Fast additive quantization for vector compression in nearest neighbor search

Vector quantization has been widely employed in nearest neighbor search because it can approximate the Euclidean distance of two vectors with the table look-up way that can be precomputed. Additive quantization (AQ) algorithm validated that low approximation error can be achieved by representing each input vector with a sum of dependent codewords, each of which is from its own codebook. However, the AQ algorithm relies on computational expensive beam search algorithm to encode each vector, which is prohibitive for the efficiency of the approximate nearest neighbor search. In this paper, we propose a fast AQ algorithm that significantly accelerates the encoding phase. We formulate the beam search algorithm as an optimization of codebook selection orders. According to the optimal order, we learn the codebooks with hierarchical construction, in which the search width can be set very small. Specifically, the codewords are firstly exchanged into proper codebooks by the indexed frequency in each step. Then the codebooks are updated successively to adapt the quantization residual of previous quantization level. In coding phase, the vectors are compressed with learned codebooks via the best order, where the search range is considerably reduced. The proposed method achieves almost the same performance as AQ, while the speed for the vector encoding phase can be accelerated dozens of times. The experiments are implemented on two benchmark datasets and the results verify our conclusion.