论文标题
矩阵完成，并通过最大化相关性提供先验子空间信息
Matrix Completion with Prior Subspace Information via Maximizing Correlation
论文作者
论文摘要
本文研究了借助先验信息，从其一些随机条目中完成低级矩阵的问题。我们建议一种策略，通过最大化原始信号与先验信息之间的相关性，将先验信息纳入标准矩阵完成过程中。我们还为提出的方法建立了绩效保证，该方法表明，通过适当的先验信息，提议的程序可以通过对数因素来降低标准矩阵完成的样本复杂性。为了说明该理论，我们进一步分析了可以使用先前的子空间信息的重要实际应用。提供合成和现实世界实验以验证理论的有效性。
This paper studies the problem of completing a low-rank matrix from a few of its random entries with the aid of prior information. We suggest a strategy to incorporate prior information into the standard matrix completion procedure by maximizing the correlation between the original signal and the prior information. We also establish performance guarantees for the proposed method, which show that with suitable prior information, the proposed procedure can reduce the sample complexity of the standard matrix completion by a logarithmic factor. To illustrate the theory, we further analyze an important practical application where the prior subspace information is available. Both synthetic and real-world experiments are provided to verify the validity of the theory.
