  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.
