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"Hierarchical Navigable Small World" (HNSW): an intriguing mouthful, designating a dense bouquet of concepts developed in the last 70 years in sociology, graph theory, and algorithmic science. In this brief tutorial, we'll examine these concepts carefully and attempt to solidify our understanding with proof-of-concept code and as many visualizations as possible.
The first thing to understand about HNSW is that it's primarily an optimized data structure, not an algorithm. Actually the algorithm used with these structures is remarkably simple: a greedy search which simply looks among all current candidates for the closest target value.
What's brilliant about HNSW therefore is not its search routine, but its optimized structure for a decentralized similarity search using a simple greedy traversal. This makes it ideal as the backbone for realtime search applications.
An important paper in 2016 introduced the term "Hierarchical Navigable Small World", designating a novel kind of approximate nearest neighbor search. But to examine HNSW, we need to unpack the term's historical layers as though it were Lisp or Polish notation: (Hierarchical (Navigable (Small World))).
