Hierarchical Navigable Small World (HNSW)
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Hierarchical Navigable Small World (HNSW) is a state-of-the-art algorithm used for approximate nearest neighbor search. It constructs optimized graph structures to efficiently index and search for nearest neighbors in high-dimensional spaces.
The main idea behind HNSW is to create a multi-layered graph where a path between any pair of vertices can be traversed in a small number of steps. The graph structure represents a hierarchy, with fewer connections on the top layers and denser regions on the bottom layers. This hierarchical structure allows for efficient navigation and search in high-dimensional spaces. HNSW incrementally builds a multi-layer structure consisting of 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 randomness helps in producing graphs similar to the previously studied Navigable Small World (NSW) structures. During the search process, HNSW explores the graph by traversing the layers and moving towards the target point. It uses a combination of greedy search and backward search to efficiently find the approximate nearest neighbors. The graph structure and the hierarchical nature of HNSW allow for fast and accurate approximate nearest neighbor queries.
HNSW has been widely used in various applications that require similarity search, such as image and video retrieval, recommendation systems, and Natural Language Processing (NLP). It is considered one of the state-of-the-art methods for approximate nearest neighbor search and has shown excellent performance in large-scale datasets.
