`1/`2 regularized non-convex low-rank matrix factorization

Low-rank matrix factorization plays a key role in a plethora of problems commonly met in machine learning applications dealing with big data as it reduces the size of the emerging optimization problems. In this work we introduce a novel low-rank promoting regularization function which gives rise to an algorithm that induces sparsity jointly on the columns of the matrix factors. Apart from the reduced computational complexity requirements it offers, the new algorithm also provides a basis of the sought low-rank subspace.