Improved Hamming Distance Search Using Variable Length Hashing

This paper addresses the problem of ultra-large-scale search in Hamming spaces. There has been considerable research on generating compact binary codes in vision, for example for visual search tasks. However the issue of efficient searching through huge sets of binary codes remains largely unsolved. To this end, we propose a novel, unsupervised approach to thresholded search in Hamming space, supporting long codes (e.g. 512-bits) with a wide-range of Hamming distance radii. Our method is capable of working efficiently with billions of codes delivering between one to three orders of magnitude acceleration, as compared to prior art. This is achieved by relaxing the equal-size constraint in the Multi-Index Hashing approach, leading to multiple hash-tables with variable length hash-keys. Based on the theoretical analysis of the retrieval probabilities of multiple hash-tables we propose a novel search algorithm for obtaining a suitable set of hash-key lengths. The resulting retrieval mechanism is shown empirically to improve the efficiency over the state-of-the-art, across a range of datasets, bit-depths and retrieval thresholds.