Correction to: An Approximate Augmented Lagrangian Method for Nonnegative Low-Rank Matrix Approximation

Schur method for low-rank matrix approximation

The usual way to compute a low-rank approximant of a matrix H is to take its truncated SVD. However, the SVD is computationally expensive. This paper describes a much simpler generalized Schur-type algorithm to compute similar low-rank approximants. For a given matrix H which has d singular values larger than ε, we find all rank d approximants Ĥ such that H − Ĥ has 2-norm less than ε. The set o...

Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization

The matrix separation problem aims to separate a low-rank matrix and a sparse matrix from their sum. This problem has recently attracted considerable research attention due to its wide range of potential applications. Nuclear-norm minimization models have been proposed for matrix separation and proved to yield exact separations under suitable conditions. These models, however, typically require...

A Nonnegative Projection Based Algorithm for Low-Rank Nonnegative Matrix Approximation

A Schur Method for Low-Rank Matrix Approximation

The usual way to compute a low-rank approximant of a matrix H is to take its singular value decomposition (SVD) and truncate it by setting the small singular values equal to 0. However, the SVD is computationally expensive. This paper describes a much simpler generalized Schur-type algorithm to compute similar low-rank approximants. For a given matrix H which has d singular values larger than ε...

Local Low-Rank Matrix Approximation

Matrix approximation is a common tool in recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model where we assume instead that the matrix is locally of low-rank, leading to a representation of the observed matrix as a weighted sum of low...