Matrix completion and low-rank SVD via fast alternating least squares
Matrix completion and low-rank SVD via fast alternating least squares
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DOI：
10.5555/2789272.2912106
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发表时间：
2014-10
期刊：
影响因子：
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通讯作者：
T. Hastie;R. Mazumder;J. Lee;R. Zadeh
中科院分区：
文献类型：
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作者：
T. Hastie;R. Mazumder;J. Lee;R. Zadeh
矩阵补全问题吸引了很多关注，主要是由于著名的Netflix竞争。解决该问题的两种流行方法是核范数正则化矩阵近似（Candès和Tao，2009; Mazumder等人，2010）和最大边缘矩阵分解（Srebro等人，2005年）。这两个程序在某些情况下解决等效问题，但使用完全不同的算法。在这篇文章中，我们将这两种方法结合在一起，导致一个有效的算法，大矩阵分解和完成，优于这两个。我们在R中开发了一个软件包softlmpute用于实现我们的方法，并使用Spark集群编程环境为非常大的矩阵开发了一个分布式版本。
The matrix-completion problem has attracted a lot of attention, largely as a result of the celebrated Netflix competition. Two popular approaches for solving the problem are nuclear-norm-regularized matrix approximation (Candès and Tao, 2009; Mazumder et al., 2010), and maximum-margin matrix factorization (Srebro et al., 2005). These two procedures are in some cases solving equivalent problems, but with quite different algorithms. In this article we bring the two approaches together, leading to an efficient algorithm for large matrix factorization and completion that outperforms both of these. We develop a software package softlmpute in R for implementing our approaches, and a distributed version for very large matrices using the Spark cluster programming environment.