# Weighted Low-Rank Approximation of Matrices and Background Modeling

arXiv: https://arxiv.org/abs/1804.06252 · HTML: https://mlsanity.com/paper/1804.06252/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Apr 2018.

## 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)
- [Reweighted Solutions for Weighted Low Rank Approximation](https://mlsanity.com/paper/2406.02431/) (2024)

## Abstract (arXiv)

We primarily study a special a weighted low-rank approximation of matrices and then apply it to solve the background modeling problem. We propose two algorithms for this purpose: one operates in the batch mode on the entire data and the other one operates in the batch-incremental mode on the data and naturally captures more background variations and computationally more effective. Moreover, we propose a robust technique that learns the background frame indices from the data and does not require any training frames. We demonstrate through extensive experiments that by inserting a simple weight in the Frobenius norm, it can be made robust to the outliers similar to the ℓ1 norm. Our methods match or outperform several state-of-the-art online and batch background modeling methods in virtually all quantitative and qualitative measures.