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

Feiping Nie, Hua Wang, Xiao Cai, Heng Huang, Chris Ding.

ICDM - 2012

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 š‘-norm and lš‘-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.


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Nie, Feiping, et al. "Robust matrix completion via joint schatten p-norm and lp-norm minimization." 2012 IEEE 12th International Conference on Data Mining. IEEE, 2012.
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  title={Robust matrix completion via joint schatten p-norm and lp-norm minimization},
  author={Nie, Feiping and Wang, Hua and Cai, Xiao and Huang, Heng and Ding, Chris},
  booktitle={2012 IEEE 12th International Conference on Data Mining},