Exact Matrix Completion via Convex Optimization
Exact Matrix Completion via Convex Optimization
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DOI：
10.1145/2184319.2184343
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发表时间：
2012-06-01
影响因子：
22.7
通讯作者：
Recht, Benjamin
中科院分区：
文献类型：
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作者：
Candes, Emmanuel;Recht, Benjamin
假设观察到从低秩矩阵中选择的条目的不完整子集。什么时候可以完成矩阵并恢复尚未看到的条目？我们证明，在非常一般的设置，可以完美地恢复所有的缺失条目从最足够大的子集，通过解决凸规划问题，找到与观察到的条目同意的最小核范数的矩阵。本分析中使用的技术借鉴了压缩感知领域的相似之处，表明可以从非常有限的信息中完美地重建信号和图像以外的对象。
Suppose that one observes an incomplete subset of entries selected from a low-rank matrix. When is it possible to complete the matrix and recover the entries that have not been seen? We demonstrate that in very general settings, one can perfectly recover all of the missing entries from most sufficiently large subsets by solving a convex programming problem that finds the matrix with the minimum nuclear norm agreeing with the observed entries. The techniques used in this analysis draw upon parallels in the field of compressed sensing, demonstrating that objects other than signals and images can be perfectly reconstructed from very limited information.