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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

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

Engineering simulations are usually based on complex, grid-based, or mesh-free methods for solving partial differential equations. The results of these methods cover large fields of physical quantities at very many discrete spatial…

Fluid Dynamics · Physics 2025-08-08 Eduardo Di Costanzo , Niklas Kühl , Jean-Christophe Marongiu , Thomas Rung

Singular Value Decomposition (SVD) is a technique based on linear projection theory, which has been frequently used for data analysis. It constitutes an optimal (in the sense of least squares) decomposition of a matrix in the most relevant…

Data Analysis, Statistics and Probability · Physics 2015-03-17 Pau Erola , Javier Borge-Holthoefer , Sergio Gomez , Alex Arenas

In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…

Machine Learning · Computer Science 2018-12-03 Longhao Yuan , Chao Li , Danilo Mandic , Jianting Cao , Qibin Zhao

Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in…

Machine Learning · Computer Science 2007-11-14 Peter D. Turney

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

We approximated the evaluation function for the game Tic-Tac-Toe by singular value decomposition (SVD) and investigated the effect of approximation accuracy on winning rate. We first prepared the perfect evaluation function of Tic-Tac-Toe…

Machine Learning · Computer Science 2023-03-22 Naoya Fujita , Hiroshi Watanabe

We consider Benders decomposition for solving two-stage stochastic programs with complete recourse based on finite samples of the uncertain parameters. We define the Benders cuts binding at the final optimal solution or the ones…

Optimization and Control · Mathematics 2020-10-16 Huiwen Jia , Siqian Shen

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

Matrix completion is a widely used technique for image inpainting and personalized recommender system, etc. In this work, we focus on accelerating the matrix completion using faster randomized singular value decomposition (rSVD). Firstly,…

Machine Learning · Computer Science 2018-10-17 Xu Feng , Wenjian Yu , Yaohang Li

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

To realize mmWave massive MIMO systems in practice, Beamspace MIMO with beam selection provides an attractive solution at a considerably reduced number of radio frequency (RF) chains. We propose low-complexity beam selection algorithms…

Information Theory · Computer Science 2022-07-12 Jinxing Yang , Jihong Yu , Shuai Wang , Hao Liu

In this paper we focus on the problem of completion of multidimensional arrays (also referred to as tensors) from limited sampling. Our approach is based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1]. Using this…

Machine Learning · Computer Science 2015-03-02 Zemin Zhang , Shuchin Aeron

This paper presents the modal truncation and singular value decomposition (SVD) technique as two main algorithms for dynamic model reduction of the power system. The significance and accuracy of the proposed methods are investigated with…

Systems and Control · Electrical Eng. & Systems 2020-04-17 Mohammad Khatibi , Fatemeh Rahmani , Tanushree Agarwal

Updating a truncated Singular Value Decomposition (SVD) is crucial in representation learning, especially when dealing with large-scale data matrices that continuously evolve in practical scenarios. Aligning SVD-based models with fast-paced…

Numerical Analysis · Mathematics 2024-01-19 Haoran Deng , Yang Yang , Jiahe Li , Cheng Chen , Weihao Jiang , Shiliang Pu

The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and…

Machine Learning · Computer Science 2015-10-30 Zhihua Zhang

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

This paper is devoted to studying the application of the block Krylov subspace method for approximation of the truncated tensor SVD (T-SVD). The theoretical results of the proposed randomized approach are presented. Several experimental…

Numerical Analysis · Mathematics 2026-03-25 Malihe Nobakht Kooshkghazi , Salman Ahmadi-Asl , Andre L. F. de Almeida

Gradient based optimization methods are the established state-of-the-art paradigm to study strongly entangled quantum systems in two dimensions with Projected Entangled Pair States. However, the key ingredient, the gradient itself, has…

Quantum Physics · Physics 2025-04-15 Anna Francuz , Norbert Schuch , Bram Vanhecke