Product Quantizer Aware Inverted Index for Scalable Nearest Neighbor Search

The inverted index is one of the most commonly used structures for non-exhaustive nearest neighbor search on large-scale datasets. It allows a significant factor of acceleration by a reduced number of distance computations with only a small fraction of the database. In particular, the inverted index enables the product quantization (PQ) to learn their codewords in the residual vector space. The quantization error of the PQ can be substantially improved in such combination since the residual vector space is much more quantization-friendly thanks to their compact distribution compared to the original data. In this paper, we first raise an unremarked but crucial question; why the inverted index and the product quantizer are optimized separately even though they are closely related? For instance, changes on the inverted index distort the whole residual vector space. To address the raised question, we suggest a joint optimization of the coarse and fine quantizers by substituting the original objective of the coarse quantizer to end-to-end quantization distortion. Moreover, our method is generic and applicable to different combinations of coarse and fine quantizers such as inverted multi-index and optimized PQ.