False positives and false negatives in ANN (Approximate Nearest Neighbor) search occur due to the trade-offs inherent in balancing speed and accuracy. A false positive in ANN happens when a result is returned as a nearest neighbor but isn’t actually among the true nearest neighbors in the dataset. For example, in a vector search for similar images, a false positive might retrieve an image that appears visually unrelated when using an approximate method. Conversely, a false negative occurs when a true nearest neighbor is excluded from the results. If a user searches for a specific product recommendation, a false negative would mean the correct item exists in the dataset but isn’t returned due to the approximation.
Precision and recall directly measure these errors. Precision quantifies the fraction of returned results that are true neighbors (minimizing false positives), while recall measures the fraction of true neighbors successfully retrieved (minimizing false negatives). For instance, if an ANN index returns 10 results with 8 being correct, precision is 80%. If there are 20 true neighbors in total and the system retrieves 8, recall is 40%. High precision implies fewer irrelevant results, while high recall indicates fewer missed true matches. However, ANN methods often sacrifice one for the other: tuning parameters to improve recall (e.g., increasing search scope) may lower precision, and vice versa.
The relationship between these metrics depends on the ANN algorithm’s design. For example, hierarchical navigable small world (HNSW) graphs use parameters like ef (search depth) to control recall. A higher ef explores more nodes, increasing recall but potentially introducing more false positives. Inverted file (IVF) methods partition data into clusters; probing more clusters improves recall but risks lower precision if irrelevant clusters are included. Developers must evaluate precision and recall against ground-truth results (exact nearest neighbors) to tune these parameters based on use-case requirements—prioritizing precision for recommendation systems (avoiding irrelevant suggestions) or recall for retrieval-augmented generation (capturing all relevant context).