Abstract
We study a weighted low-rank approximation that is inspired by a problem of constrained low-rank approximation of matrices as initiated by the work of Golub, Hoffman, and Stewart [Linear Algebra Appl., 88/89 (1987), pp. 317-327]. Our results reduce to that of Golub, Hoffman, and Stewart in the limiting cases. We also propose an algorithm based on the alternating direction method to solve our weighted low-rank approximation problem and compare it with the state-of-art general algorithms such as the weighted total alternating least squares algorithm and the expectation maximization algorithm.