An Experimental Study of Balance in Matrix Factorization

We experimentally examine how gradient descent navigates the landscape of matrix factorization to obtain a global minimum. First, we review the critical points of matrix factorization and introduce a balanced factorization. By focusing on the balanced critical point at the origin and a subspace of unbalanced critical points, we study the effect of balance on gradient descent, including an initially unbalanced factorization and adding a balance-regularizer to the objective in the MF problem. Simulations demonstrate that maintaining a balanced factorization enables faster escape from saddle points and overall faster convergence to a global minimum.