Faster Low-rank Approximation using Adaptive Gap-based Preconditioning

arXiv: Information Theory, Volume abs/1607.02925, 2016.

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Abstract:

We propose a method for rank $k$ approximation to a given input matrix $X mathbb{R}^{d times n}$ which runs in time [ tilde{O} left(d ~cdot~ minleft{n + tilde{sr}(X) ,G^{-2}_{k,p+1} , n^{3/4}, tilde{sr}(X)^{1/4} ,G^{-1/2}_{k,p+1} right} ~cdot~ text{poly}(p)right) ~, ] where $pu003ek$, $tilde{sr}(X)$ is related to stable rank of $X$, and ...More

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