A Learning-to-Rank Formulation of Clustering-Based Approximate Nearest Neighbor Search

A critical piece of the modern information retrieval puzzle is approximate nearest neighbor search. Its objective is to return a set of $k$ data points that are closest to a query point, with its accuracy measured by the proportion of exact nearest neighbors captured in the returned set. One popular approach to this question is clustering: The indexing algorithm partitions data points into non-overlapping subsets and represents each partition by a point such as its centroid. The query processing algorithm first identifies the nearest clusters -- a process known as routing -- then performs a nearest neighbor search over those clusters only. In this work, we make a simple observation: The routing function solves a ranking problem. Its quality can therefore be assessed with a ranking metric, making the function amenable to learning-to-rank. Interestingly, ground-truth is often freely available: Given a query distribution in a top-$k$ configuration, the ground-truth is the set of clusters that contain the exact top-$k$ vectors. We develop this insight and apply it to Maximum Inner Product Search (MIPS). As we demonstrate empirically on various datasets, learning a simple linear function consistently improves the accuracy of clustering-based MIPS.