By using L∞ first we obtain a set of K approximate solutions. From those K possible solutions, we use more accurate distance metrics such as L1 or L2 to find an improved solution when compared to L∞ alone (Tab. I row 5-6). While using L2 instead of L1 (Tab. II row 5-6) for the second stage would require K · D additional multiplications this is much less than the M · D multiplications of cosine distance since K