Related papers: Accurate and fast matrix factorization for low-ran…
We consider multilevel low rank (MLR) matrices, defined as a row and column permutation of a sum of matrices, each one a block diagonal refinement of the previous one, with all blocks low rank given in factored form. MLR matrices extend low…
This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for…
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…
When factorizing binary matrices, we often have to make a choice between using expensive combinatorial methods that retain the discrete nature of the data and using continuous methods that can be more efficient but destroy the discrete…
This paper describes efficient algorithms for computing rank-revealing factorizations of matrices that are too large to fit in RAM, and must instead be stored on slow external memory devices such as solid-state or spinning disk hard drives…
In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint. We first establish that a class of special rank minimization problems has closed-form solutions. Using this result,…
The overfitting is one of the cursing subjects in the deep learning field. To solve this challenge, many approaches were proposed to regularize the learning models. They add some hyper-parameters to the model to extend the generalization;…
This paper studies the problem of decomposing a low-rank matrix into a factor with binary entries, either from $\{\pm 1\}$ or from $\{0,1\}$, and an unconstrained factor. The research answers fundamental questions about the existence and…
The efficient compression of kernel matrices, for instance the off-diagonal blocks of discretized integral equations, is a crucial step in many algorithms. In this paper, we study the application of Skeletonized Interpolation to construct…
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…
We propose an efficient pipeline for large-scale landmark image retrieval that addresses the diversity of the dataset through two-stage discriminative re-ranking. Our approach is based on embedding the images in a feature-space using a…
Dimensionality reduction is a main step in the learning process which plays an essential role in many applications. The most popular methods in this field like SVD, PCA, and LDA, only can be applied to data with vector format. This means…
Dictionary learning and component analysis are part of one of the most well-studied and active research fields, at the intersection of signal and image processing, computer vision, and statistical machine learning. In dictionary learning,…
The QLP decomposition is one of the effective algorithms to approximate singular value decomposition (SVD) in numerical linear algebra. In this paper, we propose some single-pass randomized QLP decomposition algorithms for computing the…
Robust principal component analysis is an important representative method in data analysis. It is usually viewed as an optimization problem involving the rank and $\ell_0$-norm of matrices. In this paper, we study the rank and $\ell_0$…
Standard rank-revealing factorizations such as the singular value decomposition and column pivoted QR factorization are challenging to implement efficiently on a GPU. A major difficulty in this regard is the inability of standard algorithms…
We introduce novel dynamical low-rank methods for solving large-scale matrix differential equations, motivated by algorithms from randomized numerical linear algebra. In terms of performance (cost and accuracy), our methods overperform…
Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…
Low-rank matrix approximation plays an increasingly important role in signal and image processing applications. This paper presents a new rank-revealing decomposition method called randomized rank-revealing UZV decomposition (RRR-UZVD).…
This paper presents a deterministic, strongly polynomial time algorithm for computing the matrix rank for a class of symbolic matrices (whose entries are polynomials over a field). This class was introduced, in a different language, by…