Algorithms for $\ell_p$ LowRank Approximation
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Proceedings of the 34th International Conference on Machine Learning, PMLR 70:806814, 2017.
Abstract
We consider the problem of approximating a given matrix by a lowrank matrix so as to minimize the entrywise $\ell_p$approximation error, for any $p \geq 1$; the case $p = 2$ is the classical SVD problem. We obtain the first provably good approximation algorithms for this robust version of lowrank approximation that work for every value of $p$. 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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