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Recently, locality sensitive hashing (LSH) was shown to be effective for MIPSand several algorithms including $L_2$-ALSH, Sign-ALSH and Simple-LSH have beenproposed. In this paper, we introduce the norm-range partition technique, whichpartitions the original dataset into sub-datasets containing items with similar2-norms and builds hash index independently for each sub-dataset. We prove thatnorm-range partition reduces the query processing complexity for all existingLSH based MIPS algorithms under mild conditions. The key to performanceimprovement is that norm-range partition allows to use smaller normalizationfactor most sub-datasets. For efficient query processing, we also formulate aunified framework to rank the buckets from the hash indexes of differentsub-datasets. Experiments on real datasets show that norm-range partitionsignificantly reduces the number of probed for LSH based MIPS algorithms whenachieving the same recall.

Norm-Range Partition: A Universal Catalyst for LSH based Maximum Inner Product Search (MIPS)