A Continuous Technique for the Weighted Low-Rank Approximation Problem

Abstract

This paper concerns with the problem of approximating a target matrix with a matrix of lower rank with respect to a weighted norm. Weighted norms can arise in several situations: when some of the entries of the matrix are not observed or need not to be treated equally. A gradient flow approach for solving weighted low rank approximation problems is provided. This approach allows the treatment of both real and complex matrices and exploits some important features of the approximation matrix that optimization techniques do not use. Finally, some numerical examples are provided. © Springer-Verlag 2004.