Weighted Low Rank Approximation for Background Estimation Problems
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Classical principal component analysis (PCA) is not robust to the presence of sparse outliers in the data. The use of the ℓ_1 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 ℓ_1 norm. As a proof of concept, a background estimation model has been presented and compared with two ℓ_1 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.
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