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Algorithms for lp Low-Rank Approximation

2020-03-10 | |  67 |   39 |   0

Abstract

We consider the problem of approximating a given matrix by a low-rank matrix so as to minimize the entry-wise 图片.png -approximation error, for any p 图片.png 1; the case p = 2 is the classical SVD problem. We obtain the first provably good approximation algorithms for this version of lowrank approximation that work for every value of p 图片.png 1, including p = ∞. Our algorithms are simple, easy to implement, work well in practice, and illustrate interesting tradeoffs between the approx imation quality, the running time, and the rank of the approximating matrix.

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