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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

The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular…

Numerical Analysis · Mathematics 2021-02-02 Ningyu Sha , Lei Shi , Ming Yan

We develop a data-driven regularization method for the severely ill-posed problem of photoacoustic image reconstruction from limited view data. Our approach is based on the regularizing networks that have been recently introduced and…

Numerical Analysis · Mathematics 2024-12-20 Johannes Schwab , Stephan Antholzer , Robert Nuster , Günther Paltauf , Markus Haltmeier

Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of…

Machine Learning · Computer Science 2019-11-19 Samuele Battaglino , Erdem Koyuncu

We revisit a singular value decomposition (SVD) algorithm given in Chen et al. (2019b) for exploratory Item Factor Analysis (IFA). This algorithm estimates a multidimensional IFA model by SVD and was used to obtain a starting point for…

Methodology · Statistics 2025-01-08 Haoran Zhang , Yunxiao Chen , Xiaoou Li

A fast algorithm for solving the under-determined 3-D linear gravity inverse problem based on the randomized singular value decomposition (RSVD) is developed. The algorithm combines an iteratively reweighted approach for $L_1$-norm…

Numerical Analysis · Mathematics 2022-08-16 Saeed Vatankhah , Rosemary A. Renaut , Vahid E. Ardestani

The tensor Singular Value Decomposition (t-SVD) for third order tensors that was proposed by Kilmer and Martin~\cite{2011kilmer} has been applied successfully in many fields, such as computed tomography, facial recognition, and video…

Numerical Analysis · Mathematics 2016-09-23 Jiani Zhang , Arvind K. Saibaba , Misha Kilmer , Shuchin Aeron

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

A model-based collaborative filtering (CF) approach utilizing fast adaptive randomized singular value decomposition (SVD) is proposed for the matrix completion problem in recommender system. Firstly, a fast adaptive PCA frameworkis…

Machine Learning · Computer Science 2025-04-08 Xiangyun Ding , Wenjian Yu , Yuyang Xie , Shenghua Liu

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Data Structures and Algorithms · Computer Science 2021-06-07 Agniva Chowdhury , Petros Drineas , David P. Woodruff , Samson Zhou

Multiway data are becoming more and more common. While there are many approaches to extending principal component analysis (PCA) from usual data matrices to multiway arrays, their conceptual differences from the usual PCA, and the…

Methodology · Statistics 2023-02-15 Jialin Ouyang , Ming Yuan

The randomized singular value decomposition proposed in [27] has certainly become one of the most well-established randomization-based algorithms in numerical linear algebra. The key ingredient of the entire procedure is the computation of…

Numerical Analysis · Mathematics 2025-08-01 Davide Palitta , Sascha Portaro

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

Learning a dynamical system from input/output data is a fundamental task in the control design pipeline. In the partially observed setting there are two components to identification: parameter estimation to learn the Markov parameters, and…

Optimization and Control · Mathematics 2021-09-08 Han Wang , James Anderson

The singular value decomposition (SVD) of large-scale matrices is a key tool in data analytics and scientific computing. The rapid growth in the size of matrices further increases the need for developing efficient large-scale SVD…

Numerical Analysis · Mathematics 2016-08-31 Ting-Li Chen , Dawei D. Chang , Su-Yun Huang , Hung Chen , Chienyao Lin , Weichung Wang

Truncated Singular Value Decomposition (SVD) calculates the closest rank-$k$ approximation of a given input matrix. Selecting the appropriate rank $k$ defines a critical model order choice in most applications of SVD. To obtain a principled…

Information Theory · Computer Science 2013-01-08 Mario Frank , Joachim M. Buhmann

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

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

By singular value decomposition (SVD) of a numerically singular Hessian matrix and a numerically singular system of linear equations for the experimental data (accumulated in the respective ${\chi ^2}$ function) and constraints, least…

High Energy Physics - Phenomenology · Physics 2014-08-27 Mehrdad Goshtasbpour

Singular Value Decomposition (and Principal Component Analysis) is one of the most widely used techniques for dimensionality reduction: successful and efficiently computable, it is nevertheless plagued by a well-known, well-documented…

Machine Learning · Computer Science 2011-01-04 Huan Xu , Constantine Caramanis , Sujay Sanghavi