相关论文: A recursive skeletonization factorization based on…

LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly efficient but remain…

This paper presents a generalization of the "weighted least-squares" (WLS), named "weighted pairing least-squares" (WPLS), which uses a rectangular weight matrix and is suitable for data alignment problems. Two fast solving methods,…

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…

A new hybrid algorithm for LDU-factorization for large sparse matrix combining iterative solver, which can keep the same accuracy as the classical factorization, is proposed. The last Schur complement will be generated by iterative solver…

We study the robust recovery of a low-rank matrix from sparsely and grossly corrupted Gaussian measurements, with no prior knowledge on the intrinsic rank. We consider the robust matrix factorization approach. We employ a robust $\ell_1$…

Random hypothesis sampling lies at the core of many popular robust fitting techniques such as RANSAC. In this paper, we propose a novel hypothesis sampling scheme based on incremental computation of distances between partial rankings…

Skeletonization is a popular shape analysis technique that models an object's interior as opposed to just its boundary. Fitting template-based skeletal models is a time-consuming process requiring much manual parameter tuning. Recently,…

Some important applicative problems require the evaluation of functions $\Psi$ of large and sparse and/or \emph{localized} matrices $A$. Popular and interesting techniques for computing $\Psi(A)$ and $\Psi(A)\mathbf{v}$, where $\mathbf{v}$…

Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations…

A matrix algorithm runs superfast (aka at sublinear cost) if it involves much fewer flops and memory cells than an input matrix has entries. Big Data are frequently represented by matrices of immense sizes that cannot be handled directly…

Current state-of-the-art methods for differentially private model training are based on matrix factorization techniques. However, these methods suffer from high computational overhead because they require numerically solving a demanding…

A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming…

Recent SVD-free matrix factorization formulations have enabled rank minimization for systems with millions of rows and columns, paving the way for matrix completion in extremely large-scale applications, such as seismic data interpolation.…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

This paper addresses the problem of approximate MAP-MRF inference in general graphical models. Following [36], we consider a family of linear programming relaxations of the problem where each relaxation is specified by a set of nested pairs…

This paper introduces a randomized Householder QR factorization (RHQR). This factorization can be used to obtain a well conditioned basis of a vector space and thus can be employed in a variety of applications. The RHQR factorization of the…

We propose a clustering-based generalized low rank approximation method, which takes advantage of appealing features from both the generalized low rank approximation of matrices (GLRAM) and cluster analysis. It exploits a more general form…

Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale matrices. Existing algorithms can approximatively solve these problems with a given…

Continuous neural representations have recently emerged as a powerful and flexible alternative to classical discretized representations of signals. However, training them to capture fine details in multi-scale signals is difficult and…

In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…