# Weighted Low-Rank Approximation of Matrices and Background Modeling

Aritra Dutta, Xin Li, Peter Richtarik

Research output: Working paper

## Abstract

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 $\ell_1$ norm. Our methods match or outperform several state-of-the-art online and batch background modeling methods in virtually all quantitative and qualitative measures.
Original language English ArXiv Published - 15 Apr 2018

• cs.CV
• cs.NA
• math.NA
• math.OC