Related papers: Distributions of Singular Values for Some Random M…
Supervised learning methods with missing data have been extensively studied not just due to the techniques related to low-rank matrix completion. Also in unsupervised learning one often relies on imputation methods. As a matter of fact,…
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…
In this paper, we study the problem of decomposing a superposition of a low-rank matrix and a sparse matrix when a relatively few linear measurements are available. This problem arises in many data processing tasks such as aligning multiple…
Singular value decomposition (SVD) is a standard matrix factorization technique that produces optimal low-rank approximations of matrices. It has diverse applications, including machine learning, data science and signal processing. However,…
We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…
Learning to restore multiple image degradations within a single model is quite beneficial for real-world applications. Nevertheless, existing works typically concentrate on regarding each degradation independently, while their relationship…
Pore networks play a key role in understanding and quantifying flow and transport processes in complex porous media. Realistic pore-spaces may be characterized by singular regions, i.e., isolated subnetworks that do not connect inlet and…
We consider the problem of image denoising in the presence of noise whose statistical properties are a combination of two different distributions. We focus on noise distributions that are frequently considered in applications, in particular…
Convolutional Neural Networks (CNNs) have made significant progress on several computer vision benchmarks, but are fraught with numerous non-human biases such as vulnerability to adversarial samples. Their lack of explainability makes…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
We present a new method for obtaining norm bounds for random matrices, where each entry is a low-degree polynomial in an underlying set of independent real-valued random variables. Such matrices arise in a variety of settings in the…
Complex Hermitian random matrices with a unitary symmetry can be distinguished by a weight function. When this is even, it is a known result that the distribution of the singular values can be decomposed as the superposition of two…
With their ability to handle an increased amount of information, multivariate and multichannel signals can be used to solve problems normally not solvable with signals obtained from a single source. One such problem is the decomposition…
The massive scale of pretrained models has made efficient compression essential for practical deployment. Low-rank decomposition based on the singular value decomposition (SVD) provides a principled approach for model reduction, but its…
Singular Value Decomposition can be considered as an effective method for Signal Processing/especially data compression. In this short paper we investigate the application of SVD to predict data equation from data. The method is similar to…
Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
When developing a software system, a change in one part of the system may lead to unwanted changes in other parts of the system. These affected parts may interfere with system performance, so regression testing is used to deal with these…
Singular-Value Decomposition (SVD) is a ubiquitous data analysis method in engineering, science, and statistics. Singular-value estimation, in particular, is of critical importance in an array of engineering applications, such as channel…
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…