Exploring the Magic of HNSW for Vector Search in Elasticsearch

Nearest neighbor search is a fundamental problem in data science and machine learning. Given a set of points in a high-dimensional space, the goal is to efficiently find the nearest neighbors of a given query point. Elasticsearch, a popular search engine and analytics platform, provides a powerful solution to this problem through the use of the Hierarchical Navigable Small World (HNSW) algorithm. In this blog post, we’ll dive into the details of how HNSW achieves efficient nearest neighbor search in Elasticsearch.

HNSW is a type of approximate nearest neighbor (ANN) algorithm, which means that it provides an approximation of the true nearest neighbors, rather than a guarantee. The key idea behind HNSW is to build a hierarchical structure of interconnected nodes that form a small world graph. Each node in the graph represents a point in the high-dimensional space, and the edges between nodes represent the similarity between points. The graph is constructed in a way that balances the trade-off between exploration (finding new, potentially closer points) and exploitation (exploiting already discovered points that are likely to be close).

The HNSW algorithm proceeds in two main phases: construction and search.

In the construction phase, the algorithm builds the small world graph by adding…