Zhou , Hanyu Li

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

An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed…

Numerical Analysis · Computer Science 2018-08-15 Maboud F. Kaloorazi , Rodrigo C. de Lamare

We address the reduction to compact band forms, via unitary similarity transformations, for the solution of symmetric eigenvalue problems and the computation of the singular value decomposition (SVD). Concretely, in the first case we…

Mathematical Software · Computer Science 2017-11-07 Rafael Rodríguez-Sánchez , Sandra Catalán , José R. Herrero , Enrique S. Quintana-Ortí , Andrés E. Tomás

SVD (singular value decomposition) is one of the basic tools of machine learning, allowing to optimize basis for a given matrix. However, sometimes we have a set of matrices $\{A_k\}_k$ instead, and would like to optimize a single common…

Machine Learning · Computer Science 2022-04-19 Jarek Duda

In signal processing and identification, generalized singular value decomposition (GSVD), related to a sequence of matrices in product/quotient form are essential numerical linear algebra tools. On behalf of the growing demand for efficient…

Numerical Analysis · Mathematics 2025-11-13 Sitao Ling , Wenxuan Ma , Musheng Wei

This paper considers the problem of updating the rank-k truncated Singular Value Decomposition (SVD) of matrices subject to the addition of new rows and/or columns over time. Such matrix problems represent an important computational kernel…

In this paper, we propose a new sampling strategy for hyperspectral signals that is based on dictionary learning and singular value decomposition (SVD). Specifically, we first learn a sparsifying dictionary from training spectral data using…

Computer Vision and Pattern Recognition · Computer Science 2015-12-04 Mingrui Yang , Frank de Hoog , Yuqi Fan , Wen Hu

Concatenating matrices is a common technique for uncovering shared structures in data through singular value decomposition (SVD) and low-rank approximations. The fundamental question arises: How does the singular value spectrum of the…

Machine Learning · Computer Science 2025-07-01 Maksym Shamrai

Recently, the singular value decomposition (SVD) was applied to standard Gaussian ensembles of Random Matrix Theory (RMT) to determine the scale invariance in the spectral fluctuations without performing any unfolding procedure. Here, SVD…

Chaotic Dynamics · Physics 2018-08-10 G. Torres Vargas , R. Fossion , J. A. Méndez-Bermúdez , J. C. López Vieyra

In this paper, we introduce the applications of third-order reduced biquaternion tensors in color video processing. We first develop algorithms for computing the singular value decomposition (SVD) of a third-order reduced biquaternion…

Numerical Analysis · Mathematics 2024-11-21 Cui-E Yu , Xin Liu , Yang Zhang

Singular value decomposition is widely used in modal analysis, such as proper orthogonal decomposition and resolvent analysis, to extract key features from complex problems. SVD derivatives need to be computed efficiently to enable the…

Numerical Analysis · Mathematics 2025-05-29 Rohit Kanchi , Sicheng He

Analyzing complex experimental data with multiple parameters is challenging. We propose using Singular Value Decomposition (SVD) as an effective solution. This method, demonstrated through real experimental data analysis, surpasses…

Data Analysis, Statistics and Probability · Physics 2024-07-24 Judith F. Stein , Aviad Frydman , Richard Berkovits