Robust Matrix Completion via Joint Schatten p-Norm and lp-Norm Minimization

By Feiping Nie, Hua Wang, Xiao Cai, Heng Huang, Chris H. Q. Ding. 2012

141 citations recorded by the source corpus.

The low-rank matrix completion problem is a fundamental machine learning problem with many important applications. The standard low-rank matrix completion methods relax the rank minimization problem by the trace norm minimization. However, this relaxation may make the solution seriously deviate from the original solution. Meanwhile, most completion methods minimize the squared prediction errors on the observed entries, which is sensitive to outliers. In this paper, we propose a new robust matrix completion method to address these two problems. The joint Schatten p-norm and ℓp-norm are used to better approximate the rank minimization problem and enhance the robustness to outliers. The extensive experiments are performed on both synthetic data and real world applications in collaborative filtering and social network link prediction. All empirical results show our new method outperforms the standard matrix completion methods.

Subfields: Artificial Intelligence, Computational Mechanics, Computer Vision and Pattern Recognition

How researchers see this paper

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

In Artificial Intelligence

1. Bo Li
2. Yevgeniy Vorobeychik
3. Yining Wang
4. Aarti Singh
5. Percy Liang
6. Pang Wei Koh
7. Neil Zhenqiang Gong
8. Jacob Steinhardt

In Computational Mechanics

1. Yuhua Xu
2. Bo Li
3. Shuo Feng
4. Yevgeniy Vorobeychik
5. Guoru Ding
6. Yining Wang
7. Aarti Singh
8. Raquel Urtasun

In Computer Vision and Pattern Recognition

1. Bo Li
2. Yevgeniy Vorobeychik
3. Yining Wang
4. Aarti Singh
5. Raquel Urtasun
6. Xiaogang Wang
7. Luc Van Gool
8. Jiaya Jia

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].”
• A survey of machine learning for big data processing (2016, background): “Furthermore, integrating the matrix completion technologies into machine learning to solve the problem of incomplete data is also a very promising direction [106].”