What search methods do you know in vector databases? What functions are used in pgvector?

In vector databases for search, methods based on calculating the proximity between vectors are usually used, such as:

• Nearest Neighbor Search (NNS) — searching for vectors closest to a given one.
• Approximate Nearest Neighbor (ANN) — an approximate search to speed up on large datasets.
• Distance metrics: Euclidean distance, cosine similarity, Manhattan distance, etc.

In PostgreSQL with the pgvector extension, functions for working with vectors are used, such as:

• vector <-> vector — calculates Euclidean distance between two vectors.
• vector <#> vector — cosine distance.
• vector <=> vector — inner scalar product.

Example query for finding nearest vectors:

SELECT id, embedding
FROM items
ORDER BY embedding <-> '[0.1, 0.2, 0.3]'::vector
LIMIT 5;

Here, we are searching for 5 vectors closest to the given vector [0.1, 0.2, 0.3] by Euclidean distance.