Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs

Abstract: We present a new algorithm for the approximate nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW) admitting simple insertion, deletion and K-nearest neighbor queries. The Hierarchical NSW is a fully graph-based approach without a need for additional search structures (such as kd-trees or Cartesian concatenation) typically used at coarse search stage of the most proximity graph techniques. The algorithm incrementally builds a layered structure consisting from hierarchical set of proximity graphs (layers) for nested subsets of the stored elements. The maximum layer in which an element is present is selected randomly with exponentially decaying probability distribution. This allows producing graphs similar to the previously studied Navigable Small World (NSW) structures while additionally having the links separated by their characteristic distance scales. Starting search from the upper layer instead of random seeds together with utilizing the scale separation boosts the performance compared to the NSW and allows a logarithmic complexity scaling. Additional employment of a simple heuristic for selecting proximity graph neighbors increases performance at high recall and in case of highly clustered data. Performance evaluation on a large number of datasets has demonstrated that the proposed general metric space method is able to strongly outperform many previous state-of-art vector-only approaches such as FLANN, FALCONN and Annoy. Similarity of the algorithm to a well-known 1D skip list structure allows straightforward efficient and balanced distributed implementation.