A fast algorithm for a weighted low rank approximation

Aritra Dutta, Xin Li

Abstract: Matrix low rank approximation including the classical PCA and the robust PCA (RPCA) method have been applied to solve the background modeling problem in video analysis. Recently, it has been demonstrated that a special weighted low rank approximation of matrices can be made robust to the outliers similar to the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm in RPCA method. In this work, we propose a new algorithm that can speed up the existing algorithm for solving the special weighted low rank approximation and demonstrate its use in background estimation problem.