Matrix Completion From a Few Entries

Raghunandan H. Keshavan,Andrea Montanari,Sewoong Oh

IEEE Transactions on Information Theory（2010）

引用 1502|浏览7

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摘要

Let M be an n¿ × n matrix of rank r, and assume that a uniformly random subset E of its entries is observed. We describe an efficient algorithm, which we call OptSpace, that reconstructs M from |E| = O(rn) observed entries with relative root mean square error 1/2 RMSE ¿ C(¿) (nr/|E|)1/2 with probability larger than 1 - 1/n3. Further, if r = O(1) and M is sufficiently unstructured, then OptSpace re...

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关键词

Motion pictures,Root mean square,Sparse matrices,Mathematical model,Reconstruction algorithms,Optimization methods,Watches,Collaboration,Information filtering,Information filters

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