  Recently, locality sensitive hashing (LSH) was shown to be effective for MIPS
and several algorithms including $L_2$-ALSH, Sign-ALSH and Simple-LSH have been
proposed. In this paper, we introduce the norm-range partition technique, which
partitions the original dataset into sub-datasets containing items with similar
2-norms and builds hash index independently for each sub-dataset. We prove that
norm-range partition reduces the query processing complexity for all existing
LSH based MIPS algorithms under mild conditions. The key to performance
improvement is that norm-range partition allows to use smaller normalization
factor most sub-datasets. For efficient query processing, we also formulate a
unified framework to rank the buckets from the hash indexes of different
sub-datasets. Experiments on real datasets show that norm-range partition
significantly reduces the number of probed for LSH based MIPS algorithms when
achieving the same recall.
