Related papers: Why are Big Data Matrices Approximately Low Rank?

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

Complex networks representing social interactions, brain activities, molecular structures have been studied widely to be able to understand and predict their characteristics as graphs. Models and algorithms for these networks are used in…

Low-rank Matrix Completion (LRMC) describes the problem where we wish to recover missing entries of partially observed low-rank matrix. Most existing matrix completion work deals with sampling procedures that are independent of the…

The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in collaborative filtering, computer vision and…

High-dimensional inference refers to problems of statistical estimation in which the ambient dimension of the data may be comparable to or possibly even larger than the sample size. We study an instance of high-dimensional inference in…

We determine the rank of a random matrix over an arbitrary field with prescribed numbers of non-zero entries in each row and column. As an application we obtain a formula for the rate of low-density parity check codes. This formula…

In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…

The low-rank matrix completion problem asks whether a given real matrix with missing values can be completed so that the resulting matrix has low rank or is close to a low-rank matrix. The completed matrix is often required to satisfy…

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…

Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…

Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…

Permutation matrices play a key role in matching and assignment problems across the fields, especially in computer vision and robotics. However, memory for explicitly representing permutation matrices grows quadratically with the size of…

Low-rank matrices are pervasive throughout statistics, machine learning, signal processing, optimization, and applied mathematics. In this paper, we propose a novel and user-friendly Euclidean representation framework for low-rank matrices.…

The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…

Many latent (factorized) models have been proposed for recommendation tasks like collaborative filtering and for ranking tasks like document or image retrieval and annotation. Common to all those methods is that during inference the items…

Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…

Matrix completion algorithms recover a low rank matrix from a small fraction of the entries, each entry contaminated with additive errors. In practice, the singular vectors and singular values of the low rank matrix play a pivotal role for…

In many applications, it is of interest to approximate data, given by mxn matrix A, by a matrix B of at most rank k, which is much smaller than m and n. The best approximation is given by singular value decomposition, which is too time…

The class of quasiseparable matrices is defined by the property that any submatrix entirely below or above the main diagonal has small rank, namely below a bound called the order of quasiseparability. These matrices arise naturally in…

With the advent of the big data era, generative models of complex networks are becoming elusive from direct computational simulation. We present an exact, linear-algebraic reduction scheme of generative models of networks. By exploiting the…