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Joint Schatten -norm and -norm robust matrix completion for missing value recovery

机译：联合Schatten -norm和-norm鲁棒矩阵补全以实现缺失值恢复

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摘要

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 -norm and -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.
机译：低秩矩阵完成问题是具有许多重要应用程序的基本机器学习和数据挖掘问题。标准的低秩矩阵完成方法通过迹线范数最小化来缓解秩最小化问题。但是，这种放松可能会使解决方案严重偏离原始解决方案。同时，大多数完成方法会将观测到的条目的预测误差平方最小化，这对异常值很敏感。在本文中，我们提出了一种新的鲁棒矩阵完成方法来解决这两个问题。联合使用Schatten -norm和-norm可以更好地近似秩最小化问题并增强对异常值的鲁棒性。在协作过滤预测和社交网络链接恢复中，对合成数据和实际应用程序都进行了广泛的实验。所有的经验结果表明，我们的新方法优于标准的矩阵完成方法。

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