Matrix Completion with Noisy Entries and Outliers
Matrix Completion with Noisy Entries and Outliers
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发表时间：
2015-03
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通讯作者：
Raymond K. W. Wong;Thomas C.M. Lee
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作者：
Raymond K. W. Wong;Thomas C.M. Lee
本文研究了观测项含有噪声和离群值时的矩阵补全问题。首先引入一个新的优化准则，将恢复矩阵定义为其解。该标准使用鲁棒统计文献中著名的Huber函数来减轻异常值的影响。提出了一种实用的算法来解决所涉及的优化问题。该算法具有速度快、实现简单、单调收敛等特点。此外，所提出的方法在理论上被证明是稳定的。通过一系列的仿真实验，包括图像绘制，证明了其良好的经验性能。
This paper considers the problem of matrix completion when the observed entries are noisy and contain outliers. It begins with introducing a new optimization criterion for which the recovered matrix is defined as its solution. This criterion uses the celebrated Huber function from the robust statistics literature to downweigh the effects of outliers. A practical algorithm is developed to solve the optimization involved. This algorithm is fast, straightforward to implement, and monotonic convergent. Furthermore, the proposed methodology is theoretically shown to be stable in a well defined sense. Its promising empirical performance is demonstrated via a sequence of simulation experiments, including image inpainting.