Fast Exact Search in Hamming Space with Multi-Index Hashing

TL;DR

This paper presents a novel multi-index hashing method enabling fast, exact k-nearest neighbor search in Hamming space for long binary codes, achieving significant speedups over linear scans on large datasets.

Contribution

It introduces a new multi-index hashing technique for exact search in Hamming space, effective for long binary codes, with theoretical and empirical validation.

Findings

Sub-linear runtime behavior for uniformly distributed codes

Dramatic speedups over linear scan on datasets up to one billion codes

Effective for binary codes of 64, 128, and 256 bits

Abstract

There is growing interest in representing image data and feature descriptors using compact binary codes for fast near neighbor search. Although binary codes are motivated by their use as direct indices (addresses) into a hash table, codes longer than 32 bits are not being used as such, as it was thought to be ineffective. We introduce a rigorous way to build multiple hash tables on binary code substrings that enables exact k-nearest neighbor search in Hamming space. The approach is storage efficient and straightforward to implement. Theoretical analysis shows that the algorithm exhibits sub-linear run-time behavior for uniformly distributed codes. Empirical results show dramatic speedups over a linear scan baseline for datasets of up to one billion codes of 64, 128, or 256 bits.