# Weighted Low Rank Approximation for Background Estimation Problems

arXiv: https://arxiv.org/abs/1707.01753 · HTML: https://mlsanity.com/paper/1707.01753/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2017.

## Built on by (most cited first, 2 of 2)

- [When Can We Solve the Weighted Low Rank Approximation Problem in Truly Subquadratic Time?](https://mlsanity.com/paper/2502.16912/) (2025)
- [A Note on Randomized Kaczmarz Algorithm for Solving Doubly-Noisy Linear Systems](https://mlsanity.com/paper/2308.16904/) (2023)

## Abstract (arXiv)

Classical principal component analysis (PCA) is not robust to the presence of sparse outliers in the data. The use of the ℓ1 norm in the Robust PCA (RPCA) method successfully eliminates the weakness of PCA in separating the sparse outliers. In this paper, by sticking a simple weight to the Frobenius norm, we propose a weighted low rank (WLR) method to avoid the often computationally expensive algorithms relying on the ℓ1 norm. As a proof of concept, a background estimation model has been presented and compared with two ℓ1 norm minimization algorithms. We illustrate that as long as a simple weight matrix is inferred from the data, one can use the weighted Frobenius norm and achieve the same or better performance.