Weighted Low Rank Approximation for Background Estimation Problems

Classical principal component analysis (PCA) is not robust when the data contain sparse outliers. The use of the ℓ1 norm in the Robust PCA (RPCA) method successfully eliminates this weakness of PCA in separating the sparse outliers. Here we propose a weighted low rank (WLR) method, where a simple weight is inserted inside the Frobenius norm. We demonstrate how this method tackles often computationally expensive algorithms that rely on the ℓ1 norm. As a proof of concept, we present a background estimation model based on WLR, and we compare the model with RPCA method and with other state-of-the-art algorithms used for background estimation. Our empirical validation shows that the weighted low-rank approximation we propose here can perform as well as or better than that of RPCA and other state-of-the-art algorithms.