k-nearest neighbors algorithm

Graph

Metric (unit)

Hierarchy

Mathematics

Logarithm

Algorithm

Nearest neighbor search

Data mining

Mathematical analysis

Artificial intelligence

Economics

Operations management

Geometry

Computer science

Theoretical computer science

Market economy

Scaling

IEEE Transactions on Pattern Analysis and Machine Intelligence

We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional search structures (typically used at the coarse search stage of the most proximity graph techniques). Hierarchical NSW incrementally builds a multi-layer structure consisting of a 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 an 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 the search from the upper layer together with utilizing the scale separation boosts the performance compared to NSW and allows a logarithmic complexity scaling. Additional employment of a heuristic for selecting proximity graph neighbors significantly increases performance at high recall and in case of highly clustered data. Performance evaluation has demonstrated that the proposed general metric space search index is able to strongly outperform previous opensource state-of-the-art vector-only approaches. Similarity of the algorithm to the skip list structure allows straightforward balanced distributed implementation.

Efficient and Robust Approximate Nearest Neighbor Search Using Hierarchical Navigable Small World Graphs