Related papers: Use of Singular-Value Decomposition in Gravitation…

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…

We present a unified description of gravitational-wave data analysis that unites the template-based analysis used to detect deterministic signals from well-modeled sources, such as binary-black-hole mergers, with the cross-correlation…

Singular Value Decomposition (SVD) is the basic body of many statistical algorithms and few users question whether SVD is properly handling its job. SVD aims at evaluating the decomposition that best approximates a data matrix, given some…

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…

Motivated by the recent demonstration of its use as a tool for the detection and characterization of phase-shape correlations in multivariate time series, we show that eigenvalue decomposition can also be applied to a matrix of indices of…

In comparing the behavior of an energy spectrum to the predictions of random matrix theory one must transform the spectrum such that the averaged level spacing is constant, a procedure known as unfolding. Once energy spectrums belong to an…

Deep neural networks used for image classification often use convolutional filters to extract distinguishing features before passing them to a linear classifier. Most interpretability literature focuses on providing semantic meaning to…

We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…

Convergence of a matrix decomposition technique, the multi-field singular value decomposition (MFSVD) which efficiently analyzes nonlinear correlations by simultaneously decomposing multiple fields, is investigated. Toward applications in…

Singular value decomposition (SVD) has a crucial role in model order reduction. It is often utilized in the offline stage to compute basis functions that project the high-dimensional nonlinear problem into a low-dimensionsl model which is,…

The singular values $\sigma >1$ of an $n \times n$ involutory matrix $A$ appear in pairs $(\sigma, \frac{1}{\sigma}),$ while the singular values $\sigma = 1$ may appear in pairs $(1,1)$ or by themselves. The left and right singular vectors…

The large-scale focusing inversion of gravity and magnetic potential field data using $L_1$-norm regularization is considered. The use of the randomized singular value decomposition methodology facilitates tackling the computational…

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…

For the computation of the generalized singular value decomposition (GSVD) of a large matrix pair $(A,B)$ of full column rank, the GSVD is commonly formulated as two mathematically equivalent generalized eigenvalue problems, so that a…

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…

The Singular Value Decomposition (SVD) is one of the most important matrix factorizations, enjoying a wide variety of applications across numerous application domains. In statistics and data analysis, the common applications of SVD such as…

We present the application of a novel method of time-series analysis, the Hilbert-Huang Transform, to the search for gravitational waves. This algorithm is adaptive and does not impose a basis set on the data, and thus the time-frequency…

The generalized singular value decomposition (GSVD, a.k.a. "SVD triplet", "duality diagram" approach) provides a unified strategy and basis to perform nearly all of the most common multivariate analyses (e.g., principal components,…

This is a further development of Vision Transformer Pruning via matrix decomposition. The purpose of the Vision Transformer Pruning is to prune the dimension of the linear projection of the dataset by learning their associated importance…

We present a new formulation of the hyperbolic singular value decomposition (HSVD) for an arbitrary complex (or real) matrix without hyperexchange matrices and redundant invariant parameters. In our formulation, we use only the concept of…