WaldHash: sequential similarity-preserving hashing

Similarity-sensitive hashing seeks compact representation of vector data as binary codes, so that the Hamming distance between code words approximates the original similarity. In this paper, we show that using codes of fixed length is inherently inefficient as the similarity can often be approximated well using just a few bits. We formulate a sequential embedding problem and approach similarity computation as a sequential decision strategy. We show the relation of the optimal strategy that minimizes the average decision time to Wald’s sequential probability ratio test. Numerical experiments demonstrate that the proposed approach outperforms embedding into the Hamming space of fixed dimension in terms of the average decision time, while having similar accuracy.