Finding Low-Rank Solutions via Nonconvex Matrix Factorization, Efficiently and Provably

Siam Journal on Imaging Sciences, pp. 2165-2204, 2018.

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Abstract:

A rank-$r$ matrix $X mathbb{R}^{m times n}$ can be written as a product $U V^top$, where $U mathbb{R}^{m times r}$ and $V mathbb{R}^{n times r}$. One could exploit this observation in optimization: e.g., consider the minimization of a convex function $f(X)$ over rank-$r$ matrices, where the set of low-rank matrices is modeled via $UV^t...More

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