Composite Quantization

This paper studies the compact coding approach to approximate nearest neighbor search. We introduce a composite quantization framework. It uses the composition of several ($M$M) elements, each of which is selected from a different dictionary, to accurately approximate a $D$D-dimensional vector, thus yielding accurate search, and represents the data vector by a short code composed of the indices of the selected elements in the corresponding dictionaries. Our key contribution lies in introducing a near-orthogonality constraint, which makes the search efficiency is guaranteed as the cost of the distance computation is reduced to $O(M)$O(M) from $O(D)$O(D) through a distance table lookup scheme. The resulting approach is called near-orthogonal composite quantization. We theoretically justify the equivalence between near-orthogonal composite quantization and minimizing an upper bound of a function formed by jointly considering the quantization error and the search cost according to a generalized triangle inequality. We empirically show the efficacy of the proposed approach over several benchmark datasets. In addition, we demonstrate the superior performances in other three applications: combination with inverted multi-index, inner-product similarity search, and query compression for mobile search.