Stability of matrix factorization for collaborative filtering

By Yu-Xiang Wang, Huan Xu. 2012

36 citations recorded by the source corpus.

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.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering, Management Science and Operations Research

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Bo Li
2. Yevgeniy Vorobeychik
3. Yongfeng Zhang
4. Yiqun Liu
5. Yu-Xiang Wang
6. Yi Zhang
7. Min Zhang
8. Alex Smola

In Electrical and Electronic Engineering

1. Yongfeng Zhang
2. Bo Li
3. Yu-Xiang Wang
4. Alex Smola

In Management Science and Operations Research

1. Bo Li
2. Yongfeng Zhang
3. Yiqun Liu
4. Yu-Xiang Wang
5. Yi Zhang
6. Aarti Singh
7. Min Zhang
8. Alex Smola

Citations in the corpus

• Data Poisoning Attacks on Factorization-Based Collaborative Filtering (2016, background): “In terms of collaborative filtering/matrix completion, there is another line of established research that focuses on robust matrix completion, in which a small portion of elements or rows in the underlying low-rank matrix is assumed to be arbitrarily perturbed [18, 19, 20, 21].”
• Fast Differentially Private Matrix Factorization (2015, result): “This intuition is confirmed in the observed cache miss rates reported in the experiments in Section 6.”
• Understanding the Sparsity: Augmented Matrix Factorization with Sampled Constraints on Unobservables (2014, background): “The most recent work concerning the theoretical properties of MF algorithms is given in [10, 25], which investigate the optimization algorithms for MF and their stability with adversarial noise in terms of prediction accuracy.”