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Given multiple time series data, how can we efficiently find latent patterns in an arbitrary time range? Singular value decomposition (SVD) is a crucial tool to discover hidden factors in multiple time series data, and has been used in many…

Numerical Analysis · Computer Science 2018-12-21 Jun-Gi Jang , Dongjin Choi , Jinhong Jung , U Kang

This paper discusses clustering and latent semantic indexing (LSI) aspects of the singular value decomposition (SVD). The purpose of this paper is twofold. The first is to give an explanation on how and why the singular vectors can be used…

Machine Learning · Computer Science 2012-11-19 Andri Mirzal

The Randomized Singular Value Decomposition (RSVD) is a widely used algorithm for efficiently computing low-rank approximations of large matrices, without the need to construct a full-blown SVD. Of interest, of course, is the approximation…

Numerical Analysis · Mathematics 2025-10-09 Danil Akhtiamov , Reza Ghane , Babak Hassibi

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

Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although…

Quantum Physics · Physics 2021-06-30 Xin Wang , Zhixin Song , Youle Wang

Singular value decompositions of matrices are widely used in numerical linear algebra with many applications. In this paper, we extend the notion of singular value decompositions to finite complexes of real vector spaces. We provide two…

Singular Value Decomposition (SVD) has recently emerged as a new paradigm for processing different types of images. SVD is an attractive algebraic transform for image processing applications. The paper proposes an experimental survey for…

Computer Vision and Pattern Recognition · Computer Science 2012-12-03 Rowayda A. Sadek

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

Efficiently computing a subset of a correlation matrix consisting of values above a specified threshold is important to many practical applications. Real-world problems in genomics, machine learning, finance other applications can produce…

Computation · Statistics 2016-03-15 James Baglama , Michael Kane , Bryan Lewis , Alex Poliakov

The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential…

Numerical Analysis · Mathematics 2020-02-10 Arvind K. Saibaba , Joseph Hart , Bart van Bloemen Waanders

We examine holographic renormalization by the singular value decomposition (SVD) of matrix data generated by the Monte Carlo snapshot of the 2D classical Ising model at criticality. To take the continuous limit of the SVD enables us to find…

Statistical Mechanics · Physics 2016-11-03 Hiroaki Matsueda

In high-dimensional data processing and data analysis related to dual quaternion statistics, generalized singular value decomposition (GSVD) of a dual quaternion matrix pair is an essential numerical linear algebra tool for an elegant…

Numerical Analysis · Mathematics 2025-11-05 Sitao Ling , Wenxuan Ma , Musheng Wei

Filtering based on Singular Value Decomposition (SVD) provides substantial separation of clutter, flow and noise in high frame rate ultrasound flow imaging. The use of SVD as a clutter filter has greatly improved techniques such as vector…

Singular Value Decomposition (SVD) has become an important technique for reducing the computational burden of Vision Language Models (VLMs), which play a central role in tasks such as image captioning and visual question answering. Although…

Computer Vision and Pattern Recognition · Computer Science 2026-04-06 Haiyu Wang , Yutong Wang , Jack Jiang , Sai Qian Zhang

This chapter describes gene expression analysis by Singular Value Decomposition (SVD), emphasizing initial characterization of the data. We describe SVD methods for visualization of gene expression data, representation of the data using a…

Biological Physics · Physics 2007-05-23 Michael E. Wall , Andreas Rechtsteiner , Luis M. Rocha

The traditional method of computing singular value decomposition (SVD) of a data matrix is based on a least squares principle, thus, is very sensitive to the presence of outliers. Hence the resulting inferences across different applications…

Statistics Theory · Mathematics 2024-09-17 Subhrajyoty Roy , Abhik Ghosh , Ayanendranath Basu

We present a simple yet novel parameterized form of linear mapping to achieves remarkable network compression performance: a pseudo SVD called Ternary SVD (TSVD). Unlike vanilla SVD, TSVD limits the $U$ and $V$ matrices in SVD to ternary…

Machine Learning · Computer Science 2023-08-16 Boyu Chen , Hanxuan Chen , Jiao He , Fengyu Sun , Shangling Jui

We evaluate performance of associative memory in a neural network by based on the singular value decomposition (SVD) of image data stored in the network. We consider the situation in which the original image and its highly coarse-grained…

Statistical Mechanics · Physics 2017-03-08 Tatsuya Kumamoto , Mao Suzuki , Hiroaki Matsueda

Quantum-inspired singular value decomposition (SVD) is a technique to perform SVD in logarithmic time with respect to the dimension of a matrix, given access to the matrix embedded in a segment-tree data structure. The speedup is possible…

Quantum Physics · Physics 2022-09-27 Iori Takeda , Souichi Takahira , Kosuke Mitarai , Keisuke Fujii

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