Algorithms for ℓ_p Low Rank Approximation

2017/05/18 by Chierichetti, Flavio, Gollapudi, Sreenivas, Kumar, Ravi +3
#Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.1705.06730

Abstract

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

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