Consider the following matrix factorization problem: Given an $n\times m$ matrix M, find $n\times r$ and $m\times r$ matrices $U$ and $V$ such that $||UV^T - M||_F^2$ is minimized.

I have heard it many times that all the local minima are global minima for this problem, and that all other stationary points have some direction with negative curvature. I am looking for a reference that rigorously shows this for any asymmetric matrix $M$.



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy