Norm-Ranging LSH for Maximum Inner Product Search

TL;DR

This paper introduces Norm-ranging LSH, a novel hashing method for maximum inner product search that partitions datasets to improve performance and reduce query time, outperforming previous methods significantly.

Contribution

The paper proposes a new dataset partitioning approach in hashing for MIPS, addressing long-tail issues and improving efficiency over Simple-LSH.

Findings

Norm-ranging LSH reduces query time compared to Simple-LSH.

Partitioning datasets enhances hashing performance for MIPS.

Experiments demonstrate an order of magnitude speedup for the same recall.

Abstract

Neyshabur and Srebro proposed Simple-LSH, which is the state-of-the-art hashing method for maximum inner product search (MIPS) with performance guarantee. We found that the performance of Simple-LSH, in both theory and practice, suffers from long tails in the 2-norm distribution of real datasets. We propose Norm-ranging LSH, which addresses the excessive normalization problem caused by long tails in Simple-LSH by partitioning a dataset into multiple sub-datasets and building a hash index for each sub-dataset independently. We prove that Norm-ranging LSH has lower query time complexity than Simple-LSH. We also show that the idea of partitioning the dataset can improve other hashing based methods for MIPS. To support efficient query processing on the hash indexes of the sub-datasets, a novel similarity metric is formulated. Experiments show that Norm-ranging LSH achieves an order of magnitude speedup over Simple-LSH for the same recall, thus significantly benefiting applications that involve MIPS.