Norm-Ranging LSH for Maximum Inner Product Search
arXiv:1809.08782
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.
arXiv commentNIPS2018
Cited by in corpus (8)
- A Survey on Locality Sensitive Hashing Algorithms and their Applications
- Understanding and Improving Proximity Graph based Maximum Inner Product Search
- Sublinear Least-Squares Value Iteration via Locality Sensitive Hashing
- Norm-Explicit Quantization: Improving Vector Quantization for Maximum Inner Product Search
- Linear Bandit Algorithms with Sublinear Time Complexity
- ProMIPS: Efficient High-Dimensional c-Approximate Maximum Inner Product Search with a Lightweight Index
- Pyramid: A General Framework for Distributed Similarity Search
- Sublinear Maximum Inner Product Search using Concomitants of Extreme Order Statistics