Related papers: Fast Spectral Low Rank Matrix Approximation

We study distributed low rank approximation in which the matrix to be approximated is only implicitly represented across the different servers. For example, each of $s$ servers may have an $n \times d$ matrix $A^t$, and we may be interested…

Low rank approximation of a matrix (LRA) is a highly important area of Numerical Linear and Multilinear Algebra and Data Mining and Analysis. One can operate with an LRA superfast -- by using much fewer memory cells and flops than an input…

We provide new approximation guarantees for greedy low rank matrix estimation under standard assumptions of restricted strong convexity and smoothness. Our novel analysis also uncovers previously unknown connections between the low rank…

Rank minimization can be converted into tractable surrogate problems, such as Nuclear Norm Minimization (NNM) and Weighted NNM (WNNM). The problems related to NNM, or WNNM, can be solved iteratively by applying a closed-form proximal…

We propose an algorithm that approximates a given matrix polynomial of degree $d$ by another skew-symmetric matrix polynomial of a specified rank and degree at most $d$. The algorithm is built on recent advances in the theory of generic…

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…

Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…

We consider the approximate computation of spectral projectors for symmetric banded matrices. While this problem has received considerable attention, especially in the context of linear scaling electronic structure methods, the presence of…

We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…

Generalized singular values (GSVs) play an essential role in the comparative analysis. In the real world data for comparative analysis, both data matrices are usually numerically low-rank. This paper proposes a randomized algorithm to first…

We introduce efficient $(1+\varepsilon)$-approximation algorithms for the binary matrix factorization (BMF) problem, where the inputs are a matrix $\mathbf{A}\in\{0,1\}^{n\times d}$, a rank parameter $k>0$, as well as an accuracy parameter…

The problem of low rank approximation is ubiquitous in science. Traditionally this problem is solved in unitary invariant norms such as Frobenius or spectral norm due to existence of efficient methods for building approximations. However,…

In the past few years, the problem of distributed consensus has received a lot of attention, particularly in the framework of ad hoc sensor networks. Most methods proposed in the literature address the consensus averaging problem by…

We study the problem of approximating a matrix $\mathbf{A}$ with a matrix that has a fixed sparsity pattern (e.g., diagonal, banded, etc.), when $\mathbf{A}$ is accessed only by matrix-vector products. We describe a simple randomized…

In this paper, we consider the generalized low rank approximation of the correlation matrices problem which arises in the asset portfolio. We first characterize the feasible set by using the Gramian representation together with a special…

Many link prediction algorithms require the computation of a similarity metric on each vertex pair, which is quadratic in the number of vertices and infeasible for large networks. We develop a class of link prediction algorithms based on a…

This paper addresses the problem of finding the closest generalized essential matrix from a given $6\times 6$ matrix, with respect to the Frobenius norm. To the best of our knowledge, this nonlinear constrained optimization problem has not…

This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops $l_1$-norm penalty to encourage the sparsity and…

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…