相关论文: Untangling the SVD's of Random Matrix Sample Paths

To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the…

We present a variational quantum circuit that produces the Singular Value Decomposition of a bipartite pure state. The proposed circuit, that we name Quantum Singular Value Decomposer or QSVD, is made of two unitaries respectively acting on…

Randomized subspace approximation with "matrix sketching" is an effective approach for constructing approximate partial singular value decompositions (SVDs) of large matrices. The performance of such techniques has been extensively…

The study of chaos and complexity in non-Hermitian quantum systems poses significant challenges due to the emergence of complex eigenvalues in their spectra. Recently, the singular value decomposition (SVD) method was proposed to address…

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…

In this paper, we propose a new sampling strategy for hyperspectral signals that is based on dictionary learning and singular value decomposition (SVD). Specifically, we first learn a sparsifying dictionary from training spectral data using…

In this paper, we study randomized methods for feedback design of uncertain systems. The first contribution is to derive the sample complexity of various constrained control problems. In particular, we show the key role played by the…

Computing eigenvalue decomposition (EVD) of a given linear operator, or finding its leading eigenvalues and eigenfunctions, is a fundamental task in many machine learning and scientific computing problems. For high-dimensional eigenvalue…

Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…

This article introduces a novel methodology that integrates singular value decomposition (SVD) with a shallow linear neural network for forecasting high resolution fluid mechanics data. The method, termed LC-SVD-DLinear, combines a low-cost…

This paper aims at a better understanding of matrix factorization (MF), factorization machines (FM), and their combination with deep algorithms' application in recommendation systems. Specifically, this paper will focus on Singular Value…

This paper presents a new method capable of reconstructing datasets with great precision and very low computational cost using a novel variant of the singular value decomposition (SVD) algorithm that has been named low-cost SVD (lcSVD).…

This paper provides an advanced mathematical theory of the Generalized Singular Value Decomposition (GSVD) and its applications. We explore the geometry of the GSVD which provides a long sought for ellipse picture which includes a…

Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…

This manuscript describes the randomized algorithm randUTV for computing a so called UTV factorization efficiently. Given a matrix $A$, the algorithm computes a factorization $A = UTV^{*}$, where $U$ and $V$ have orthonormal columns, and…

Consider the problem of estimating the entries of a large matrix, when the observed entries are noisy versions of a small random fraction of the original entries. This problem has received widespread attention in recent times, especially…

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…

In this job we have introduced a filtered adaptive technique that allows highlighting selective seismic events according to its polarization. This technique consists in the implementation of a polarizing filter based on the Single Value…

A well known result from functional analysis states that any compact operator between Hilbert spaces admits a singular value decomposition (SVD). This decomposition is a powerful tool that is the workhorse of many methods both in…

Recursive adaptive filtering methods are often used for solving the problem of simultaneous state and parameters estimation arising in many areas of research. The gradient-based schemes for adaptive Kalman filtering (KF) require the…