Related papers: Randomized Quaternion Singular Value Decomposition…
The soft SVD is a robust matrix decomposition algorithm and a key component of matrix completion methods. However, computing the soft SVD for large sparse matrices is often impractical using conventional numerical methods for the SVD due to…
A new algorithm to compute the restricted singular value decomposition of dense matrices is presented. Like Zha's method \cite{Zha92}, the new algorithm uses an implicit Kogbetliantz iteration, but with four major innovations. The first…
High throughput biomedical measurements normally capture multiple overlaid biologically relevant signals and often also signals representing different types of technical artefacts like e.g. batch effects. Signal identification and…
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…
Singular value decomposition (SVD) is the mathematical basis of principal component analysis (PCA). Together, SVD and PCA are one of the most widely used mathematical formalism/decomposition in machine learning, data mining, pattern…
Lossy image compression is essential for efficient transmission and storage. Traditional compression methods mainly rely on discrete cosine transform (DCT) or singular value decomposition (SVD), both of which represent image data in…
In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…
The selection of most informative and discriminative features from high-dimensional data has been noticed as an important topic in machine learning and data engineering. Using matrix factorization-based techniques such as nonnegative matrix…
Recent years have witnessed intense development of randomized methods for low-rank approximation. These methods target principal component analysis (PCA) and the calculation of truncated singular value decompositions (SVD). The present…
Very deep convolutional neural networks (CNNs) have been firmly established as the primary methods for many computer vision tasks. However, most state-of-the-art CNNs are large, which results in high inference latency. Recently, depth-wise…
The problem of recovering a low-rank matrix from the linear constraints, known as affine matrix rank minimization problem, has been attracting extensive attention in recent years. In general, affine matrix rank minimization problem is a…
Historically, analysis for multiscale PDEs is largely unified while numerical schemes tend to be equation-specific. In this paper, we propose a unified framework for computing multiscale problems through random sampling. This is achieved by…
Many applications in scientific computing and data science require the computation of a rank-revealing factorization of a large matrix. In many of these instances the classical algorithms for computing the singular value decomposition are…
Low-rank approximation methods such as singular value decomposition (SVD) and its variants (e.g., Fisher-weighted SVD, Activation SVD) have recently emerged as effective tools for neural network compression. In this setting, decomposition…
Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…
Weighted singular value decomposition (WSVD) and a representation of the weighted Moore-Penrose inverse of a quaternion matrix by WSVD have been derived. Using this representation, limit and determinantal representations of the weighted…
In this work, we present a mixed precision algorithm that leverages the Gram matrix and Jacobi methods to compute the singular value decomposition (SVD) of tall-and-skinny matrices. By constructing the Gram matrix in higher precision and…
Low-rank matrix approximations play a fundamental role in numerical linear algebra and signal processing applications. This paper introduces a novel rank-revealing matrix decomposition algorithm termed Compressed Randomized UTV (CoR-UTV)…
Storing data is particularly a challenge when dealing with image data which often involves large file sizes due to the high resolution and complexity of images. Efficient image compression algorithms are crucial to better manage data…
RSVDPACK is a library of functions for computing low rank approximations of matrices. The library includes functions for computing standard (partial) factorizations such as the Singular Value Decomposition (SVD), and also so called…