Stability of matrix factorization for collaborative filtering

TL;DR

This paper analyzes the stability of matrix factorization in collaborative filtering, providing bounds on errors and insights into system robustness against adversarial noise and manipulator attacks.

Contribution

It introduces new stability bounds for matrix factorization, treating it as a subspace fitting problem and analyzing prediction errors under adversarial conditions.

Findings

Bounded the gap between estimated and true matrices in RMSE

Analyzed subspace stability and its impact on prediction accuracy

Provided guidelines for designing robust collaborative filtering systems

Abstract

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.