Stability of matrix factorization for collaborative filtering
This addresses the problem of robust collaborative filtering systems against manipulator attacks, providing guidelines for design, but it appears incremental as it builds on existing matrix factorization methods.
The paper tackles the stability of matrix factorization for collaborative filtering under adversarial noise, bounding the error between the solution and ground truth in terms of root mean square error and analyzing subspace and prediction errors.
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 factorization as a subspace fitting problem and analyze the difference between the solution subspace 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 filtering under manipulator attack, which leads to useful insights and guidelines for collaborative filtering system design.