We study the problem of entrywise $\ell_1$ low rank approximation. We give the first polynomial time column subset selectionbased $\ell_1$ low rank approximation algorithm sampling $\tilde{O}(k)$ columns and achieving an $\tilde{O}(k^{1/2})$approximation for any $k$, improving upon the previous best $\tilde{O}(k)$approximation and matching a prior lower bound for column subset selectionbased $\ell_1$low rank approximation which holds for any $\text{poly}(k)$ number of columns... (read more)
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