Joint Schatten p-Norm and lp-Norm Robust Matrix Completion for Missing Value Recovery

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Authors Feiping Nie, Hua Wang, Heng Huang, Chris Ding
Journal/Conference Name Knowledge and Information Systems (KAIS)
Paper Category
Paper Abstract The low-rank matrix completion problem is a fundamental machine learning and data mining 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 $$p$$ p -norm and $$\ell _p$$ ℓ p -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 prediction and social network link recovery. All empirical results show that our new method outperforms the standard matrix completion methods
Date of publication 2013
Code Programming Language MATLAB

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