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We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

Machine Learning · Computer Science 2022-02-09 John Paul Ryan , Anil Damle

Minimizing the nuclear norm of a matrix has been shown to be very efficient in reconstructing a low-rank sampled matrix. Furthermore, minimizing the sum of nuclear norms of matricizations of a tensor has been shown to be very efficient in…

Machine Learning · Statistics 2017-07-26 Morteza Ashraphijuo , Xiaodong Wang

The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, a drawback of the known approaches is that the rank parameter has to be fixed a priori. In this paper, we consider the…

Optimization and Control · Mathematics 2022-02-21 Bin Gao , P. -A. Absil

We consider a Canonical Polyadic (CP) decomposition approach to low-rank tensor completion (LRTC) by incorporating external pairwise similarity relations through graph Laplacian regularization on the CP factor matrices. The usage of graph…

Numerical Analysis · Mathematics 2023-11-14 Yu Guan , Shuyu Dong , Bin Gao , P. -A. Absil , François Glineur

We introduce an optimal strategy to sample quantum outcomes of local measurement strings for isometric tensor network states. Our method generates samples based on an exact cumulative bounding function, without prior knowledge, in the…

Quantum Physics · Physics 2025-04-23 Marco Ballarin , Pietro Silvi , Simone Montangero , Daniel Jaschke

We solve tensor balancing, rescaling an Nth order nonnegative tensor by multiplying N tensors of order N - 1 so that every fiber sums to one. This generalizes a fundamental process of matrix balancing used to compare matrices in a wide…

Methodology · Statistics 2018-10-30 Mahito Sugiyama , Hiroyuki Nakahara , Koji Tsuda

In recent studies, the tensor ring (TR) rank has shown high effectiveness in tensor completion due to its ability of capturing the intrinsic structure within high-order tensors. A recently proposed TR rank minimization method is based on…

Computer Vision and Pattern Recognition · Computer Science 2020-05-21 Meng Ding , Ting-Zhu Huang , Xi-Le Zhao , Tian-Hui Ma

We consider the problem of minimizing a sum of $n$ functions over a convex parameter set $\mathcal{C} \subset \mathbb{R}^p$ where $n\gg p\gg 1$. In this regime, algorithms which utilize sub-sampling techniques are known to be effective. In…

Machine Learning · Statistics 2015-12-03 Murat A. Erdogdu , Andrea Montanari

We propose an algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors. Our algorithm, which we call TBMC (\emph{Tiling for Binary Matrix Completion}), gives interpretable output in the…

Numerical Analysis · Mathematics 2020-06-23 Melanie Beckerleg , Andrew Thompson

We propose a sampling-based method for computing the tensor ring (TR) decomposition of a data tensor. The method uses leverage score sampled alternating least squares to fit the TR cores in an iterative fashion. By taking advantage of the…

Numerical Analysis · Mathematics 2021-07-12 Osman Asif Malik , Stephen Becker

Performance tuning, software/hardware co-design, and job scheduling are among the many tasks that rely on models to predict application performance. We propose and evaluate low-rank tensor decomposition for modeling application performance.…

Performance · Computer Science 2023-08-30 Edward Hutter , Edgar Solomonik

Low-Rank Tensor Completion, a method which exploits the inherent structure of tensors, has been studied extensively as an effective approach to tensor completion. Whilst such methods attained great success, none have systematically…

Computer Vision and Pattern Recognition · Computer Science 2024-06-19 Shiran Yuan , Kaizhu Huang

We give a new framework for solving the fundamental problem of low-rank matrix completion, i.e., approximating a rank-$r$ matrix $\mathbf{M} \in \mathbb{R}^{m \times n}$ (where $m \ge n$) from random observations. First, we provide an…

Machine Learning · Computer Science 2023-08-08 Jonathan A. Kelner , Jerry Li , Allen Liu , Aaron Sidford , Kevin Tian

Tensor decomposition is a popular technique for tensor completion, However most of the existing methods are based on linear or shallow model, when the data tensor becomes large and the observation data is very small, it is prone to over…

Numerical Analysis · Mathematics 2021-05-21 Qianxi Wu , An-Bao Xu

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…

Information Theory · Computer Science 2016-02-18 Holger Rauhut , Reinhold Schneider , Zeljka Stojanac

The low-rank tensor approximation is very promising for the compression of deep neural networks. We propose a new simple and efficient iterative approach, which alternates low-rank factorization with a smart rank selection and fine-tuning.…

Machine Learning · Computer Science 2019-11-18 Julia Gusak , Maksym Kholiavchenko , Evgeny Ponomarev , Larisa Markeeva , Ivan Oseledets , Andrzej Cichocki

Real-world spatio-temporal data is often incomplete or inaccurate due to various data loading delays. For example, a location-disease-time tensor of case counts can have multiple delayed updates of recent temporal slices for some locations…

Machine Learning · Computer Science 2021-05-13 Cheng Qian , Nikos Kargas , Cao Xiao , Lucas Glass , Nicholas Sidiropoulos , Jimeng Sun

Fabrication process variations can significantly influence the performance and yield of nano-scale electronic and photonic circuits. Stochastic spectral methods have achieved great success in quantifying the impact of process variations,…

Machine Learning · Statistics 2021-06-29 Zichang He , Zheng Zhang

Recently, low-rank tensor completion has become increasingly attractive in recovering incomplete visual data. Considering a color image or video as a three-dimensional (3D) tensor, existing studies have put forward several definitions of…

Computer Vision and Pattern Recognition · Computer Science 2019-01-09 Shengke Xue , Wenyuan Qiu , Fan Liu , Xinyu Jin

Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises, where traditional methods for matrix completion may perform poorly due to utilizing $l_2$ error norm in optimization. In…

Information Theory · Computer Science 2020-02-19 Yicong He , Fei Wang , Yingsong Li , Jing Qin , Badong Chen