Hierarchical Navigable Small World Graphs
The Hierarchical navigable small world (HNSW) algorithm is a graph (discrete mathematics), graph-based Nearest neighbor search#Approximation methods, approximate nearest neighbor search technique used in many vector databases. Nearest neighbor search without an index involves computing the distance from the query to each point in the database, which for large datasets is computationally prohibitive. For high-dimensional data, tree-based exact vector search techniques such as the k-d tree and R-tree do not perform well enough because of the curse of dimensionality. To remedy this, ''approximate'' k-nearest neighbor searches have been proposed, such as locality-sensitive hashing (LSH) and product quantization (PQ) that trade performance for accuracy. The HNSW graph offers an approximate k-nearest neighbor search which scales logarithmically even in high-dimensional data. It is an extension of the earlier work on navigable small world graphs presented at the Similarity Search and Ap ...
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Graph (discrete Mathematics)
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a Set (mathematics), set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' means that ''A'' owes money to ''B'', then this graph is directed, because owing mon ...
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