  Matrix factorization is an important mathematical problem encountered in the
context of dictionary learning, recommendation systems and machine learning. We
introduce a new `decimation' scheme that maps it to neural network models of
associative memory and provide a detailed theoretical analysis of its
performance, showing that decimation is able to factorize extensive-rank
matrices and to denoise them efficiently. We introduce a decimation algorithm
based on ground-state search of the neural network, which shows performances
that match the theoretical prediction.
