Approximate nearest neighbor (ANN) search is a technique that efficiently finds data points close to a query point in a dataset, without guaranteeing the exact closest matches. Unlike exact nearest neighbor methods, which compare the query to every item in the dataset, ANN algorithms use strategies like hashing, graph traversal, or tree-based partitioning to prioritize speed over precision. For example, libraries like FAISS or algorithms like Hierarchical Navigable Small World (HNSW) create data structures that group similar vectors together, allowing faster but less precise lookups. This trade-off means results might miss the absolute closest matches but often return sufficiently nearby candidates in a fraction of the time.
Exact nearest neighbor search becomes impractical in high-dimensional spaces due to the "curse of dimensionality." As the number of dimensions increases, the distance between points grows less meaningful—most pairs of points become roughly equidistant, making it harder to distinguish true neighbors. Additionally, computational complexity explodes: a brute-force search in a dataset with (N) vectors has (O(N)) time complexity per query, which is untenable for large (N) (e.g., millions of vectors). For example, searching a 1000-dimensional dataset of 10 million vectors with exact methods could take seconds per query, while ANN might reduce this to milliseconds with minimal accuracy loss.
ANN is necessary for real-world applications involving high-dimensional data, such as recommendation systems, image retrieval, or natural language processing. These domains often use embeddings—dense vector representations of data—where exact searches would be too slow. For instance, a video streaming service using 512-dimensional embeddings to recommend content cannot wait hours for exact matches but can use ANN to deliver results in real time. Similarly, semantic search engines leveraging transformer-based embeddings (e.g., BERT) rely on ANN libraries like Annoy or ScaNN to balance speed and relevance. The slight drop in accuracy is justified by orders-of-magnitude speed improvements, enabling scalable, responsive systems that exact methods cannot support.