Stability of matrix factorization for collaborative filtering

We study the stability vis a vis adversarial noise of matrix factorization algorithm for matrix completion. In particular, our results include: (I) we bound the gap between the solution matrix of the factorization method and the ground truth in terms of root mean square error; (II) we treat the matrix factor-ization as a subspace fitting problem and an-alyze the difference between the solution sub-space and the ground truth; (III) we analyze the prediction error of individual users based on the subspace stability. We apply these results to the problem of collaborative filter-ing under manipulator attack, which leads to useful insights and guidelines for collabora-tive filtering system design. 1