Related papers: Randomized Quaternion Singular Value Decomposition…
This paper considers the problem of updating the rank-k truncated Singular Value Decomposition (SVD) of matrices subject to the addition of new rows and/or columns over time. Such matrix problems represent an important computational kernel…
In this paper, we propose a general framework for tensor singular value decomposition (tensor SVD), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data. Comprehensive…
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…
Affine rank minimization problem is the generalized version of low rank matrix completion problem where linear combinations of the entries of a low rank matrix are observed and the matrix is estimated from these measurements. We propose a…
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…
Distributions measured in high energy physics experiments are usually distorted and/or transformed by various detector effects. A regularization method for unfolding these distributions is re-formulated in terms of the 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).…
Singular Value Decomposition (SVD) is a well studied research topic in many fields and applications from data mining to image processing. Data arising from these applications can be represented as a matrix where it is large and sparse. Most…
We revisit the use of Stochastic Gradient Descent (SGD) for solving convex optimization problems that serve as highly popular convex relaxations for many important low-rank matrix recovery problems such as \textit{matrix completion},…
Vision problems ranging from image clustering to motion segmentation to semi-supervised learning can naturally be framed as subspace segmentation problems, in which one aims to recover multiple low-dimensional subspaces from noisy and…
While Convolutional Neural Networks (CNNs) excel at learning complex latent-space representations, their over-parameterization can lead to overfitting and reduced performance, particularly with limited data. This, alongside their high…
We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…
Neural networks in the real domain have been studied for a long time and achieved promising results in many vision tasks for recent years. However, the extensions of the neural network models in other number fields and their potential…
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…
The singular value decomposition (SVD) is commonly used in applications requiring a low rank matrix approximation. However, the singular vectors cannot be interpreted in terms of the original data. For applications requiring this type of…
In color image processing, image completion aims to restore missing entries from the incomplete observation image. Recently, great progress has been made in achieving completion by approximately solving the rank minimization problem. In…
The color video inpainting problem is one of the most challenging problem in the modern imaging science. It aims to recover a color video from a small part of pixels that may contain noise. However, there are less of robust models that can…
We present Flip-Flop Spectrum-Revealing QR (Flip-Flop SRQR) factorization, a significantly faster and more reliable variant of the QLP factorization of Stewart, for low-rank matrix approximations. Flip-Flop SRQR uses SRQR factorization to…
The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…
This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…